# A Level Maths Tutor
> I’m Jaisul — a UCL graduate with 9 years’ experience tutoring A-Level and International A-Level Maths (Edexcel & OCR), with a 100% five-star reputation across 100+ reviews.
Public Ghost content for AI and LLM tooling. This file includes a bounded export of public pages first, then recent public posts.
Append `.md` to any post or page URL to get the content in Markdown (for example, `/example-post.md`).
## Pages
### About Me | A-Level Maths Tutor
URL: https://www.a-level-maths-tutor.com/about/
Last updated: 2026-04-07T11:12:29.000Z
### A-Level Maths Tutor | 94+ Five-Star Reviews

**My name is Jaisul. I'm a UCL Economics graduate and I've tutored A-Level and International A-Level Mathematics since 2017\. Having studied the same specification as today's students, I understand the content, exam technique and common areas of difficulty. With 9 years of experience and thousands of teaching hours, I've developed a clear, structured and relatable teaching style that helps students build confidence and understanding from the very first session.**

### My passion for Mathematics

I was first introduced to A-Level Mathematics in sixth form, where I had an excellent teacher. It quickly became one of my favourite subjects and complemented A-Level Economics very well. Mathematics was essential for my goal of studying Economics at a top university — UCL required an **A\* in A-Level Maths**, which I achieved.

At **UCL**, I studied **Economics**; a highly mathematical degree, covering modules in econometrics, statistics and applied mathematics. This deepened my understanding of mathematical concepts an,d their real-world applications. I **graduated** with a 2:1 in **2020**.

Having studied the same specification as today's students, combined with the advanced mathematical training from my degree, I'm in a strong position to **support** and **mentor** students effectively — and it's something I genuinely enjoy doing.

### My passion for Teaching

My interest in teaching began with the challenges I faced during Year 13\. Our Maths teacher left at the end of Year 12, and we were required to complete much of the course through **independent study**. Despite this, I was determined to achieve the **A\*** **grade** I needed to study **Economics** at **UCL**, which had always been my goal.

While working through the textbook, I found that although many online resources existed, they often provided explanations that were difficult to remember or methods that weren't the most efficient. This meant I wasted too much time trying to learn the content and didn't have enough time to properly practice exam questions.

Since completing my A-Levels, I have **helped** **hundreds of students** achieve A\*–B grades in Mathematics, and I have created my own **practice questions** and **worked solutions** to provide students with clear, reliable material. You can read my **94+ five-star reviews** here.

[94+ 5-star Google Reviews](https://www.a-level-maths-tutor.com/reviews/)

### 94+ 5-star Google Reviews

The notes I originally made for myself have been improved and expanded so that every student I work with has access to concise topic summaries. I am also developing a growing bank of worked solutions to help students understand how to approach exam questions under exam conditions.

I **relate** strongly to students who find Mathematics difficult at school, and I always teach in a way that keeps topics simple, structured and easy to understand.

### How I can help

I'm happy to work with any student who would benefit from **clear explanations** and **structured support** in **Mathematics**. All lessons are taught by me and are available as **one-to-one sessions** or **small groups**. You can find out more here.

[A-Level Maths Tutoring and FAQ](https://www.a-level-maths-tutor.com/maths-tutoring/)

[Contact Me](https://www.a-level-maths-tutor.com/contact/)
### A-Level Maths Tutor
URL: https://www.a-level-maths-tutor.com/a-level-maths-tutor/
Last updated: 2026-07-04T11:06:31.000Z
## A-Level & International A-Level Mathematics Tutoring | 2025/26

I am always welcoming new enquiries for **A-Level Mathematics tutoring** and **International A-Level Mathematics tutoring**. I offer both **one-to-one** and **small group tutoring** for students in the UK and internationally.

You can get in touch with me via WhatsApp, or use the contact form listed below and I will get back to you.

[Whatsapp](https://wa.me/447378262000?ref=tootingtutors.co.uk)

[Contact Form](https://www.a-level-maths-tutor.com/contact/)

You can also call me directly at **(+44) 0737 8262 000**

## A-Level Mathematics Tutoring Services

For the 2025/26 academic year, I offer one-to-one tutoring (with limited availability) and small group tutoring in A-Level and International A-Level Mathematics.

### One-to-one A-Level Mathematics Tutoring — £60 per hour

I offer one-to-one tutoring to a small number of students. Where possible, a daytime slot is preferred for these sessions.

One-to-one tutoring is suited to students who want **fully personalised support**, flexible pacing, and targeted help with specific areas of the specification or exam technique.

### Small Group A-Level Mathematics Tutoring — £35 per hour

I also tutor A-Level Mathematics in small groups of **2–4 students**.

All students within a group:

- Study the same exam board
- Are working at similar grades
- Share similar goals and motivations

This allows sessions to remain just as effective as one-to-one tutoring.

Small group sessions also allow students to benefit from hearing others' questions and learning from different approaches. This can be particularly helpful for students who are less confident asking questions themselves.

Group tutoring also allows me to offer high-quality **A-Level Mathematics tutoring** at a more **affordable** price.

I understand that small groups do not suit everyone, and students are always welcome to move to one-to-one tutoring if they prefer.

## Free A-Level Mathematics Trial Session

All students are offered a **free taster session**. This gives us a chance to ensure the tutoring is a good fit and agree on a clear plan moving forward.

During the taster session, we will discuss:

- Current grades and recent progress
- Target grades
- Topics or areas you are finding difficult
- Availability and preferred timings
- A short example lesson on a challenging topic (to demonstrate immediate progress and boost confidence)
- Any questions you may have

After this, we can agree on a plan to maximise progress over the coming months.

## Student Outcomes & Reviews

I have been tutoring A-Level Mathematics **since 2017**, initially working with students locally and online before expanding to support students across the UK and internationally.

I encourage students to aim for the **top grades** in A-Level Mathematics. With the right support and consistent effort, strong outcomes are achievable. I also work with a small number of students who need to catch up, and have a proven track record of supporting significant improvements over relatively short periods of time.

You can read my **94+ five-star reviews** here.

[Reviews](https://www.a-level-maths-tutor.com/reviews)

## A-Level Mathematics Tutoring FAQs

### Do you follow the syllabus?

Yes. I have **full** **knowledge** of the **Edexcel**, **Edexcel International**, **OCR A** and **OCR MEI** Mathematics **specifications**. While much of the content overlaps, the exam technique and the style of questions differ between exam boards. This allows me to teach content in the most effective way for each exam board and then work through relevant past-paper questions so students become confident applying their knowledge under exam conditions.

---

### Which exam boards do you cover?

I have **9 years' experience** tutoring A-Level Mathematics. I specialise in:

- Edexcel A-Level Mathematics
- Edexcel International A-Level Mathematics
- OCR A A-Level Mathematics
- OCR MEI A-Level Mathematics

---

### How much does tutoring cost?

For the 2025/26 academic year:

- **One-to-one tutoring**: £60 per hour
- **Small group tutoring**: £35 per hour

---

### How long are your sessions?

Sessions are **one hour per week**. This provides enough time to make meaningful progress each week while allowing students to ask questions and fully understand a key topic or exam skill.

I also provide **optional homework**, including **exam questions**, as well as **lesson notes** and **session recordings**.

---

### Do you give homework?

I'm mindful that students already receive a significant workload from school, so sessions are designed to make strong progress without relying on extra work.

For students who want to go further, I set optional **practice questions and exam questions** to help consolidate learning.

---

### What is your availability?

I tutor every day of the week, except Friday evenings and weekend evenings. I reply quickly and do my best to be flexible with timings.

---

### How many students are in each small group?

Small groups contain **2–4 students**. All students in a group study the same exam board and are working towards the same grades. Some groups focus more on exam practice, while others focus on building strong understanding before moving on to exam technique.

---

### What payment methods do you accept?

Payments can be made via bank transfer, card or PayPal.

---

### Get in Touch

If you’d like to arrange **A-Level Maths tutoring** or ask any questions, you can get in touch with me directly via WhatsApp, or use the contact form listed below and I will get back to you.[](https://wa.me/447378262000?ref=tootingtutors.co.uk)

[Whatsapp](https://wa.me/447378262000?ref=tootingtutors.co.uk)

[Contact Form](https://www.a-level-maths-tutor.com/contact/)

You can also call me directly at **(+44) 0737 8262 000**
### Contact
URL: https://www.a-level-maths-tutor.com/contact/
Last updated: 2026-02-14T11:32:47.000Z
I’m happy to answer any questions about **A-Level Maths tutoring** and always reply on the same day.

Please feel free to get in touch directly via **Phone or WhatsApp** (preferred).

## [**(+44) 0737 8262 000**](https://wa.me/447378262000?ref=tootingtutors.co.uk)

Alternatively, you can complete the contact form below and I’ll get back to you by message or phone at your preferred time.

Loading…
### A-Level Maths Tutor | Reviews & Feedback
URL: https://www.a-level-maths-tutor.com/reviews/
Last updated: 2026-04-07T11:17:04.000Z
### What Students and Parents Say

I've been tutoring A-Level Mathematics since 2017, working with students across the UK and internationally. Here's what they have to say:

### Clear Explanations & Understanding

> "His lessons were clear, well planned and made complex topics much easier to understand." — Khushal, August 2024

> "Their patient and clear teaching style makes even the most challenging topics easy to understand." — Andrius, August 2024

> "He has a structured way of explaining topics, making it easy to understand which helped me build up my knowledge and confidence." — Elsie, August 2024

### Grade Improvements

> "Two months before her A-levels, my daughter was only getting a grade D in her maths mock exams. However, after starting tutoring, she improved significantly and achieved a B in her final A-level exam." — Paramama, August 2024

> "He was my GCSE tutor and A level maths tutor. Just got back my grades and Jaisul secured me an A in maths A level." — Jack, August 2024

> "This year my youngest son got an A\* in both Maths and Economics." — Saima, August 2024

> "Jaisul helped me to secure an A\* in A-level maths and I couldn't recommend him more." — Ula, August 2024

> "Our daughter was so happy with the sessions. She achieved an A\* in her A-level maths exam." — Simon, August 2024

> "He helped me get from a E to an engineering course at university." — Jamie, August 2024

### Exam Technique & Resources

> "His lessons were super specific to what I needed help with and he always catered to my needs which helped me to achieve my target grade." — Anonymous, August 2024

> "Gives useful exam advice and top tips for A Level Maths." — Luxshmi, August 2024

> "Very valuable revision resources which have set me up well for my year 12 end of year exams, not only for economics but also for maths." — Money in a Minute, November 2024

### Communication & Support

> "I can honestly say I highly recommend Tooting Tutors over the last 4 years from GCSE to A levels. Their help has been pivotal in helping my son to achieve the high grades that he has gained." — Sharon, August 2024

> "A great tutor for economics and maths. He has helped me and others a lot through A level. Would recommend 100%." — Krish, April 2024

> "He is very knowledgeable and makes sure he knows the curriculum set for his pupils. Results speak for themselves, highly recommend." — Ali, September 2024

### 94+ Five-Star Google Reviews

View all my reviews here.

[94+ 5 star Google Reviews](https://share.google/d93OfNBMtOIQIBVv5?ref=a-level-economics-tutor.com)

### Get in Touch

If you'd like to discuss tutoring, feel free to contact me or message me on WhatsApp.

[Contact Me](https://www.a-level-maths-tutor.com/contact/)

[Whatsapp](https://wa.me/447378262000?ref=tootingtutors.co.uk)
### GCSE Maths Tutor
URL: https://www.a-level-maths-tutor.com/gcse-maths-tutor/
Last updated: 2026-07-23T16:07:47.000Z
## GCSE Mathematics Tutoring | 2026/27

I am always welcoming new enquiries for **GCSE Mathematics tutoring**. I offer both **one-to-one** and **small group tutoring** for students in the UK and internationally.

You can get in touch with me via WhatsApp, or use the contact form listed below and I will get back to you.

[Whatsapp](https://wa.me/447378262000?ref=tootingtutors.co.uk)

[Contact Form](https://www.a-level-maths-tutor.com/contact/)

You can also call me directly at **(+44) 0737 8262 000**

## GCSE Mathematics Tutoring Services

For the 2026/27 academic year, I offer **one-to-one tutoring** (with limited availability) and **small group tutoring** in GCSE Mathematics.

### One-to-one GCSE Mathematics Tutoring — £65 per hour

I offer one-to-one tutoring to a small number of students. Where possible, a daytime or early-evening slot is preferred for these sessions.

One-to-one tutoring is suited to students who want **fully personalised support**, flexible pacing, and targeted help with specific areas of the specification or exam technique.

### Small Group GCSE Mathematics Tutoring — £35 per hour

I also tutor GCSE Mathematics in small groups of **2–4 students**.

All students within a group:

- Study the same exam board
- Are working at similar grades
- Share similar goals and motivations

This allows sessions to remain just as effective as one-to-one tutoring.

Small group sessions also allow students to benefit from hearing others' questions and learning from different approaches. This can be particularly helpful for students who are less confident asking questions themselves.

Group tutoring also allows me to offer high-quality **GCSE Mathematics tutoring** at a more **affordable price**.

I understand that small groups do not suit everyone, and students are always welcome to move to one-to-one tutoring if they prefer.

## Free GCSE Mathematics Trial Session

All students are offered a **free taster session**. This gives us a chance to ensure the tutoring is a good fit and agree on a clear plan moving forward.

During the taster session, we will discuss:

- Current grades and recent progress
- Target grades
- Topics or areas you are finding difficult
- Availability and preferred timings
- A short example lesson on a challenging topic (to demonstrate immediate progress and boost confidence)
- Any questions you may have

After this, we can agree on a plan to maximise progress over the coming months.

## Student Outcomes & Reviews

I have been tutoring GCSE Mathematics **since 2017**, initially working with students locally and online before expanding to support students across the UK and internationally.

I encourage students to aim for the **top grades** in GCSE Mathematics. With the right support and consistent effort, strong outcomes are achievable. I also work with a small number of students who need to catch up, and have a proven track record of supporting significant improvements over relatively short periods of time.

You can read my **94+ five-star reviews** here.

[Reviews](https://www.a-level-maths-tutor.com/reviews)

## GCSE Mathematics Tutoring FAQs

**Do you follow the syllabus?**  
Yes. I have full knowledge of the Edexcel GCSE, AQA GCSE and Edexcel International GCSE (iGCSE) Mathematics specifications. While much of the content overlaps, the exam technique and the style of questions differ between exam boards. This allows me to teach content in the most effective way for each exam board and then work through relevant past-paper questions so students become confident applying their knowledge under exam conditions.

**Which exam boards do you cover?**  
I have **9 years' experience** tutoring GCSE Mathematics. I specialise in:

- Edexcel GCSE Mathematics
- AQA GCSE Mathematics
- Edexcel International GCSE (iGCSE) Mathematics

I'm also happy to discuss other exam boards on enquiry.

**How much does tutoring cost?**  
For the 2026/27 academic year:

- **One-to-one tutoring**: £65 per hour
- **Small group tutoring**: £35 per hour

**How long are your sessions?**  
Sessions are **one hour per week**. This provides enough time to make meaningful progress each week while allowing students to ask questions and fully understand a key topic or exam skill.

I also provide **optional homework**, including **exam questions**, as well as **lesson notes** and **session recordings**.

**Do you give homework?**  
I'm mindful that students already receive a significant workload from school, so sessions are designed to make strong progress without relying on extra work.

For students who want to go further, I set optional **practice questions and exam questions** to help consolidate learning.

**What is your availability?**  
I tutor every day of the week, except Friday evenings and weekend evenings. I reply quickly and do my best to be flexible with timings.

**How many students are in each small group?**  
Small groups contain **2–4 students**. All students in a group study the same exam board and are working towards the same grades. Some groups focus more on exam practice, while others focus on building strong understanding before moving on to exam technique.

**What payment methods do you accept?**  
Payments can be made via bank transfer, card or PayPal.

**Get in Touch**

If you'd like to arrange **GCSE Maths tutoring** or ask any questions, you can get in touch with me directly via WhatsApp, or use the contact form listed below and I will get back to you.

[Whatsapp](https://wa.me/447378262000?ref=tootingtutors.co.uk)

[Contact Form](https://www.a-level-maths-tutor.com/contact/)

You can also call me directly at **(+44) 0737 8262 000**
## Posts
### A-Level Maths | Constant Acceleration
URL: https://www.a-level-maths-tutor.com/a-level-maths-constant-acceleration/
Last updated: 2026-09-12T10:57:26.000Z
Horizontal motion

### Question 1

A particle passes through the point $A$ with speed $35$ ms⁻¹, moving along a straight horizontal path with constant deceleration $0.8$ ms⁻². The particle passes through the point $B$, $15$ s after passing through $A$.

Find the distance $AB$.

Show Answers 

$|AB| = 435$ m

### Question 2

A particle passes through the point $A$ with speed $8$ ms⁻¹, moving along a straight horizontal path with constant acceleration $2$ ms⁻². The particle passes through the point $B$, where $AB = 56.25$ m.

Find the speed of the particle as it passes through $B$.

Show Answers 

$v = 17$ ms⁻¹

### Question 3

The points $A$, $B$ and $C$ lie in that order on a straight road. A car passes through $A$ with speed $11$ ms⁻¹, through $B$ with speed $17$ ms⁻¹, and through $C$ with speed $29$ ms⁻¹. The distance $AB = 28$ m. By modelling the car as a particle:

a) Find the distance $AC$.

b) Find the time it takes the car to travel from $A$ to $C$.

Show Answers 

a) $|AC| = 120$ m

b) $t = 6$ s

Vertical motion

### Question 4

A particle is projected vertically upwards with speed $U$ ms⁻¹ from level horizontal ground. The particle is moving freely under gravity and returns to its starting position $5$ s later.

a) Determine the value of $U$.

b) Calculate the greatest height the particle reaches above the ground.

Show Answers 

a) $U = 24.5$ ms⁻¹

b) $H\_{\\max} = 30.625$ m

### Question 5

A particle is projected vertically downwards from a great height. It hits the ground with speed $28$ ms⁻¹.

Determine the time it took the particle to cover the last $15$ m of its motion.

Show Answers 

$t \\approx 0.598$ s

### Question 6

A particle is projected vertically upwards from a balcony which is $2.48$ m above level horizontal ground. The particle is moving freely under gravity, takes $2.45$ s to reach the highest point in its path, before it strikes the ground with speed $v$ ms⁻¹.

Calculate the value of $v$.

Show Answers 

$v \\approx 25.0$ ms⁻¹

### Question 7

A particle is projected vertically upwards with speed $29$ ms⁻¹ from a balcony which is $h$ m above level horizontal ground. The particle is moving freely under gravity and strikes the ground $6$ s later with speed $v$ ms⁻¹.

a) Calculate the value of $h$.

b) Determine the value of $v$.

Show Answers 

a) $h = 2.4$ m

b) $v = 29.8$ ms⁻¹

### Question 8

A particle is projected vertically upwards from level ground with a speed of $14$ ms⁻¹.

a) Determine the speed of the particle and the distance of the particle from the ground, $0.5$ s after projection.

b) Calculate the total distance travelled by the particle during the first $2$ s of its motion.

Show Answers 

a) $v = 9.1$ ms⁻¹, $d\_{0.5} = 5.775$ m

b) $d\_2 = 11.6$ m

### Question 9

A raindrop falls freely from rest from the top of a cliff. After it has fallen a distance of $40$ m, another raindrop falls freely from rest from the top of the same cliff. The height of the cliff is $80$ m.

Calculate, correct to three significant figures, the distance between the two raindrops at the instant the first raindrop reaches the ground.

Show Answers 

$\\approx 73.1$ m

---

### A-Level Maths Tutoring

I offer one-to-one and small group A-Level Maths tutoring for students across the UK and internationally. With 94+ five-star Google reviews and tutoring experience since 2017, I specialise in helping students understand difficult concepts and improve their exam technique.

[A-Level Maths Tutoring](https://www.a-level-maths-tutor.com/a-level-maths-tutor/)

[94+ 5-star Google Reviews](https://www.a-level-maths-tutor.com/reviews/)

[Contact Me](https://www.a-level-maths-tutor.com/contact/)

[Back to A-Level Maths Revision](https://www.a-level-maths-tutor.com/a-level-maths-revision/)
### A-Level Maths | Projectiles
URL: https://www.a-level-maths-tutor.com/a-level-maths-projectiles/
Last updated: 2026-09-11T17:52:55.000Z
### Question 1

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/09/CleanShot-2026-09-11-at-17.47.14@2x.png)

Show Answers 

a) Given — $t = 3.13$ s

b) $40.2$ m

### Question 2

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/CleanShot-2026-03-03-at-13.27.56@2x.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/CleanShot-2026-03-03-at-13.28.09@2x.png)

Show Answers 

a) $t = 3.10$ s

b) $h = 0.734$ m

c) (i) $23.7$ ms⁻¹

c) (ii) $39.1°$ below the horizontal

### Question 3

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/CleanShot-2026-03-03-at-13.32.45@2x.png)

Show Answers 

a) Maximum height $= 52.7$ m

b) $t = 6.37$ s

### Question 4

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/09/CleanShot-2026-09-11-at-18.14.16@2x.png)

Show Answers 

a) $t = \\dfrac{60}{7}$ s

b) $OP = 150$ m, $H = 90$ m

c) $v \\approx 17.72$ ms⁻¹

### Question 5

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/09/CleanShot-2026-09-11-at-18.15.45@2x-1.png)

Show Answers 

a) Maximum height $= 10$ m

b) $t = 2$ s

c) $v \\approx 24.9$ ms⁻¹

### Question 6

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/09/CleanShot-2026-09-11-at-18.16.03@2x.png)

Show Answers 

a) Maximum height $= 10$ m

b) $t = 2$ s

c) $v \\approx 24.9$ ms⁻¹

---

### A-Level Maths Tutoring

I offer one-to-one and small group A-Level Maths tutoring for students across the UK and internationally. With 94+ five-star Google reviews and tutoring experience since 2017, I specialise in helping students understand difficult concepts and improve their exam technique.

[A-Level Maths Tutoring](https://www.a-level-maths-tutor.com/a-level-maths-tutor/)

[94+ 5-star Google Reviews](https://www.a-level-maths-tutor.com/reviews/)

[Contact Me](https://www.a-level-maths-tutor.com/contact/)

[Back to A-Level Maths Revision](https://www.a-level-maths-tutor.com/a-level-maths-revision/)
### A-Level Maths | Radians
URL: https://www.a-level-maths-tutor.com/a-level-maths-radians/
Last updated: 2026-09-09T13:51:32.000Z
Area of a sector $= \\dfrac{1}{2}r^2\\theta$

Arc length $= r\\theta$

$\\theta$ must be in radians

Degrees to radians: multiply by $\\pi$, divide by $180$

Radians to degrees: multiply by $180$, divide by $\\pi$

### Question 1

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/07/CleanShot-2026-07-14-at-15.40.30@2x.png)

Show Answers 

a) $3\\pi$ cm

b) $5\\pi$ cm

c) $\\frac{15\\pi}{2}$ mm

### Question 2

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/07/CleanShot-2026-07-14-at-15.40.36@2x.png)

Show Answers 

a) $16.6$ cm

b) $80.3$ cm

c) $31.4$ cm

### Question 3

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/07/CleanShot-2026-07-14-at-15.40.58@2x.png)

Show Answers 

a) $\\theta \\approx 0.69$

b) $\\theta \\approx 0.21$

c) $\\theta \\approx 0.88$

### Question 4

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/07/CleanShot-2026-07-14-at-15.42.08@2x.png)

Show Answers 

a) $1309.0$ cm²

b) $165.4$ cm²

c) $105.3$ cm²

### Question 5

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/07/CleanShot-2026-07-14-at-15.42.23@2x.png)

Show Answers 

a) $24.0$ cm²

b) $40.1$ mm²

c) $2940$ cm²

---

### A-Level Maths Tutoring

I offer one-to-one and small group A-Level Maths tutoring for students across the UK and internationally. With 94+ five-star Google reviews and tutoring experience since 2017, I specialise in helping students understand difficult concepts and improve their exam technique.

[A-Level Maths Tutoring](https://www.a-level-maths-tutor.com/a-level-maths-tutor/)

[94+ 5-star Google Reviews](https://www.a-level-maths-tutor.com/reviews/)

[Contact Me](https://www.a-level-maths-tutor.com/contact/)

[Back to A-Level Maths Revision](https://www.a-level-maths-tutor.com/a-level-maths-revision/)
### GCSE Maths | Algebra
URL: https://www.a-level-maths-tutor.com/gcse-maths-algebra/
Last updated: 2026-09-09T16:46:23.000Z
# GCSE Maths | Algebra

Collecting like terms

$$3a + 2b + 4a + b$$ $$= (3a+4a) + (2b+b)$$ $$= 7a + 3b$$ 

### Question 1

(a) $3a+2b+4a+b$

(b) $7y+5y+2h+2h$

(c) $g+8a+2a+g$

(d) $7m+7p+8m+p+2p$

(e) $9e+2+e+2$

(f) $4+3a+2a+8$

(g) $2y+4+3y-1$

(h) $8+3w-w-3$

(i) $5-4s-2+10s$

(j) $3x+6y+5x-2y$

(k) $6m-2s+11s+m$

(l) $2a+3b-2+a+3b+4$

Show Answers 

(a) $7a+3b$

(b) $12y+4h$

(c) $10a+2g$

(d) $15m+10p$

(e) $10e+4$

(f) $5a+12$

(g) $5y+3$

(h) $2w+5$

(i) $6s+3$

(j) $8x+4y$

(k) $7m+9s$

(l) $3a+6b+2$

### Question 2

(a) $3y^2+4ab+7y^2+ab$

(b) $9x^2-2x-11x^2+5x$

(c) $7ac-3ab+9ab-7ac$

Show Answers 

(a) $10y^2+5ab$

(b) $-2x^2+3x$

(c) $6ab$

Expanding brackets

$$5(y+3)$$ $$= 5 \\times y + 5 \\times 3$$ $$= 5y+15$$ 

### Question 3

(a) $5(y+3)$

(b) $4(a+2)$

(c) $8(w+10)$

(d) $3(x-7)$

(e) $9(s-1)$

(f) $2(8-t)$

(g) $7(4+h)$

(h) $10(a+2b+3c)$

Show Answers 

(a) $5y+15$

(b) $4a+8$

(c) $8w+80$

(d) $3x-21$

(e) $9s-9$

(f) $16-2t$

(g) $7h+28$

(h) $10a+20b+30c$

A minus sign outside the bracket flips the sign of every term inside it. $$-2(w+5)$$ $$= -2 \\times w + (-2) \\times 5$$ $$= -2w-10$$ 

### Question 4

(a) $-2(w+5)$

(b) $-3(c+7)$

(c) $-8(c+7)$

(d) $-10(y-2)$

(e) $-7(g-3)$

(f) $-4(2w+3)$

(g) $-9(3w-5)$

(h) $-9(5x-1)$

Show Answers 

(a) $-2w-10$

(b) $-3c-21$

(c) $-8c-56$

(d) $20-10y$

(e) $21-7g$

(f) $-8w-12$

(g) $45-27w$

(h) $9-45x$

### Question 5

(a) $a(a+2)$

(b) $y(y-5)$

(c) $w(a+w)$

(d) $c(9-c)$

(e) $p(2p+5)$

(f) $2w(3w-1)$

(g) $9y(2y+3)$

(h) $4c(2a+5c)$

Show Answers 

(a) $a^2+2a$

(b) $y^2-5y$

(c) $aw+w^2$

(d) $9c-c^2$

(e) $2p^2+5p$

(f) $6w^2-2w$

(g) $18y^2+27y$

(h) $8ac+20c^2$

Expand each bracket separately first, then collect like terms. $$5(y+3)+2(y+7)$$ $$= (5y+15)+(2y+14)$$ $$= 7y+29$$ 

### Question 6

(a) $5(y+3)+2(y+7)$

(b) $6(2w+5)+9(w+2)$

(c) $3(y-2)+4(2y+5)$

(d) $7(2g+3)-5(g+2)$

(e) $6(x-2)-4(x-8)$

(f) $2(3y-8)-5(2y-1)$

(g) $8(5+2m)+3(5-3m)$

(h) $4(w+7)-2(2w+1)$

(i) $9(1+2y)+3(3-y)$

Show Answers 

(a) $7y+29$

(b) $21w+48$

(c) $11y+14$

(d) $9g+11$

(e) $2x+20$

(f) $-4y-11$

(g) $7m+55$

(h) $26$

(i) $15y+18$

Multiply every term in the first bracket by every term in the second. $$(2c+1)(2c+3)$$ $$= 2c(2c+3) + 1(2c+3)$$ $$= 4c^2+6c+2c+3$$ $$= 4c^2+8c+3$$ 

### Question 7

(a) $(2c+1)(2c+3)$

(b) $(5x+1)(2x+5)$

(c) $(3w+2)(w+1)$

(d) $(3p+2)(2p-1)$

(e) $(5g-4)(g+1)$

(f) $(2a-3)(4a+7)$

Show Answers 

(a) $4c^2+8c+3$

(b) $10x^2+27x+5$

(c) $3w^2+5w+2$

(d) $6p^2+p-2$

(e) $5g^2+g-4$

(f) $8a^2+2a-21$

Factorising expressions

$$x^2+7x$$ The highest common factor of $x^2$ and $7x$ is $x$. $$= x(x+7)$$ 

### Question 8

(a) $x^2+7x$

(b) $x^2-3x$

(c) $y^2+y$

(d) $w^2+9w$

(e) $x^2-7x$

(f) $4w^2+10w$

(g) $6x^2-8x$

(h) $9y^2-6y$

(i) $10c+c^2$

(j) $5g-g^2$

(k) $14x^2+35x$

(l) $40x^2-50x$

(m) $12x^2+18x$

(n) $24x^2-18x$

(o) $45y^2+60y$

(p) $7w^2+2w$

Show Answers 

(a) $x(x+7)$

(b) $x(x-3)$

(c) $y(y+1)$

(d) $w(w+9)$

(e) $x(x-7)$

(f) $2w(2w+5)$

(g) $2x(3x-4)$

(h) $3y(3y-2)$

(i) $c(c+10)$

(j) $g(5-g)$

(k) $7x(2x+5)$

(l) $10x(4x-5)$

(m) $6x(2x+3)$

(n) $6x(4x-3)$

(o) $15y(3y+4)$

(p) $w(7w+2)$

### Question 9

(a) $x^2+xy$

(b) $a^2-ab$

(c) $xy+xz$

(d) $ab+ac-ad$

(e) $6c^2-4cd$

(f) $10x^2+15xy$

(g) $12ab+18bc$

(h) $8xy+4y^2$

(i) $8cdf+10cde$

(j) $7w^2+6w+wy$

(k) $8ab^2-10ab$

(l) $4xy^2+6xy+2x^2y$

(m) $6mn-7m^2n$

(n) $11g^2h+22h^2$

Show Answers 

(a) $x(x+y)$

(b) $a(a-b)$

(c) $x(y+z)$

(d) $a(b+c-d)$

(e) $2c(3c-2d)$

(f) $5x(2x+3y)$

(g) $6b(2a+3c)$

(h) $4y(2x+y)$

(i) $2cd(4f+5e)$

(j) $w(7w+6+y)$

(k) $2ab(4b-5)$

(l) $2xy(2y+3+x)$

(m) $mn(6-7m)$

(n) $11h(g^2+2h)$

### Question 10

(a) $x^3+2x^2$

(b) $5x^3-x^2$

(c) $8c^3+12c$

(d) $10w^2-15w^3$

(e) $32y^3+24y^2$

(f) $12x^4+15x$

(g) $4a^5-12a^2$

(h) $8w^9+w^7$

Show Answers 

(a) $x^2(x+2)$

(b) $x^2(5x-1)$

(c) $4c(2c^2+3)$

(d) $5w^2(2-3w)$

(e) $8y^2(4y+3)$

(f) $3x(4x^3+5)$

(g) $4a^2(a^3-3)$

(h) $w^7(8w^2+1)$

Rearranging equations

$$y+7=x$$ Subtract $7$ from both sides: $$y = x-7$$ 

### Question 11

a) $y+7=x$

b) $y+m=a$

c) $y+p=q$

d) $y+k=t$

e) $y+\\frac{1}{2}=a$

f) $y+b=x-c$

g) $y+n=2m$

h) $y+d=a+b$

i) $y+r=s-t$

j) $y+f=g-h$

Show Answers 

a) $y=x-7$

b) $y=a-m$

c) $y=q-p$

d) $y=t-k$

e) $y=a-\\frac{1}{2}$

f) $y=x-b-c$

g) $y=2m-n$

h) $y=a+b-d$

i) $y=s-t-r$

j) $y=g-h-f$

### Question 12

a) $y-5=x$

b) $y-n=m$

c) $y-c=p$

d) $y-t=a+b$

e) $y-d=\\frac{x}{2}$

f) $y-k=3m$

g) $y-r=s$

h) $y-(a+b)=c$

i) $y-p=q-r$

j) $y-f=g+h$

Show Answers 

a) $y=x+5$

b) $y=m+n$

c) $y=p+c$

d) $y=a+b+t$

e) $y=\\frac{x}{2}+d$

f) $y=3m+k$

g) $y=s+r$

h) $y=a+b+c$

i) $y=q-r+p$

j) $y=g+h+f$

$$4y=x$$ Divide both sides by $4$: $$y = \\frac{x}{4}$$ 

### Question 13

a) $4y=x$

b) $ay=b$

c) $ty=m$

d) $-3y=p$

e) $ky=a+b$

f) $ny=x-c$

g) $7y=3a$

h) $\\pi y=r$

i) $(a+b)y=c$

j) $my=n(p+q)$

Show Answers 

a) $y=\\frac{x}{4}$

b) $y=\\frac{b}{a}$

c) $y=\\frac{m}{t}$

d) $y=-\\frac{p}{3}$

e) $y=\\frac{a+b}{k}$

f) $y=\\frac{x-c}{n}$

g) $y=\\frac{3a}{7}$

h) $y=\\frac{r}{\\pi}$

i) $y=\\frac{c}{a+b}$

j) $y=\\frac{n(p+q)}{m}$

$$\\frac{y}{5}=x$$ Multiply both sides by $5$: $$y = 5x$$ 

### Question 14

a) $\\frac{y}{5}=x$

b) $\\frac{y}{k}=a$

c) $\\frac{y}{m}=p$

d) $\\frac{y}{a+b}=t$

e) $\\frac{y}{r}=s-t$

f) $\\frac{y}{2}=3x$

g) $\\frac{y}{d}=\\frac{a}{b}$

h) $\\frac{y}{\\pi}=r^2$

i) $\\frac{y}{f}=g+h$

j) $\\frac{y}{n}=m(k-t)$

Show Answers 

a) $y=5x$

b) $y=ak$

c) $y=mp$

d) $y=t(a+b)$

e) $y=r(s-t)$

f) $y=6x$

g) $y=\\frac{ad}{b}$

h) $y=\\pi r^2$

i) $y=f(g+h)$

j) $y=mn(k-t)$

$$2y+8=x$$ Subtract $8$, then divide by $2$: $$2y = x-8 \\implies y = \\frac{x-8}{2} = \\frac{x}{2}-4$$ 

### Question 15

a) $2y+8=x$

b) $ay-b=c$

c) $3y+k=m$

d) $-4y+p=q$

e) $\\frac{y}{2}+6=a$

f) $ny+t=x$

g) $ry-s=t$

h) $2y-b=a+b$

i) $\\frac{y}{3}+d=e$

j) $-y+a=b-c$

Show Answers 

a) $y=\\frac{x}{2}-4$

b) $y=\\frac{b+c}{a}$

c) $y=\\frac{m-k}{3}$

d) $y=\\frac{p-q}{4}$

e) $y=2a-12$

f) $y=\\frac{x-t}{n}$

g) $y=\\frac{s+t}{r}$

h) $y=\\frac{a}{2}+b$

i) $y=3(e-d)$

j) $y=a-b+c$

$$4(y+2)=x$$ Divide by $4$ first, then subtract $2$: $$y+2 = \\frac{x}{4} \\implies y = \\frac{x}{4}-2$$ 

### Question 16

a) $4(y+2)=x$

b) $a(y-b)=c$

c) $m(y+n)=p$

d) $-2(y+k)=t$

e) $\\frac{y+a}{b}=c$

f) $r(y-s)=t$

g) $y-d=\\frac{x}{k}$

h) $5(y-m)=n(p+q)$

i) $\\frac{y-t}{r}=s$

j) $a(y+b)=c(y-d)$

Show Answers 

a) $y=\\frac{x}{4}-2$

b) $y=\\frac{c}{a}+b$

c) $y=\\frac{p}{m}-n$

d) $y=-\\frac{t}{2}-k$

e) $y=bc-a$

f) $y=\\frac{t}{r}+s$

g) $y=\\frac{x}{k}+d$

h) $y=m+\\frac{n(p+q)}{5}$

i) $y=rs+t$

j) $y=\\frac{ab+cd}{c-a}$

$$-y=x$$ Divide both sides by $-1$ (i.e. flip every sign): $$y = -x$$ 

### Question 17

a) $-y=x$

b) $-y=a$

c) $a-y=b$

d) $-y+c=d$

e) $m-y=n$

f) $x+y=-y$

g) $p-y=q+r$

h) $-y=\\frac{a}{b}$

i) $k(-y+m)=n$

j) $a-y=b+y$

Show Answers 

a) $y=-x$

b) $y=-a$

c) $y=a-b$

d) $y=c-d$

e) $y=m-n$

f) $y=-\\frac{x}{2}$

g) $y=p-q-r$

h) $y=-\\frac{a}{b}$

i) $y=m-\\frac{n}{k}$

j) $y=\\frac{a-b}{2}$

When $y$ is in the denominator, multiply both sides by $y$ first, then divide by whatever's on the other side. $$\\frac{5}{y}=x$$ $$5 = xy \\implies y = \\frac{5}{x}$$ 

### Question 18

a) $\\frac{5}{y}=x$

b) $\\frac{a}{y}=b$

c) $\\frac{m}{y}=n$

d) $\\frac{p+q}{y}=r$

e) $\\frac{k}{y}=t$

f) $\\frac{a}{y}=b+c$

g) $\\frac{m}{y}=\\frac{n}{p}$

h) $\\frac{r}{y}=\\frac{s}{t}$

i) $\\frac{1}{y}=a$

j) $\\frac{a+b}{y}=c(d-e)$

Show Answers 

a) $y=\\frac{5}{x}$

b) $y=\\frac{a}{b}$

c) $y=\\frac{m}{n}$

d) $y=\\frac{p+q}{r}$

e) $y=\\frac{k}{t}$

f) $y=\\frac{a}{b+c}$

g) $y=\\frac{mp}{n}$

h) $y=\\frac{rt}{s}$

i) $y=\\frac{1}{a}$

j) $y=\\frac{a+b}{c(d-e)}$

If $y$ appears on both sides, collect all $y$ terms on one side, then factorise out $y$ and divide. $$ay=by+c$$ $$ay-by=c$$ $$y(a-b)=c$$ $$y=\\frac{c}{a-b}$$ 

### Question 19

a) $3y+2=ay+b$

b) $py+q=ry+s$

c) $ay=by+c$

d) $2(y+a)=by+c$

e) $y(a+b)=c+dy$

f) $ay+b=c(y+d)$

g) $a(y+b)=cy+d$

h) $y-m=2y+n$

i) $\\frac{y}{a}=y-b$

j) $f(y+g)=h(y-j)$

Show Answers 

a) $y=\\frac{b-2}{3-a}$

b) $y=\\frac{s-q}{p-r}$

c) $y=\\frac{c}{a-b}$

d) $y=\\frac{c-2a}{2-b}$

e) $y=\\frac{c}{a+b-d}$

f) $y=\\frac{cd-b}{a-c}$

g) $y=\\frac{d-ab}{a-c}$

h) $y=-m-n$

i) $y=\\frac{ab}{a-1}$

j) $y=\\frac{fg+hj}{h-f}$

---

### GCSE Maths Tutoring

I offer one-to-one and small group GCSE Maths tutoring for students across the UK and internationally. With 94+ five-star Google reviews and tutoring experience since 2017, I specialise in helping students understand difficult concepts and improve their exam technique.

[GCSE Maths Tutoring](https://www.a-level-maths-tutor.com/gcse-maths-tutor/)

[94+ 5-star Google Reviews](https://www.a-level-maths-tutor.com/reviews/)

[Contact Me](https://www.a-level-maths-tutor.com/contact/)

[Back to GCSE Maths Revision](https://a-level-maths-tutor.com/gcse-maths-revision/?ref=a-level-maths-tutor.com)
### GCSE Maths | Trigonometry
URL: https://www.a-level-maths-tutor.com/gcse-maths-trigonometry/
Last updated: 2026-08-03T14:27:42.000Z
![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/02/CleanShot-2026-02-12-at-16.47.14@2x.png)

### What is the sine rule?

**a/sin(A) = b/sin(B)**

**sin(A)/a = sin(B)/b**

### Question 1 - finding a length using the sine rule

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/02/CleanShot-2026-02-12-at-16.53.14@2x.png)

Show Answers 

**a)** $x = 6.39$ cm

**b)** $x = 6.65$ cm

**c)** $x = 60.5$ mm

### Question 2 - finding an angle using the sine rule

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/02/CleanShot-2026-02-12-at-16.54.17@2x.png)

Show Answers 

**a)** $\\theta = 37.1°$

**b)** $\\theta = 26.8°$

**c)** $\\theta = 40.5°$

### What is the cosine rule?

**a2 \= b2 \+ c2 \- 2bc cos(A)**

### Question 3 - finding a length using the cosine rule

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/02/CleanShot-2026-02-12-at-16.57.48@2x.png)

Show Answers 

**a)** $x = 9.17$ cm

**b)** $x = 30.41$ cm

**c)** $x = 36.67$ mm

### How do you rearrange the cosine rule to make cos(A) the subject?

**a2 \= b2 \+ c2 \- 2bc cos(A)**

**2bc cos(A)** \= **b2 \+ c2 \- a2** 

**cos(A) = (b2 \+ c2 \- a2)/2bc**

### Question 4 - finding an angle using the cosine rule

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/02/CleanShot-2026-02-12-at-16.58.07@2x.png)

Show Answers 

**a)** $\\theta = 49.5°$

**b)** $\\theta = 60.0°$

**c)** $\\theta = 87.2°$

### What is the area of any triangle?

**Area = (1/2) ab sin(C)**

### Question 5 - finding the area of any triangle

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/02/CleanShot-2026-02-12-at-16.59.20@2x.png)

Show Answers 

**a)** $45.0$ cm²

**b)** $156.32$ cm²

**c)** $52.62$ cm²

### Question 6 - using the area of a triangle to work out a missing length

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/02/CleanShot-2026-02-12-at-16.59.35@2x.png)

Show Answers 

**a)** $y = 8.51$ cm

**b)** $y = 6.96$ cm

**c)** $y = 7.95$ cm

### Question 7 - using the area of a triangle to work out a missing angle

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/02/CleanShot-2026-02-12-at-17.02.58@2x.png)

Show Answers 

**a)** $x = 78.9°$

**b)** $x = 31.6°$

**c)** $x = 30.0°$

---

### GCSE Maths Tutoring

I offer one-to-one and small group GCSE Maths tutoring for students across the UK and internationally. With 94+ five-star Google reviews and tutoring experience since 2017, I specialise in helping students understand difficult concepts and improve their exam technique.

[GCSE Maths Tutoring](https://www.a-level-maths-tutor.com/gcse-maths-tutor/)

[94+ 5-star Google Reviews](https://www.a-level-maths-tutor.com/reviews/)

[Contact Me](https://www.a-level-maths-tutor.com/contact/)

[Back to GCSE Maths Revision](https://a-level-maths-tutor.com/gcse-maths-revision/?ref=a-level-maths-tutor.com)
### GCSE Maths | Surds
URL: https://www.a-level-maths-tutor.com/gcse-maths-surds/
Last updated: 2026-07-29T14:35:54.000Z
Square numbers: $1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144$

Cube numbers: $1, 8, 27, 64, 125$

Powers of 4: $1, 16, 81$

**Worked Example**

$(\\sqrt{10})^2 = 10$

## Question 1

**a)** $(\\sqrt{15})^2$

**b)** $(\\sqrt{2})^2$

**c)** $(\\sqrt{20})^2$

**d)** $(\\sqrt{11})^2$

**e)** $(\\sqrt{31})^2$

**f)** $(\\sqrt{8})^2$

**g)** $(\\sqrt{45})^2$

**h)** $(\\sqrt{99})^2$

**i)** $(\\sqrt{12})^2$

**j)** $(\\sqrt{18})^2$

Show Answers 

**a)** $15$ **b)** $2$ **c)** $20$ **d)** $11$ **e)** $31$

**f)** $8$ **g)** $45$ **h)** $99$ **i)** $12$ **j)** $18$

**Worked Example**

$(\\sqrt{2})^3 = 2\\sqrt{2}$

$(\\sqrt{2})^4 = 4$

## Question 2

**a)** $(\\sqrt{7})^3$

**b)** $(\\sqrt{11})^3$

**c)** $(\\sqrt{5})^4$

**d)** $(\\sqrt{6})^4$

**e)** $(\\sqrt{2})^5$

**f)** $(\\sqrt{3})^5$

**g)** $(\\sqrt{10})^5$

**h)** $(\\sqrt{2})^6$

**i)** $(\\sqrt{5})^6$

**j)** $(\\sqrt{3})^7$

Show Answers 

**a)** $7\\sqrt{7}$ **b)** $11\\sqrt{11}$ **c)** $25$ **d)** $36$ **e)** $4\\sqrt{2}$

**f)** $9\\sqrt{3}$ **g)** $100\\sqrt{10}$ **h)** $8$ **i)** $125$ **j)** $27\\sqrt{3}$

$\\sqrt{a} \\times \\sqrt{b} = \\sqrt{ab}$

**Worked Example**

$3\\sqrt{2} \\times 4\\sqrt{5} = 12\\sqrt{10}$

## Question 3

**a)** $2\\sqrt{5} \\times 3\\sqrt{7}$

**b)** $4\\sqrt{2} \\times 5\\sqrt{3}$

**c)** $6\\sqrt{11} \\times 2\\sqrt{5}$

**d)** $3\\sqrt{2} \\times 7\\sqrt{13}$

**e)** $5\\sqrt{3} \\times 2\\sqrt{10}$

**f)** $8\\sqrt{7} \\times \\sqrt{2}$

**g)** $4\\sqrt{11} \\times 3\\sqrt{3}$

**h)** $9\\sqrt{5} \\times 2\\sqrt{6}$

**i)** $10\\sqrt{3} \\times 3\\sqrt{11}$

**j)** $7\\sqrt{2} \\times 6\\sqrt{17}$

Show Answers 

**a)** $6\\sqrt{35}$ **b)** $20\\sqrt{6}$ **c)** $12\\sqrt{55}$ **d)** $21\\sqrt{26}$ **e)** $10\\sqrt{30}$

**f)** $8\\sqrt{14}$ **g)** $12\\sqrt{33}$ **h)** $18\\sqrt{30}$ **i)** $30\\sqrt{33}$ **j)** $42\\sqrt{34}$

*\[Video: "Surds (Part 1) Simplifying" goes here\]*

To simplify a surd, find the largest square-number factor and split it out.

**Worked Example**

$\\sqrt{72} = \\sqrt{36 \\times 2} = 6\\sqrt{2}$

## Question 4

**a)** $\\sqrt{8}$

**b)** $\\sqrt{75}$

**c)** $\\sqrt{20}$

**d)** $\\sqrt{32}$

**e)** $\\sqrt{48}$

**f)** $\\sqrt{200}$

**g)** $\\sqrt{300}$

**h)** $\\sqrt{80}$

**i)** $\\sqrt{50}$

**j)** $\\sqrt{98}$

Show Answers 

**a)** $2\\sqrt{2}$ **b)** $5\\sqrt{3}$ **c)** $2\\sqrt{5}$ **d)** $4\\sqrt{2}$ **e)** $4\\sqrt{3}$

**f)** $10\\sqrt{2}$ **g)** $10\\sqrt{3}$ **h)** $4\\sqrt{5}$ **i)** $5\\sqrt{2}$ **j)** $7\\sqrt{2}$

## Question 5

Multiply and simplify each of the following.

**a)** $2\\sqrt{3} \\times 4\\sqrt{5}$

**b)** $5\\sqrt{2} \\times 3\\sqrt{6}$

**c)** $7\\sqrt{3} \\times 2\\sqrt{3}$

**d)** $6\\sqrt{5} \\times 3\\sqrt{10}$

**e)** $4\\sqrt{7} \\times 2\\sqrt{14}$

**f)** $10\\sqrt{2} \\times 3\\sqrt{8}$

**g)** $3\\sqrt{6} \\times 5\\sqrt{15}$

**h)** $8\\sqrt{3} \\times \\sqrt{12}$

**i)** $2\\sqrt{11} \\times 5\\sqrt{22}$

**j)** $9\\sqrt{7} \\times 2\\sqrt{21}$

Show Answers 

**a)** $8\\sqrt{15}$ **b)** $30\\sqrt{3}$ **c)** $42$ **d)** $90\\sqrt{2}$ **e)** $56\\sqrt{2}$

**f)** $120$ **g)** $45\\sqrt{10}$ **h)** $48$ **i)** $110\\sqrt{2}$ **j)** $126\\sqrt{3}$

*\[Video: "Surds (Part 2) Adding & Subtracting" goes here\]*

You can only add or subtract surds once they share the same number under the root — simplify first, then combine.

**Worked Example**

$\\sqrt{12} + \\sqrt{27} = 2\\sqrt{3} + 3\\sqrt{3} = 5\\sqrt{3}$

## Question 6

**a)** $\\sqrt{8} + \\sqrt{18}$

**b)** $\\sqrt{50} + \\sqrt{8}$

**c)** $\\sqrt{75} + \\sqrt{27}$

**d)** $\\sqrt{200} - \\sqrt{32}$

**e)** $\\sqrt{8} + \\sqrt{2} + \\sqrt{72}$

**f)** $\\sqrt{300} - \\sqrt{48}$

**g)** $\\sqrt{1000} + \\sqrt{90}$

**h)** $\\sqrt{28} + \\sqrt{63}$

**i)** $\\sqrt{20} + \\sqrt{45}$

**j)** $\\sqrt{54} - \\sqrt{24}$

Show Answers 

**a)** $5\\sqrt{2}$ **b)** $7\\sqrt{2}$ **c)** $8\\sqrt{3}$ **d)** $6\\sqrt{2}$ **e)** $9\\sqrt{2}$

**f)** $6\\sqrt{3}$ **g)** $13\\sqrt{10}$ **h)** $5\\sqrt{7}$ **i)** $5\\sqrt{5}$ **j)** $\\sqrt{6}$

## Question 7

Simplify each of the following, using coefficients in front of the surds.

**a)** $3\\sqrt{8} + \\sqrt{2}$

**b)** $4\\sqrt{27} - \\sqrt{75}$

**c)** $2\\sqrt{50} + 5\\sqrt{32}$

**d)** $\\sqrt{200} - 3\\sqrt{18}$

**e)** $4\\sqrt{80} + 3\\sqrt{45}$

**f)** $6\\sqrt{75} - 2\\sqrt{12}$

**g)** $10\\sqrt{7} + 2\\sqrt{175}$

**h)** $3\\sqrt{28} + 2\\sqrt{63}$

**i)** $5\\sqrt{48} - 2\\sqrt{27}$

**j)** $4\\sqrt{54} - 3\\sqrt{24}$

Show Answers 

**a)** $7\\sqrt{2}$ **b)** $7\\sqrt{3}$ **c)** $30\\sqrt{2}$ **d)** $\\sqrt{2}$ **e)** $25\\sqrt{5}$

**f)** $26\\sqrt{3}$ **g)** $20\\sqrt{7}$ **h)** $12\\sqrt{7}$ **i)** $14\\sqrt{3}$ **j)** $6\\sqrt{6}$

*\[Video: "Surds (Part 4) Expanding Double Brackets" goes here\]*

Expand brackets containing surds the same way as with algebra — multiply every term in the first bracket by every term in the second, then simplify.

**Worked Example**

$(2+\\sqrt{3})(1-\\sqrt{3}) = 2 - 2\\sqrt{3} + \\sqrt{3} - 3 = -1 - \\sqrt{3}$

## Question 8

**a)** $(3+\\sqrt{5})(4-\\sqrt{5})$

**b)** $(\\sqrt{7}-1)(\\sqrt{7}-1)$

**c)** $(5-\\sqrt{3})(5+\\sqrt{3})$

**d)** $(\\sqrt{7}+\\sqrt{2})(\\sqrt{8}+\\sqrt{7})$

**e)** $(1+2\\sqrt{2})(2-\\sqrt{2})$

**f)** $(3\\sqrt{5}+7)(2\\sqrt{5}+1)$

**g)** $(3+\\sqrt{2})^2$

**h)** $(1+\\sqrt{5})^2$

**i)** $(10-\\sqrt{2})^2$

**j)** $(2\\sqrt{3}-3)^2$

Show Answers 

**a)** $7+\\sqrt{5}$ **b)** $8-2\\sqrt{7}$ **c)** $22$ **d)** $11+3\\sqrt{14}$ **e)** $3\\sqrt{2}-2$

**f)** $37+17\\sqrt{5}$ **g)** $11+6\\sqrt{2}$ **h)** $6+2\\sqrt{5}$ **i)** $102-20\\sqrt{2}$ **j)** $21-12\\sqrt{3}$

*\[Video: "Surds (Part 5) Rationalising the Denominator 1" goes here\]*

To rationalise a single-term surd denominator, multiply top and bottom by that surd.

**Worked Example**

$\\dfrac{6}{\\sqrt{2}} = \\dfrac{6}{\\sqrt{2}} \\times \\dfrac{\\sqrt{2}}{\\sqrt{2}} = \\dfrac{6\\sqrt{2}}{2} = 3\\sqrt{2}$

## Question 9

**a)** $\\dfrac{1}{\\sqrt{5}}$

**b)** $\\dfrac{4}{\\sqrt{3}}$

**c)** $\\dfrac{12}{\\sqrt{6}}$

**d)** $\\dfrac{\\sqrt{2}}{\\sqrt{7}}$

**e)** $\\dfrac{3\\sqrt{5}}{\\sqrt{2}}$

**f)** $\\dfrac{8}{3\\sqrt{2}}$

**g)** $\\dfrac{10}{\\sqrt{8}}$

**h)** $\\dfrac{15}{\\sqrt{12}}$

**i)** $\\dfrac{20}{\\sqrt{50}}$

**j)** $\\dfrac{2\\sqrt{3}}{\\sqrt{27}}$

Show Answers 

**a)** $\\dfrac{\\sqrt{5}}{5}$ **b)** $\\dfrac{4\\sqrt{3}}{3}$ **c)** $2\\sqrt{6}$ **d)** $\\dfrac{\\sqrt{14}}{7}$ **e)** $\\dfrac{3\\sqrt{10}}{2}$

**f)** $\\dfrac{4\\sqrt{2}}{3}$ **g)** $\\dfrac{5\\sqrt{2}}{2}$ **h)** $\\dfrac{5\\sqrt{3}}{2}$ **i)** $2\\sqrt{2}$ **j)** $\\dfrac{2}{3}$

*\[Video: "Surds (Part 6) Rationalising the Denominator 2" goes here\]*

To rationalise a two-term denominator, multiply top and bottom by its conjugate (same terms, opposite sign in the middle).

**Worked Example**

$\\dfrac{2}{3+\\sqrt{2}} = \\dfrac{2}{3+\\sqrt{2}} \\times \\dfrac{3-\\sqrt{2}}{3-\\sqrt{2}} = \\dfrac{2(3-\\sqrt{2})}{7} = \\dfrac{6-2\\sqrt{2}}{7}$

## Question 10

**a)** $\\dfrac{1}{3+\\sqrt{2}}$

**b)** $\\dfrac{6}{4-\\sqrt{5}}$

**c)** $\\dfrac{10}{\\sqrt{7}-2}$

**d)** $\\dfrac{12}{\\sqrt{3}+1}$

**e)** $\\dfrac{\\sqrt{5}}{6+\\sqrt{5}}$

**f)** $\\dfrac{2\\sqrt{3}}{\\sqrt{3}-1}$

**g)** $\\dfrac{3+\\sqrt{2}}{5-\\sqrt{2}}$

**h)** $\\dfrac{\\sqrt{3}+1}{\\sqrt{3}-1}$

**i)** $\\dfrac{1}{\\sqrt{7}-\\sqrt{3}}$

**j)** $\\dfrac{4\\sqrt{2}}{\\sqrt{5}+\\sqrt{3}}$

Show Answers 

**a)** $\\dfrac{3-\\sqrt{2}}{7}$ **b)** $\\dfrac{24+6\\sqrt{5}}{11}$ **c)** $\\dfrac{20+10\\sqrt{7}}{3}$ **d)** $6\\sqrt{3}-6$ **e)** $\\dfrac{6\\sqrt{5}-5}{31}$

**f)** $3+\\sqrt{3}$ **g)** $\\dfrac{17+8\\sqrt{2}}{23}$ **h)** $2+\\sqrt{3}$ **i)** $\\dfrac{\\sqrt{7}+\\sqrt{3}}{4}$ **j)** $2\\sqrt{10}-2\\sqrt{6}$

---

### GCSE Maths Tutoring

I offer one-to-one and small group GCSE Maths tutoring for students across the UK and internationally. With 94+ five-star Google reviews and tutoring experience since 2017, I specialise in helping students understand difficult concepts and improve their exam technique.

[GCSE Maths Tutoring](https://www.a-level-maths-tutor.com/gcse-maths-tutor/)

[94+ 5-star Google Reviews](https://www.a-level-maths-tutor.com/reviews/)

[Contact Me](https://www.a-level-maths-tutor.com/contact/)

[Back to A-Level Maths Revision](https://www.a-level-maths-tutor.com/a-level-maths-revision/)
### AS-Level Maths | Integration
URL: https://www.a-level-maths-tutor.com/as-level-maths-integration/
Last updated: 2026-07-23T15:40:30.000Z
To integrate: raise the power by one, then divide the coefficient by the new power.

$\\displaystyle\\int ax^n \\, dx = \\frac{a}{n+1}x^{n+1} + C$

Using limits gives the area between the curve and the $x$-axis.

## Question 1

Integrate the following expressions with respect to $x$.

**a)** $\\displaystyle\\int 2\\sqrt{x} - \\frac{1}{x^2} \\, dx$

**b)** $\\displaystyle\\int 4\\sqrt{x} - 2\\sqrt{x^5} \\, dx$

**c)** $\\displaystyle\\int \\frac{3}{4\\sqrt{x}} + \\frac{1}{x^3} \\, dx$

**d)** $\\displaystyle\\int 2x\\sqrt{x} - \\frac{4}{3x^2} \\, dx$

**e)** $\\displaystyle\\int 2\\sqrt{x} + \\frac{1}{2\\sqrt{x}} \\, dx$

Show Answers 

**a)** $\\dfrac{4}{3}x^{\\frac{3}{2}} + \\dfrac{1}{x} + C$

**b)** $\\dfrac{8}{3}x^{\\frac{3}{2}} - \\dfrac{4}{7}x^{\\frac{7}{2}} + C$

**c)** $\\dfrac{3}{2}\\sqrt{x} - \\dfrac{1}{2x^2} + C$

**d)** $\\dfrac{4}{5}x^{\\frac{5}{2}} + \\dfrac{4}{3}x^{-1} + C$

**e)** $\\dfrac{4}{3}x^{\\frac{3}{2}} + \\sqrt{x} + C$

## Question 2

The point $P(8,18)$ lies on the curve $C$, whose gradient function is given by $\\displaystyle\\frac{dy}{dx} = 8\\sqrt\[3\]{x} - 10, \\; x \\geq 0$.

Find an equation for $C$.

Show Answers 

$y = 6x^{\\frac{4}{3}} - 10x + 2$

### Question 3

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/07/CleanShot-2026-07-23-at-16.23.29@2x.png)

Show Answers 

**a)** $(-5, 0)$ and $(3, 0)$

**b)** $-27$

### Question 4

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/07/CleanShot-2026-07-23-at-16.36.52@2x.png)

Show Answers 

**a)** $(0,0)$, $(2,0)$ and $(3,0)$

**b)** Total area $= \\dfrac{8}{3} + \\dfrac{5}{12} = 3\\dfrac{1}{12}$

### Question 5

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/07/CleanShot-2026-07-23-at-16.24.20@2x.png)

Show Answers 

**a)** $(1, 2)$ and $(3, 4)$

**b)** Area $= \\dfrac{4}{3}$

### Question 6

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/07/CleanShot-2026-07-23-at-16.37.33@2x-1.png)

Show Answers 

**a)** $3$

**b)** Area $= 9$

### Question 7

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/07/CleanShot-2026-07-23-at-16.26.27@2x.png)

Show Answers 

**a)** $y = 2 - x$

**b)** Area $= \\dfrac{5}{6}$

### Question 8

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/07/CleanShot-2026-07-23-at-16.25.43@2x.png)

Show Answers 

**a)** $y = 4 - x$

**b)** Area $= \\dfrac{5}{3}$

---

### A-Level Maths Tutoring

I offer one-to-one and small group A-Level Maths tutoring for students across the UK and internationally. With 94+ five-star Google reviews and tutoring experience since 2017, I specialise in helping students understand difficult concepts and improve their exam technique.

[A-Level Maths Tutoring](https://www.a-level-maths-tutor.com/a-level-maths-tutor/)

[94+ 5-star Google Reviews](https://www.a-level-maths-tutor.com/reviews/)

[Contact Me](https://www.a-level-maths-tutor.com/contact/)

[Back to A-Level Maths Revision](https://www.a-level-maths-tutor.com/a-level-maths-revision/)
### GCSE Maths | Ratios
URL: https://www.a-level-maths-tutor.com/gcse-maths-ratios/
Last updated: 2026-07-22T14:50:00.000Z
# Simple Ratios

**Worked Example**

Share £40 in the ratio 3:5

$3 : 5 \\quad (8)$

$? : ? \\quad (40)$

$sf = 40 \\div 8 = 5$

$3 \\times 5 = 15, \\quad 5 \\times 5 = 25$

## Question 1

**a)** Share £20 in the ratio 2:3

**b)** Share 15cm in the ratio 1:2

**c)** Divide £24 in the ratio 1:3

**d)** Share 35 sweets in the ratio 4:3

**e)** Divide 55g in the ratio 3:2

**f)** Divide 54kg in the ratio 1:5

**g)** Share £104 in the ratio 3:5

**h)** Divide 161 miles in the ratio 6:1

**i)** Divide 315ml in the ratio 2:7

**j)** Share $650 in the ratio 4:9

**k)** Share £800 in the ratio 11:14

**l)** Share 1200kg in the ratio 3:37

Show Answers 

**a)** £8, £12

**b)** 5cm, 10cm

**c)** £6, £18

**d)** 20, 15 sweets

**e)** 33g, 22g

**f)** 9kg, 45kg

**g)** £39, £65

**h)** 138, 23 miles

**i)** 70ml, 245ml

**j)** $200, $450

**k)** £352, £448

**l)** 90kg, 1110kg

# Applying Ratios

**Worked Example**

The ratio of cats to dogs in a shelter is 3:4\. There are 12 cats. How many dogs are there?

$3 : 4$

$12 : ?$

$sf = 12 \\div 3 = 4$

Dogs $= 4 \\times 4 = 16$

## Question 2

**a)** James has some apples and oranges. The ratio of apples to oranges is 2:5\. He has 15 oranges. How many apples does James have?

**b)** The ratio of lemon sweets to strawberry sweets in a tub is 5:3\. There are 120 lemon sweets in the tub. How many strawberry sweets are in the tub?

**c)** Rachel has some first class and some second class stamps. The ratio of first class to second class stamps is 3:4\. Rachel has 18 first class stamps. (i) How many second class stamps does Rachel have? (ii) How many stamps does Rachel have in total?

**d)** Abby, Neil and Dylan share a sum of money in the ratio 2:4:5\. Neil receives £60\. Work out how much money Dylan receives.

**e)** Isaac and Victoria share money in the ratio 2:5\. Victoria receives £6.60\. Work out the difference between how much money Isaac and Victoria receive.

**f)** Rachel has some apples and bananas. The ratio of apples to bananas is 2:3\. She has 14 apples. Work out how many bananas Rachel has.

**g)** Chris and Molly win money in a competition. They share the money in the ratio 2:3\. Molly receives £240\. How much money does Chris receive?

**h)** The ratio of boys to girls in a school is 4:5\. There are 220 boys in the school. How many students attend the school?

**i)** Three angles are in the ratio 2:3:5\. The smallest angle is 50°. Work out the sizes of the other two angles.

Show Answers 

**a)** 6 apples

**b)** 72 strawberry sweets

**c)** (i) 24 second class stamps (ii) 42 stamps in total

**d)** £75

**e)** £3.96

**f)** 21 bananas

**g)** £160

**h)** 495 students

**i)** 75° and 125°

# Comparing Ratios

If you know the difference between two shares, that difference corresponds to a whole number of parts. Divide the difference by that number of parts to find one share.

**Worked Example**

Sam and Tia share sweets in the ratio 2:5\. Tia gets 18 more sweets than Sam. How many sweets does each person get?

Difference in parts $= 5-2 = 3$

One share $= 18 \\div 3 = 6$

Sam $= 2 \\times 6 = 12$, Tia $= 5 \\times 6 = 30$

## Question 3

**a)** Charlene and Danielle share some money in ratio 2:3\. Danielle gets £25 more than Charlene. How much does each girl receive?

**b)** The costs of building a single-storey house extension are in the ratio labour : materials : professional fees $= 7:5:1$. The cost of materials is £6,400 more than the amount paid in professional fees. Work out the total cost of building this house extension.

**c)** Three quantities $A$, $B$ and $C$ are in the ratio $A:B:C$ is $13:7:2$. Given that $A - B = 48$, find the value of $A + B + C$.

**d)** Last season, the number of goals scored by Arjun, by Simon and by Kath for their football team were in the ratios 2:5:8\. Simon scored 12 more goals than Arjun. Work out the number of goals scored by Kath.

Show Answers 

**a)** Charlene: £50, Danielle: £75

**b)** £20,800

**c)** $A+B+C = 176$

**d)** $32$ goals

# Combining Ratios

**Worked Example**

$a:b = 2:3$ and $b:c = 6:5$. Find $a:b:c$.

$a:b = 4:6$ and $b:c = 6:5$

$a:b:c = 4:6:5$

## Question 4

Combine the following ratios, or find $a:b:c$.

**a)** $a:b$ is $3:2$ and $b:c$ is $2:5$

**b)** $a:b$ is $3:1$ and $b:c$ is $2:3$

**c)** $a:b$ is $7:4$ and $b:c$ is $2:1$

**d)** $a:b$ is $2:3$ and $b:c$ is $2:5$

**e)** $a:b$ is $9:2$, $b:c$ is $6:7$, and $a+b+c = 200$. Find $a$, $b$ and $c$.

Show Answers 

**a)** $a:b:c = 3:2:5$

**b)** $a:b:c = 6:2:3$

**c)** $a:b:c = 7:4:2$

**d)** $a:b:c = 4:6:15$

**e)** $a = 135$, $b = 30$, $c = 35$

# Ratios and Equations

**Worked Example (ratio to equation)**

$a:b = 4:7$

$7a = 4b$

**Worked Example (equation to ratio)**

$3a = 8b$

$a:b = 8:3$

## Question 5

Turn each ratio into an equation.

**a)** $a:b = 6:5$

**b)** $a:b = 3:4$

**c)** $a:b = 7:2$

**d)** $a:b = 5:9$

**e)** $a:b = 8:3$

Turn each equation into a ratio $a:b$.

**f)** $6a = 5b$

**g)** $4a = 9b$

**h)** $3a = 7b$

**i)** $2a = 5b$

**j)** $5a = 8b$

Show Answers 

**a)** $5a = 6b$

**b)** $4a = 3b$

**c)** $2a = 7b$

**d)** $9a = 5b$

**e)** $3a = 8b$

**f)** $a:b = 5:6$

**g)** $a:b = 9:4$

**h)** $a:b = 7:3$

**i)** $a:b = 5:2$

**j)** $a:b = 8:5$

---

### GCSE Maths Tutoring

I offer one-to-one and small group GCSE Maths tutoring for students across the UK and internationally. With 94+ five-star Google reviews and tutoring experience since 2017, I specialise in helping students understand difficult concepts and improve their exam technique.

[GCSE Maths Tutoring](https://www.a-level-maths-tutor.com/gcse-maths-tutor/)

[94+ 5-star Google Reviews](https://www.a-level-maths-tutor.com/reviews/)

[Contact Me](https://www.a-level-maths-tutor.com/contact/)

[Back to A-Level Maths Revision](https://www.a-level-maths-tutor.com/a-level-maths-revision/)
### GCSE Maths | Compound Interest
URL: https://www.a-level-maths-tutor.com/gcse-maths-compound-interest/
Last updated: 2026-07-22T11:08:21.000Z
Final value = original value $\\times$ multiplier$^{\\text{(number of years)}}$

**Worked Example**

£1000 is invested at 4% per year for 3 years.

Multiplier $= 1.04$

Final value $= 1000 \\times 1.04^3 = £1124.86$

## Question 1

Find the total value after the given number of years, to the nearest penny.

**a)** £500 is invested at 5% compound interest per year for 3 years.

**b)** £1200 is invested at 3% per year for 4 years.

**c)** £800 grows at 4.5% per year for 5 years.

**d)** £1000 is invested at 2.5% per year for 2 years.

**e)** £2000 increases by 6% each year for 3 years.

**f)** £1500 is invested at 1.2% per year for 6 years.

**g)** £600 grows at 7% compound interest for 4 years.

**h)** £1800 increases by 2% a year for 10 years.

**i)** £100 grows at 10% interest per year for 3 years.

**j)** £2500 is invested at 3.5% per year for 8 years.

Show Answers 

**a)** £578.81

**b)** £1350.61

**c)** £996.95

**d)** £1050.63

**e)** £2382.03

**f)** £1611.29

**g)** £786.48

**h)** £2194.19

**i)** £133.10

**j)** £3292.02

**Worked Example**

£900 depreciates at 20% per year for 3 years.

Multiplier $= 0.8$

Final value $= 900 \\times 0.8^3 = £460.80$

## Question 2

Find the value after the given number of years, to the nearest penny.

**a)** A car worth £12,000 depreciates at 10% per year for 3 years.

**b)** A laptop worth £800 loses 15% of its value each year for 2 years.

**c)** A phone bought for £1000 depreciates 20% annually for 4 years.

**d)** A machine costing £6000 depreciates at 5% per year for 5 years.

**e)** A sofa worth £1500 loses 12% of its value per year for 3 years.

**f)** A TV valued at £400 depreciates 25% a year for 2 years.

**g)** A bike costing £700 depreciates at 7% for 6 years.

**h)** A fridge bought for £300 depreciates 10% per year for 5 years.

**i)** A printer costing £500 loses 18% value annually for 3 years.

**j)** A used van worth £9000 depreciates by 8% a year for 4 years.

Show Answers 

**a)** £8748.00

**b)** £578.00

**c)** £409.60

**d)** £4642.69

**e)** £1022.21

**f)** £225.00

**g)** £452.89

**h)** £177.15

**i)** £275.68

**j)** £6447.54

**Worked Example**

Naoby invests £6000 for 5 years. The investment gets compound interest of $x\\%$ per annum. At the end of 5 years the investment is worth £8029.35\. Work out the value of $x$.

$6000 \\times x^5 = 8029.35$

Divide by 6000: $x^5 = 1.338225$

5th root both sides: $x = 1.06$

Convert the multiplier to a percentage: $x = 6$

## Question 3

Each of the following investments grows for 5 years at a fixed annual compound interest rate. Find the interest rate in each case, correct to 1 decimal place.

**a)** £4000 grows to £4416.32 after 5 years.

**b)** £5500 grows to £6376.01 after 5 years.

**c)** £3000 grows to £3649.96 after 5 years.

**d)** £7200 grows to £9189.23 after 5 years.

**e)** £2500 grows to £2828.52 after 5 years.

**f)** £6000 grows to £7126.12 after 5 years.

**g)** £8000 grows to £9969.46 after 5 years.

**h)** £1500 grows to £2007.34 after 5 years.

**i)** £9000 grows to £9695.56 after 5 years.

**j)** £4800 grows to £6732.25 after 5 years.

Show Answers 

**a)** $2.0\\%$

**b)** $3.0\\%$

**c)** $4.0\\%$

**d)** $5.0\\%$

**e)** $2.5\\%$

**f)** $3.5\\%$

**g)** $4.5\\%$

**h)** $6.0\\%$

**i)** $1.5\\%$

**j)** $7.0\\%$

---

### GCSE Maths Tutoring

I offer one-to-one and small group GCSE Maths tutoring for students across the UK and internationally. With 94+ five-star Google reviews and tutoring experience since 2017, I specialise in helping students understand difficult concepts and improve their exam technique.

[A-Level Maths Tutoring](https://www.a-level-maths-tutor.com/a-level-maths-tutor/)

[94+ 5-star Google Reviews](https://www.a-level-maths-tutor.com/reviews/)

[Contact Me](https://www.a-level-maths-tutor.com/contact/)

[Back to A-Level Maths Revision](https://www.a-level-maths-tutor.com/a-level-maths-revision/)
### GCSE Maths | Percentages
URL: https://www.a-level-maths-tutor.com/gcse-maths-percentages/
Last updated: 2026-07-22T13:09:04.000Z
Percentage change $= \\dfrac{\\text{new} - \\text{old}}{\\text{old}} \\times 100$

**Worked Example**

Original: 60, New: 72

Percentage change $= \\dfrac{72-60}{60} \\times 100 = \\dfrac{12}{60}\\times 100 = 20\\%$ increase

## Question 1

Calculate the percentage change.

**a)** Original: 50, New: 65

**b)** Original: 80, New: 68

**c)** Original: £120, New: £138

**d)** Original: 25g, New: 30g

**e)** Original: 600ml, New: 450ml

**f)** Original: £75, New: £90

**g)** Original: 12cm, New: 15cm

**h)** Original: 250 people, New: 235 people

**i)** Original: 40km, New: 52km

**j)** Original: £950, New: £1,045

Show Answers 

**a)** $+30\\%$

**b)** $-15\\%$

**c)** $+15\\%$

**d)** $+20\\%$

**e)** $-25\\%$

**f)** $+20\\%$

**g)** $+25\\%$

**h)** $-6\\%$

**i)** $+30\\%$

**j)** $+10\\%$

**Worked Example (non-calculator)**

Increase 160 by 12.5%

$100\\% = 160$

$10\\% = 16$

$2.5\\% = 4$

$12.5\\% = 10\\% + 2.5\\% = 16 + 4 = 20$

$160 + 20 = 180$

## Question 2 (Non-Calculator)

Find the new amount after the percentage increase.

**a)** Increase 100 by 10%

**b)** Increase 200 by 15%

**c)** Increase 80 by 25%

**d)** Increase £60 by 50%

**e)** Increase 40 by 5%

**f)** Increase 120 by 12.5%

**g)** Increase 300 by 1%

**h)** Increase 250 by 20%

**i)** Increase 180 by 75%

**j)** Increase 16 by 150%

Show Answers 

**a)** $110$

**b)** $230$

**c)** $100$

**d)** $£90$

**e)** $42$

**f)** $135$

**g)** $303$

**h)** $300$

**i)** $315$

**j)** $40$

**Worked Example (non-calculator)**

Decrease 240 by 17.5%

$100\\% = 240$

$10\\% = 24$

$5\\% = 12$

$2.5\\% = 6$

$17.5\\% = 10\\% + 5\\% + 2.5\\% = 24 + 12 + 6 = 42$

$240 - 42 = 198$

## Question 3 (Non-Calculator)

Find the new amount after the percentage decrease.

**a)** Decrease 100 by 10%

**b)** Decrease 200 by 25%

**c)** Decrease 80 by 50%

**d)** Decrease £60 by 5%

**e)** Decrease 150 by 20%

**f)** Decrease 120 by 75%

**g)** Decrease 400 by 1%

**h)** Decrease 240 by 12.5%

**i)** Decrease 180 by 15%

**j)** Decrease 32 by 150%

Show Answers 

**a)** $90$

**b)** $150$

**c)** $40$

**d)** $£57$

**e)** $120$

**f)** $30$

**g)** $396$

**h)** $210$

**i)** $153$

**j)** $-16$

**Worked Example (calculator)**

Increase 350 by 8%

$350 \\times 1.08 = 378$

## Question 4 (Calculator)

Find the new amount after the percentage increase.

**a)** Increase 134 by 17%

**b)** Increase 278 by 23%

**c)** Increase £85.50 by 12%

**d)** Increase 643 by 8.5%

**e)** Increase 92 by 14.5%

**f)** Increase 1250 by 3.7%

**g)** Increase 87.6 by 21%

**h)** Increase 455 by 16.4%

**i)** Increase £12.99 by 9%

**j)** Increase 782 by 0.5%

Show Answers 

**a)** $156.78$

**b)** $341.94$

**c)** $£95.76$

**d)** $697.66$

**e)** $105.34$

**f)** $1296.25$

**g)** $106.00$

**h)** $529.62$

**i)** $£14.16$

**j)** $785.91$

**Worked Example (calculator)**

Decrease 480 by 22%

$480 \\times 0.78 = 374.40$

## Question 5 (Calculator)

Find the new amount after the percentage decrease.

**a)** Decrease 156 by 18%

**b)** Decrease 289 by 32%

**c)** Decrease £74.80 by 15%

**d)** Decrease 821 by 6.5%

**e)** Decrease 105 by 12.8%

**f)** Decrease 1450 by 4.3%

**g)** Decrease 67.9 by 11%

**h)** Decrease 522 by 17.8%

**i)** Decrease £25.50 by 22%

**j)** Decrease 950 by 1.2%

Show Answers 

**a)** $127.92$

**b)** $196.52$

**c)** $£63.58$

**d)** $767.64$

**e)** $91.56$

**f)** $1387.65$

**g)** $60.43$

**h)** $429.08$

**i)** $£19.89$

**j)** $938.60$

**Worked Example (decrease)**

After a 30% decrease, a chair costs £77\. Find the original price.

$70\\% = £77$

$10\\% = £77 \\div 7 = £11$

$100\\% = £11 \\times 10 = £110$

## Question 6 (Reverse Percentages (Decrease) — Non-Calculator)

Find the original price in each case.

**a)** After a 20% decrease, a jacket costs £64\. What was the original price?

**b)** A bike is sold for £72 after a 10% discount. What was the original price?

**c)** A tablet's value dropped by 30% to £84\. What was the original value?

**d)** A sale reduces a phone's price by 25% to £180\. What was the original price?

**e)** After a 15% reduction, a microwave costs £102\. What was its original price?

**f)** A sofa is sold for £340 after a 15% discount. Find its original price.

Show Answers 

**a)** £80

**b)** £80

**c)** £120

**d)** £240

**e)** £120

**f)** £400

**Worked Example (increase)**

After a 40% increase, a watch costs £98\. Find the original price.

$140\\% = £98$

$10\\% = £98 \\div 14 = £7$

$100\\% = £7 \\times 10 = £70$

## Question 7 (Reverse Percentages (Increase) — Non-Calculator)

Find the original price in each case.

**a)** After a 20% increase, a concert ticket costs £84\. What was the original price?

**b)** A coat was increased by 25% to £75\. What was the price before the increase?

**c)** The price of petrol rose by 10% to £1.65 per litre. What was the original price?

**d)** After a 50% increase, a trampoline costs £150\. What was the original price?

**e)** A laptop's price rose by 30% to £520\. What was its price before the rise?

**f)** A phone plan increased by 25% to £62.50\. What was the price before?

Show Answers 

**a)** £70

**b)** £60

**c)** £1.50

**d)** £100

**e)** £400

**f)** £50

When the percentage isn't a multiple of 10, find 1% instead, then scale up to 100%.

**Worked Example (decrease)**

After a 15% decrease, a laptop costs £425\. Find the original price.

$85\\% = £425$

$1\\% = £425 \\div 85 = £5$

$100\\% = £5 \\times 100 = £500$

## Question 8 (Reverse Percentages (Decrease) — Calculator)

Find the original price in each case.

**a)** A jacket is £68.40 after a 12% discount. What was the original price?

**b)** A fridge is £336.70 after a 15% decrease. What was the full price?

**c)** A tablet dropped 8.5% in value to £293.38\. What was the original value?

**d)** After a 17% decrease, a coat costs £141.27\. What was the price before?

**e)** A gym membership now costs £445.50 after a 10.5% discount. What was the full price?

**f)** A washing machine is £742.32 after a 22% discount. What was the original price?

Show Answers 

**a)** £77.73

**b)** £396.12

**c)** £320.63

**d)** £170.20

**e)** £497.77

**f)** £951.69

**Worked Example (increase)**

After a 9% increase, a subscription costs £272.50\. Find the original price.

$109\\% = £272.50$

$1\\% = £272.50 \\div 109 = £2.50$

$100\\% = £2.50 \\times 100 = £250$

## Question 9 (Reverse Percentages (Increase) - Calculator)

Find the original price in each case.

**a)** A phone rose by 12.5% to £675\. What was the original price?

**b)** A gym membership increased by 15.6% to £580.62\. What was the original price?

**c)** The cost of heating went up 18% to £885.40\. What was it before?

**d)** A sofa price increased by 20.5% to £1,150\. What was its original price?

**e)** A subscription rose by 7.2% to £128.64\. What was it originally?

**f)** A house deposit increased by 25% to £62,500\. What was it before?

Show Answers 

**a)** £600.00

**b)** £502.27

**c)** £750.34

**d)** £954.36

**e)** £120.00

**f)** £50,000.00

---

### GCSE Maths Tutoring

I offer one-to-one and small group GCSE Maths tutoring for students across the UK and internationally. With 94+ five-star Google reviews and tutoring experience since 2017, I specialise in helping students understand difficult concepts and improve their exam technique.

[A-Level Maths Tutoring](https://www.a-level-maths-tutor.com/a-level-maths-tutor/)

[94+ 5-star Google Reviews](https://www.a-level-maths-tutor.com/reviews/)

[Contact Me](https://www.a-level-maths-tutor.com/contact/)

[Back to A-Level Maths Revision](https://www.a-level-maths-tutor.com/a-level-maths-revision/)
### Edexcel AS-Level Maths | Trigonometry
URL: https://www.a-level-maths-tutor.com/edexcel-as-level-maths-trigonometry/
Last updated: 2026-06-30T14:25:37.000Z
### Question 1

### Q12 - Edexcel AS-Level Maths Paper 1 June 2018

![Q12 - Edexcel AS-Level Maths Paper 1 June 2018](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-610.png)

### Question 2

### Q12 - Edexcel AS-Level Maths Paper 1 June 2019

![Q12 - Edexcel AS-Level Maths Paper 1 June 2019](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-628.png)

### Question 3

### Q9 - Edexcel AS-Level Maths Paper 1 June 2020

![Q9 - Edexcel AS-Level Maths Paper 1 June 2020](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-645.png)

![Q9 - Edexcel AS-Level Maths Paper 1 June 2020](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-646.png)

### Question 4

### Q12 - Edexcel AS-Level Maths Paper 1 June 2021

![Q12 - Edexcel AS-Level Maths Paper 1 June 2021](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-664.png)

![Q12 - Edexcel AS-Level Maths Paper 1 June 2021](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-665.png)

### Question 5

### Edexcel AS-Level Maths Paper 1 June 2022

![Q13 - Edexcel AS-Level Maths Paper 1 June 2022](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-691.png)

### Question 6

### Q12 - Edexcel AS-Level Maths Paper 1 June 2023

![Q12 - Edexcel AS-Level Maths Paper 1 June 2023](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-709.png)

### Question 7

### Q13 - Edexcel AS-Level Maths Paper 1 June 2024

![Q13 - Edexcel AS-Level Maths Paper 1 June 2024](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-734.png)

![Q13 - Edexcel AS-Level Maths Paper 1 June 2024](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-735.png)

### Question 8

### Q8 - Edexcel A-Level Maths Paper 1 June 2025

![Q8 - Edexcel AS-Level Maths Paper 1 June 2025](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-749.png)

### Question 9

### Q8 - Edexcel A-Level Maths Paper 1 June 2026

![Q8 - Edexcel AS-Level Maths Paper 1 June 2026](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-769.png)

---

### A-Level Maths Tutoring

I offer one-to-one and small group **A-Level Maths tutoring** for students across the UK and internationally. With 94+ five-star Google reviews and tutoring experience since 2017, I specialise in helping students understand difficult concepts and improve their exam technique.

[A-Level Maths Tutoring](https://www.a-level-maths-tutor.com/a-level-maths-tutor/)

[94+ 5-star Google Reviews](https://www.a-level-maths-tutor.com/reviews/)

[Contact Me](https://www.a-level-maths-tutor.com/contact/)

[Back to A-Level Maths Revision](https://www.a-level-maths-tutor.com/a-level-maths-revision/)
### A-Level Maths | Indices
URL: https://www.a-level-maths-tutor.com/a-level-maths-indices/
Last updated: 2026-06-27T14:47:31.000Z
**Rules of Indices**

$x^{\\frac{1}{n}} = \\sqrt\[n\]{x}$

$x^{\\frac{m}{n}} = \\left(\\sqrt\[n\]{x}\\right)^m$

$x^{-n} = \\dfrac{1}{x^n}$

## Question 1

Solve each equation.

**a)** $x^{\\frac{1}{2}} = 6$

**b)** $x^{\\frac{1}{3}} = 5$

**c)** $x^{-\\frac{1}{2}} = 2$

**d)** $x^{-\\frac{1}{4}} = \\tfrac{1}{3}$

**e)** $x^{\\frac{3}{2}} = 8$

**f)** $x^{\\frac{2}{3}} = 16$

**g)** $x^{\\frac{4}{3}} = 81$

**h)** $x^{-\\frac{3}{2}} = 27$

Show Answers 

**a)** $x = 36$ **b)** $x = 125$ **c)** $x = \\tfrac{1}{4}$ **d)** $x = 81$

**e)** $x = 4$ **f)** $x = 64$ **g)** $x = 27$ **h)** $x = \\tfrac{1}{9}$
  
  
## Question 2

Express in the form $x^k$.

**a)** $\\sqrt{x}$

**b)** $\\dfrac{1}{\\sqrt\[3\]{x}}$

**c)** $x^2 \\times \\sqrt{x}$

**d)** $\\dfrac{\\sqrt\[4\]{x}}{x}$

**e)** $\\sqrt{x^3}$

**f)** $\\sqrt{x} \\times \\sqrt\[3\]{x}$

**g)** $(\\sqrt{x})^5$

**h)** $\\sqrt\[3\]{x^2} \\times (\\sqrt{x})^3$

Show Answers 

**a)** $x^{\\frac{1}{2}}$ **b)** $x^{-\\frac{1}{3}}$ **c)** $x^{\\frac{5}{2}}$ **d)** $x^{-\\frac{3}{4}}$

**e)** $x^{\\frac{3}{2}}$ **f)** $x^{\\frac{5}{6}}$ **g)** $x^{\\frac{5}{2}}$ **h)** $x^{\\frac{13}{6}}$
  
  
## Question 3

Express each of the following in the form $ax^b$, where $a$ and $b$ are rational constants.

**a)** $\\dfrac{4}{\\sqrt{x}}$

**b)** $\\dfrac{1}{2x}$

**c)** $\\dfrac{3}{4x^3}$

**d)** $\\dfrac{1}{(3x)^2}$

**e)** $\\dfrac{2}{5\\sqrt\[3\]{x}}$

**f)** $\\dfrac{1}{\\sqrt{9x^3}}$

show Answers 

**a)** $4x^{-\\frac{1}{2}}$ **b)** $\\tfrac{1}{2}x^{-1}$ **c)** $\\tfrac{3}{4}x^{-3}$

**d)** $\\tfrac{1}{9}x^{-2}$ **e)** $\\tfrac{2}{5}x^{-\\frac{1}{3}}$ **f)** $\\tfrac{1}{3}x^{-\\frac{3}{2}}$
  
  
## Question 4

Simplify each of the following.

**a)** $\\dfrac{x^3 + 2x}{x}$

**b)** $\\dfrac{4t^5 - 6t^3}{2t^2}$

**c)** $\\dfrac{x^{\\frac{3}{2}} - 3x}{x^{\\frac{1}{2}}}$

**d)** $\\dfrac{y^2(y^3 - 6)}{3y}$

**e)** $\\dfrac{p + p^{\\frac{3}{2}}}{p^{\\frac{3}{4}}}$

**f)** $\\dfrac{8w - 2w^{\\frac{1}{2}}}{4w^{-\\frac{1}{2}}}$

**g)** $\\dfrac{x + 1}{x^{\\frac{1}{2}} + x^{-\\frac{1}{2}}}$

**h)** $\\dfrac{2t^3 - 4t}{t^{\\frac{3}{2}} - 2t^{-\\frac{1}{2}}}$

Show Answers 

**a)** $x^2 + 2$ **b)** $2t^3 - 3t$ **c)** $x - 3x^{\\frac{1}{2}}$ **d)** $\\tfrac{1}{3}y^4 - 2y$

**e)** $p^{\\frac{1}{4}} + p^{\\frac{3}{4}}$ **f)** $2w^{\\frac{3}{2}} - \\tfrac{1}{2}w$ **g)** $x^{\\frac{1}{2}}$ **h)** $2t^{\\frac{3}{2}}$

---

### A-Level Maths Tutoring

I offer one-to-one and small group A-Level Maths tutoring for students across the UK and internationally. With 94+ five-star Google reviews and tutoring experience since 2017, I specialise in helping students understand difficult concepts and improve their exam technique.

[A-Level Maths Tutoring](https://www.a-level-maths-tutor.com/a-level-maths-tutor/)

[94+ 5-star Google Reviews](https://www.a-level-maths-tutor.com/reviews/)

[Contact Me](https://www.a-level-maths-tutor.com/contact/)

[Back to A-Level Maths Revision](https://www.a-level-maths-tutor.com/a-level-maths-revision/)
### Edexcel A-Level Maths | Sequences & Series
URL: https://www.a-level-maths-tutor.com/edexcel-a-level-maths-sequences-series/
Last updated: 2026-06-16T14:48:55.000Z
## Question 1

### Q4 - Edexcel A-Level Maths Paper 2 June 2018

![Q4 - Edexcel A-Level Maths Paper 2 June 2018](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-183.png)

## Question 2

### Q11 - Edexcel A-Level Maths Paper 1 June 2019

![Q11 - Edexcel A-Level Maths Paper 1 June 2019](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-210.png)

## Question 3

### Q5 - Edexcel A-Level Maths Paper 1 June 2020

![Q5 - Edexcel A-Level Maths Paper 1 June 2020](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-244.png)

## Question 4

### Q13 - Edexcel A-Level Maths Paper 1 June 2020

![Q13 - Edexcel A-Level Maths Paper 1 June 2020](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-255.png)

![Q13 - Edexcel A-Level Maths Paper 1 June 2020](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-256.png)

## Question 5

### Q15 - Edexcel A-Level Maths Paper 2 June 2020

![Q15 - Edexcel A-Level Maths Paper 2 June 2020](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-280.png)

## Question 6

### Q3 - Edexcel A-Level Maths Paper 1 June 2021

![Q3 - Edexcel A-Level Maths Paper 1 June 2021](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-284.png)

## Question 7

### Q5 - Edexcel A-Level Maths Paper 1 June 2021

![Q5 - Edexcel A-Level Maths Paper 1 June 2021](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-287.png)

## Question 8

### Q1 - Edexcel A-Level Maths Paper 2 June 2021

![Q1 - Edexcel A-Level Maths Paper 2 June 2021](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-301.png)

## Question 9

### Q9 - Edexcel A-Level Maths Paper 2 June 2021

![Q9 - Edexcel A-Level Maths Paper 2 June 2021](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-311.png)

## Question 10

### Q13 - Edexcel A-Level Maths Paper 1 June 2022

![Q13 - Edexcel A-Level Maths Paper 1 June 2022](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-338.png)

![Q13 - Edexcel A-Level Maths Paper 1 June 2022](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-339.png)

## Question 11

### Q3 - Edexcel A-Level Maths Paper 2 June 2022

![Q3 - Edexcel A-Level Maths Paper 2 June 2022](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-347.png)

## Question 12

### Q15 - Edexcel A-Level Maths Paper 2 June 2022

![Q15 - Edexcel A-Level Maths Paper 2 June 2022](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-364.png)

## Question 13

### Q9 - Edexcel A-Level Maths Paper 1 June 2023

![Q9 - Edexcel A-Level Maths Paper 1 June 2023](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-376.png)

## Question 14

### Q2 - Edexcel A-Level Maths Paper 2 June 2023

![Q2 - Edexcel A-Level Maths Paper 2 June 2023](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-389.png)

## Question 15

### Q8 - Edexcel A-Level Maths Paper 2 June 2023

![Q8 - Edexcel A-Level Maths Paper 2 June 2023](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-395-1.png)

## Question 16

### Q9 - Edexcel A-Level Maths Paper 1 June 2024

![Q9 - Edexcel A-Level Maths Paper 1 June 2024](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-419.png)

## Question 17

### Q2 - Edexcel A-Level Maths Paper 2 June 2024

![Q2 - Edexcel A-Level Maths Paper 2 June 2024](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-431.png)

## Question 18

### Q4 - Edexcel A-Level Maths Paper 2 June 2024

![Q4 - Edexcel A-Level Maths Paper 2 June 2024](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-433.png)

## Question 19

### Q3 - Edexcel A-Level Maths Paper 1 June 2025

![Q3 - Edexcel A-Level Maths Paper 1 June 2025](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-456.png)

## Question 20

### Q13 - Edexcel A-Level Maths Paper 1 June 2026

![Q13 - Edexcel A-Level Maths Paper 1 June 2026](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-521.png)

## Question 21

### Edexcel A-Level Maths Paper 2 June 2026

---

### A-Level Maths Tutoring

I offer one-to-one and small group A-Level Maths tutoring for students across the UK and internationally. With 94+ five-star Google reviews and tutoring experience since 2017, I specialise in helping students understand difficult concepts and improve their exam technique.

[A-Level Maths Tutoring](https://www.a-level-maths-tutor.com/a-level-maths-tutor/)

[94+ 5-star Google Reviews](https://www.a-level-maths-tutor.com/reviews/)

[Contact Me](https://www.a-level-maths-tutor.com/contact/)

[Back to A-Level Maths Revision](https://www.a-level-maths-tutor.com/a-level-maths-revision/)
### Edexcel A-Level Maths | Binomial Distribution
URL: https://www.a-level-maths-tutor.com/edexcel-a-level-maths-binomial-distribution/
Last updated: 2026-06-15T10:19:57.000Z
## Question 1

### Q3 - Edexcel A-Level Maths Paper 3 June 2018

![Q3 - Edexcel A-Level Maths Paper 3 June 2018](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-78.png)

![Q3 - Edexcel A-Level Maths Paper 3 June 2018](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-79.png)

## Question 2

### Q4 - Edexcel A-Level Maths Paper 3 June 2019

![Q4 - Edexcel A-Level Maths Paper 3 June 2019](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-88.png)

![Q4 - Edexcel A-Level Maths Paper 3 June 2019](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-89.png)

## Question 3

### Q1 - Edexcel A-Level Maths Paper 3 June 2022

![Q1 - Edexcel A-Level Maths Paper 3 June 2022](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-115.png)

## Question 4

### Q4 - Edexcel A-Level Maths Paper 3 June 2022

![Q4 - Edexcel A-Level Maths Paper 3 June 2022](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-120.png)

![Q4 - Edexcel A-Level Maths Paper 3 June 2022](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-121.png)

## Question 5

### Q2 - Edexcel A-Level Maths Paper 3 June 2023

![Q1 - Edexcel A-Level Maths Paper 3 June 2023](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-130.png)

![Q2 - Edexcel A-Level Maths Paper 3 June 2023](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-131.png)

## Question 6

### Q1 - Edexcel A-Level Maths Paper 3 June 2024

![Q1 - Edexcel A-Level Maths Paper 3 June 2024](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-141.png)

## Question 7

### Q4 - Edexcel A-Level Maths Paper 3 June 2024

![Q4 - Edexcel A-Level Maths Paper 3 June 2024](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-146.png)

## Question 8

### Q3 - Edexcel A-Level Maths Paper 3 June 2025

![Q3 - Edexcel A-Level Maths Paper 3 June 2025](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-155.png)

---

### A-Level Maths Tutoring

I offer one-to-one and small group A-Level Maths tutoring for students across the UK and internationally. With 94+ five-star Google reviews and tutoring experience since 2017, I specialise in helping students understand difficult concepts and improve their exam technique.

[A-Level Maths Tutoring](https://www.a-level-maths-tutor.com/a-level-maths-tutor/)

[94+ 5-star Google Reviews](https://www.a-level-maths-tutor.com/reviews/)

[Contact Me](https://www.a-level-maths-tutor.com/contact/)

[Back to A-Level Maths Revision](https://www.a-level-maths-tutor.com/a-level-maths-revision/)
### Edexcel A-Level Maths | Probability Distribution
URL: https://www.a-level-maths-tutor.com/edexcel-a-level-maths-probability-distribution/
Last updated: 2026-07-22T15:46:36.000Z
## Question 1

### Q1 - Edexcel A-Level Maths Paper 3 June 2018

![Q1 - Edexcel A-Level Maths Paper 3 June 2018](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-76.png)

## Question 2

### Q4 - Edexcel A-Level Maths Paper 3 June 2020

![Q4 - Edexcel A-Level Maths Paper 3 June 2020](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-98.png)

![Q4 - Edexcel A-Level Maths Paper 3 June 2020](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-99.png)

## Question 3

### Q6 - Edexcel A-Level Maths Paper 3 June 2021

![Q6 - Edexcel A-Level Maths Paper 3 June 2021](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/07/image-113.png)

![Q6 - Edexcel A-Level Maths Paper 3 June 2021](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/07/image-114.png)

## Question 4

### Q1 - Edexcel A-Level Maths Paper 3 June 2022

![Q1 - Edexcel A-Level Maths Paper 3 June 2022](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-115.png)

## Question 5

### Q5 - Edexcel A-Level Maths Paper 3 June 2023

![Q5 - Edexcel A-Level Maths Paper 3 June 2023](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-136.png)

![Q5 - Edexcel A-Level Maths Paper 3 June 2023](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-137.png)

## Question 6

### Q6 - Edexcel A-Level Maths Paper 3 June 2025

![Q6 - Edexcel A-Level Maths Paper 3 June 2025](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-159.png)

---

### A-Level Maths Tutoring

I offer one-to-one and small group A-Level Maths tutoring for students across the UK and internationally. With 94+ five-star Google reviews and tutoring experience since 2017, I specialise in helping students understand difficult concepts and improve their exam technique.

[A-Level Maths Tutoring](https://www.a-level-maths-tutor.com/a-level-maths-tutor/)

[94+ 5-star Google Reviews](https://www.a-level-maths-tutor.com/reviews/)

[Contact Me](https://www.a-level-maths-tutor.com/contact/)

[Back to A-Level Maths Revision](https://www.a-level-maths-tutor.com/a-level-maths-revision/)
### A-Level Maths | Sequences & Series
URL: https://www.a-level-maths-tutor.com/a-level-maths-sequences-series/
Last updated: 2026-07-29T12:19:58.000Z
### Sequences

$n$: the position of a term · $a$: first term · $d$: common difference · $r$: common ratio

## Question 1

Write down the first four terms of each sequence.

**a)** $u\_n = u\_{n-1} + 4, \\quad n > 1, \\quad u\_1 = 3$

**b)** $u\_n = 3u\_{n-1} + 1, \\quad n > 1, \\quad u\_1 = 2$

**c)** $u\_{n+1} = 2u\_n + 5, \\quad n > 0, \\quad u\_1 = -2$

**d)** $u\_n = 7 - u\_{n-1}, \\quad n \\geq 2, \\quad u\_1 = 5$

**e)** $u\_n = 2(5 - 2u\_{n-1}), \\quad n > 1, \\quad u\_1 = -1$

**f)** $u\_n = \\tfrac{1}{10}(u\_{n-1} + 20), \\quad n \\geq 2, \\quad u\_1 = 10$

**g)** $u\_{n+1} = 1 - \\tfrac{1}{3}u\_n, \\quad n \\geq 1, \\quad u\_1 = 6$

**h)** $u\_{n+1} = \\dfrac{1}{2 + u\_n}, \\quad n \\geq 1, \\quad u\_1 = 0$

Show Answers 

**a)** $3, 7, 11, 15$ **b)** $2, 7, 22, 67$ **c)** $-2, 1, 7, 19$ **d)** $5, 2, 5, 2$

**e)** $-1, 14, -46, 194$ **f)** $10, 3, 2.3, 2.23$ **g)** $6, -1, \\tfrac{4}{3}, \\tfrac{5}{9}$ **h)** $0, \\tfrac{1}{2}, \\tfrac{2}{5}, \\tfrac{5}{12}$

### Arithmetic Sequences

$n$th term: $a + (n-1)d$

Sum of first $n$ terms: $S\_n = \\tfrac{1}{2}n\\left\[2a + (n-1)d\\right\]$

## Question 2

The $n$th term of each of the following sequences is given by $u\_n = an + b$, for $n \\geq 1$. Find the values of the constants $a$ and $b$ in each case.

**a)** $4, 7, 10, 13, 16, \\ldots$

**b)** $0, 7, 14, 21, 28, \\ldots$

**c)** $16, 14, 12, 10, 8, \\ldots$

**d)** $0.4, 1.7, 3.0, 4.3, 5.6, \\ldots$

**e)** $100, 83, 66, 49, 32, \\ldots$

**f)** $-13, -5, 3, 11, 19, \\ldots$

Show Answers 

**a)** $a = 3,\\ b = 1$ **b)** $a = 7,\\ b = -7$ **c)** $a = -2,\\ b = 18$

**d)** $a = 1.3,\\ b = -0.9$ **e)** $a = -17,\\ b = 117$ **f)** $a = 8,\\ b = -21$

## Question 3

For each of the following arithmetic series, write down the common difference and find the value of the 40th term.

**a)** $4, 10, 16, 22, \\ldots$

**b)** $30, 27, 24, 21, \\ldots$

**c)** $8.9, 11.2, 13.5, 15.8, \\ldots$

Show Answers 

**a)** $d = 6$, $u\_{40} = 238$ **b)** $d = -3$, $u\_{40} = -87$ **c)** $d = 2.3$, $u\_{40} = 98.6$

## Question 4

Find the sum of the first 30 terms of each of the following arithmetic series.

**a)** $8, 12, 16, 20, \\ldots$

**b)** $60, 53, 46, 39, \\ldots$

**c)** $7\\tfrac{1}{4}, 8\\tfrac{3}{4}, 10\\tfrac{1}{4}, 11\\tfrac{3}{4}, \\ldots$

Show Answers 

**a)** $1980$ **b)** $-1245$ **c)** $870$

## Question 5

The first and third terms of an arithmetic series are $21$ and $27$ respectively.

**a)** Find the common difference of the series.

**b)** Find the sum of the first 40 terms of the series.

Show Answers 

**a)** $d = 3$ **b)** $S\_{40} = 3180$

## Question 6

The sum of the first six terms of an arithmetic series is $213$ and the sum of the first ten terms of the series is $295$.

**a)** Find the first term and common difference of the series.

**b)** Find the number of positive terms in the series.

**c)** Hence find the maximum value of $S\_n$, the sum of the first $n$ terms of the series.

Show Answers 

**a)** $a = 43$, $d = -3$ **b)** $15$ **c)** $S\_{15} = 330$

### Geometric Sequences

$n$th term: $ar^{n-1}$

Sum of first $n$ terms: $S\_n = \\dfrac{a(1 - r^n)}{1 - r}$ or $\\dfrac{a(r^n - 1)}{r - 1}$

Sum to infinity (when $|r| < 1$): $S\_\\infty = \\dfrac{a}{1 - r}$

## Question 7

For each of the following geometric series, write down the common ratio and find the value of the eighth term.

**a)** $3, 9, 27, 81, \\ldots$

**b)** $1024, 256, 64, 16, \\ldots$

**c)** $1, -2, 4, -8, \\ldots$

Show Answers 

**a)** $r = 3$, $u\_8 = 6561$ **b)** $r = \\tfrac{1}{4}$, $u\_8 = \\tfrac{1}{16}$ **c)** $r = -2$, $u\_8 = -128$

## Question 8

For each of the following geometric series, find an expression for the $n$th term.

**a)** $1, 5, 25, 125, \\ldots$

**b)** $3, -12, 48, -192, \\ldots$

**c)** $81, 54, 36, 24, \\ldots$

Show Answers 

**a)** $u\_n = 5^{n-1}$ **b)** $u\_n = 3 \\times (-4)^{n-1}$ **c)** $u\_n = 81 \\times \\left(\\tfrac{2}{3}\\right)^{n-1}$

## Question 9

Given the first term $a$, the common ratio $r$, and the number of terms $n$, find the sum of each of the following geometric series. Give your answers to 3 decimal places where appropriate.

**a)** $a = 4,\\ r = 3,\\ n = 8$

**c)** $a = -1,\\ r = -4,\\ n = 12$

**d)** $a = 200,\\ r = 0.7,\\ n = 20$

Show Answers 

**a)** $13\\,120$ **c)** $3\\,355\\,443$ **d)** $666.135$

## Question 10

Evaluate to an appropriate degree of accuracy.

**a)** $\\displaystyle\\sum\_{r=1}^{9} 3^r$ **c)** $\\displaystyle\\sum\_{r=1}^{10} (10 \\times 2^r)$ **e)** $\\displaystyle\\sum\_{r=1}^{10} \\left\[12 \\times \\left(\\tfrac{1}{6}\\right)^r\\right\]$ **h)** $\\displaystyle\\sum\_{r=3}^{9} \\left\[2 \\times (-3)^r\\right\]$

Show Answers 

**a)** $29\\,523$ **c)** $20\\,460$ **e)** $2.400$ **h)** $-29\\,538$

## Question 11

The second and third terms of a geometric series are $2$ and $10$ respectively.

**a)** Find the common ratio of the series.

**b)** Find the first term of the series.

**c)** Find the sum of the first eight terms of the series.

Show Answers 

**a)** $r = 5$ **b)** $a = 0.4$ **c)** $S\_8 = 39\\,062.4$

## Question 12

The first and fourth terms of a geometric series are $2$ and $54$ respectively.

**a)** Find the common ratio of the series.

**b)** Find the ninth term of the series.

Show Answers 

**a)** $r = 3$ **b)** $u\_9 = 13\\,122$

## Question 13

The sum of the first four terms of a geometric series is $130$ and its common ratio is $1\\tfrac{1}{2}$.

**a)** Find the first term of the series.

**b)** Find the eighth term of the series.

**c)** Find the least value of $n$ for which the sum of the first $n$ terms of the series is greater than $30\\,000$.

Show Answers 

**a)** $a = 16$ **b)** $u\_8 = 273\\tfrac{3}{8}$ **c)** $n = 17$

## Question 14

For each of the following geometric series, either find its sum to infinity or explain why this cannot be found.

**a)** $12, 6, 3, 1.5, \\ldots$

**b)** $270, 90, 30, 10, \\ldots$

**d)** $216, 144, 96, 64, \\ldots$

**f)** $500, -300, 180, -108, \\ldots$

Show Answers 

**a)** $24$ **b)** $405$ **d)** $648$ **f)** $312.5$

## Question 15

The first three terms of a geometric series are $(k + 10)$, $k$ and $(k - 6)$ respectively.

**a)** Find the value of the constant $k$.

**b)** Find the sum to infinity of the series.

Show Answers 

**a)** $k = 15$ **b)** $S\_\\infty = 62.5$

\`\`\` 

---

### A-Level Maths Tutoring

I offer one-to-one and small group A-Level Maths tutoring for students across the UK and internationally. With 94+ five-star Google reviews and tutoring experience since 2017, I specialise in helping students understand difficult concepts and improve their exam technique.

[A-Level Maths Tutoring](https://www.a-level-maths-tutor.com/a-level-maths-tutor/)

[94+ 5-star Google Reviews](https://www.a-level-maths-tutor.com/reviews/)

[Contact Me](https://www.a-level-maths-tutor.com/contact/)

[Back to A-Level Maths Revision](https://www.a-level-maths-tutor.com/a-level-maths-revision/)
### Edexcel A-Level Maths | Probability
URL: https://www.a-level-maths-tutor.com/edexcel-a-level-maths-probability/
Last updated: 2026-06-17T11:46:58.000Z
## Question 1

### Q1 - Edexcel A-Level Maths Paper 3 June 2019

![Q1 - Edexcel A-Level Maths Paper 3 June 2019](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-84.png)

## Question 2

### Q1 - Edexcel A-Level Maths Paper 3 June 2020

![Q1 - Edexcel A-Level Maths Paper 3 June 2020](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-91.png)

![Q1 - Edexcel A-Level Maths Paper 3 June 2020](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-92.png)

## Question 3

### Q4 - Edexcel A-Level Maths Paper 3 June 2021

![Q4 - Edexcel A-Level Maths Paper 3 June 2021](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-109.png)

![Q4 - Edexcel A-Level Maths Paper 3 June 2021](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-110.png)

## Question 4

### Q5 - Edexcel A-Level Maths Paper 3 June 2022

![Q5 - Edexcel A-Level Maths Paper 3 June 2022](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-122.png)

![Q5 - Edexcel A-Level Maths Paper 3 June 2022](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-123.png)

![Q5 - Edexcel A-Level Maths Paper 3 June 2022](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-124.png)

## Question 5

### Q1 - Edexcel A-Level Maths Paper 3 June 2023

![Q1 - Edexcel A-Level Maths Paper 3 June 2023](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-128-1.png)

![Q1 - Edexcel A-Level Maths Paper 3 June 2023](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-129-1.png)

## Question 6

### Q6 - Edexcel A-Level Maths Paper 3 June 2024

![Q6 - Edexcel A-Level Maths Paper 3 June 2024](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-149.png)

![Q6 - Edexcel A-Level Maths Paper 3 June 2024](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-150.png)

## Question 8

### Q1 - Edexcel A-Level Maths Paper 3 June 2025

![Q1 - Edexcel A-Level Maths Paper 3 June 2024](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-151.png)

![Q1 - Edexcel A-Level Maths Paper 3 June 2025](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-152.png)

![Q1 - Edexcel A-Level Maths Paper 3 June 2025](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-153.png)

---

### A-Level Maths Tutoring

I offer one-to-one and small group A-Level Maths tutoring for students across the UK and internationally. With 94+ five-star Google reviews and tutoring experience since 2017, I specialise in helping students understand difficult concepts and improve their exam technique.

[A-Level Maths Tutoring](https://www.a-level-maths-tutor.com/a-level-maths-tutor/)

[94+ 5-star Google Reviews](https://www.a-level-maths-tutor.com/reviews/)

[Contact Me](https://www.a-level-maths-tutor.com/contact/)

[Back to A-Level Maths Revision](https://www.a-level-maths-tutor.com/a-level-maths-revision/)
### Edexcel A-Level Maths | Measures of Location & Spread
URL: https://www.a-level-maths-tutor.com/edexcel-a-level-maths-measures-of-location-spread/
Last updated: 2026-06-12T15:44:00.000Z
## Question 1

### Q4 - Edexcel A-Level Maths Paper 3 June 2018

![Q4 - Edexcel A-Level Maths Paper 3 June 2018](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-80.png)

![Q4 - Edexcel A-Level Maths Paper 3 June 2018](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-81.png)

## Question 2

### Q2 - Edexcel A-Level Maths Paper 3 June 2019

![Q2 - Edexcel A-Level Maths Paper 3 June 2019](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-85.png)

![Q2 - Edexcel A-Level Maths Paper 3 June 2019](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-86.png)

## Question 3

### Q3 - Edexcel A-Level Maths Paper 3 June 2020

![Q3 - Edexcel A-Level Maths Paper 3 June 2020](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-96.png)

![Q3 - Edexcel A-Level Maths Paper 3 June 2020](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-97.png)

## Question 4

### Q3 - Edexcel A-Level Maths Paper 3 June 2021

![Q3 - Edexcel A-Level Maths Paper 3 June 2021](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-107.png)

![Q3 - Edexcel A-Level Maths Paper 3 June 2021](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-108.png)

## Question 5

### Q3 - Edexcel A-Level Maths Paper 3 June 2022

![Q3 - Edexcel A-Level Maths Paper 3 June 2022](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-118.png)

![Q3 - Edexcel A-Level Maths Paper 3 June 2022](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-119.png)

## Question 6

### Q3 - Edexcel A-Level Maths Paper 3 June 2023

![Q3 - Edexcel A-Level Maths Paper 3 June 2023](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-132.png)

![Q3 - Edexcel A-Level Maths Paper 3 June 2023](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-133.png)

## Question 7

### Q3 - Edexcel A-Level Maths Paper 3 June 2024

![Q3 - Edexcel A-Level Maths Paper 3 June 2024](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-145.png)

## Question 8

### Q2 - Edexcel A-Level Maths Paper 3 June 2025

![Q2 - Edexcel A-Level Maths Paper 3 June 2025](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-154.png)

---

### A-Level Maths Tutoring

I offer one-to-one and small group A-Level Maths tutoring for students across the UK and internationally. With 94+ five-star Google reviews and tutoring experience since 2017, I specialise in helping students understand difficult concepts and improve their exam technique.

[A-Level Maths Tutoring](https://www.a-level-maths-tutor.com/a-level-maths-tutor/)

[94+ 5-star Google Reviews](https://www.a-level-maths-tutor.com/reviews/)

[Contact Me](https://www.a-level-maths-tutor.com/contact/)

[Back to A-Level Maths Revision](https://www.a-level-maths-tutor.com/a-level-maths-revision/)
### Edexcel A-Level Maths | Correlation
URL: https://www.a-level-maths-tutor.com/edexcel-a-level-maths-correlation/
Last updated: 2026-06-12T15:19:56.000Z
## Question 1

### Q2 - Edexcel A-Level Maths Paper 3 June 2018

![Q2 - Edexcel A-Level Maths Paper 3 June 2018](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-77.png)

## Question 2

### Q3 - Edexcel A-Level Maths Paper 3 June 2019

![Q3 - Edexcel A-Level Maths Paper 3 June 2019](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-87.png)

## Question 3

### Q2 - Edexcel A-Level Maths Paper 3 June 2020

![Q2 - Edexcel A-Level Maths Paper 3 June 2020](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-93.png)

![Q2 - Edexcel A-Level Maths Paper 3 June 2020](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-94.png)

![Q2 - Edexcel A-Level Maths Paper 3 June 2020](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-95.png)

## Question 4

### Q2 - Edexcel A-Level Maths Paper 3 June 2021

![Q2 - Edexcel A-Level Maths Paper 3 June 2021](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-104.png)

![Q2 - Edexcel A-Level Maths Paper 3 June 2021](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-105.png)

## Question 5

### Q6 - Edexcel A-Level Maths Paper 3 June 2022

![Q6 - Edexcel A-Level Maths Paper 3 June 2022](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-125.png)

![Q6 - Edexcel A-Level Maths Paper 3 June 2022](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-126.png)

![Q6 - Edexcel A-Level Maths Paper 3 June 2022](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-127.png)

### 

## Question 6

### Q2 - Edexcel A-Level Maths Paper 3 June 2024

![Q2 - Edexcel A-Level Maths Paper 3 June 2024](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-142.png)

![Q2 - Edexcel A-Level Maths Paper 3 June 2024](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-143.png)

![Q2 - Edexcel A-Level Maths Paper 3 June 2024](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-144.png)

## Question 7

### Q4 - Edexcel A-Level Maths Paper 3 June 2025

![Q4 - Edexcel A-Level Maths Paper 3 June 2025](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-156.png)

![Q4 - Edexcel A-Level Maths Paper 3 June 2025](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-157.png)

---

### A-Level Maths Tutoring

I offer one-to-one and small group A-Level Maths tutoring for students across the UK and internationally. With 94+ five-star Google reviews and tutoring experience since 2017, I specialise in helping students understand difficult concepts and improve their exam technique.

[A-Level Maths Tutoring](https://www.a-level-maths-tutor.com/a-level-maths-tutor/)

[94+ 5-star Google Reviews](https://www.a-level-maths-tutor.com/reviews/)

[Contact Me](https://www.a-level-maths-tutor.com/contact/)

[Back to A-Level Maths Revision](https://www.a-level-maths-tutor.com/a-level-maths-revision/)
### Edexcel A-Level Maths | Mechanics Other
URL: https://www.a-level-maths-tutor.com/edexcel-a-level-maths-mechanics-other/
Last updated: 2026-06-12T12:16:27.000Z
## Question 1

### Q1 - Edexcel A-Level Maths Paper 3 June 2023

![Q1 - Edexcel A-Level Maths Paper 3 June 2023](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-42.png)

## Question 2

### Q2 - Edexcel A-Level Maths Paper 3 June 2024

![Q2 - Edexcel A-Level Maths Paper 3 June 2024](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-53.png)

![Q2 - Edexcel A-Level Maths Paper 3 June 2024](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-54.png)

---

### A-Level Maths Tutoring

I offer one-to-one and small group A-Level Maths tutoring for students across the UK and internationally. With 94+ five-star Google reviews and tutoring experience since 2017, I specialise in helping students understand difficult concepts and improve their exam technique.

[A-Level Maths Tutoring](https://www.a-level-maths-tutor.com/a-level-maths-tutor/)

[94+ 5-star Google Reviews](https://www.a-level-maths-tutor.com/reviews/)

[Contact Me](https://www.a-level-maths-tutor.com/contact/)

[Back to A-Level Maths Revision](https://www.a-level-maths-tutor.com/a-level-maths-revision/)
### Edexcel A-Level Maths | Vector Applications
URL: https://www.a-level-maths-tutor.com/edexcel-a-level-maths-vector-applications/
Last updated: 2026-06-12T12:11:03.000Z
## Question 1

### Q6 - Edexcel A-Level Maths Paper 3 June 2018

![Q6 - Edexcel A-Level Maths Paper 3 June 2018](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image.png)

## Question 2

### Q8 - Edexcel A-Level Maths Paper 3 June 2018

![Q8 - Edexcel A-Level Maths Paper 3 June 2018](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-3.png)

## Question 3

### Q1 - Edexcel A-Level Maths Paper 3 June 2019

![Q1 - Edexcel A-Level Maths Paper 3 June 2019](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-8.png)

## Question 4

### Q2 - Edexcel A-Level Maths Paper 3 June 2019

![Q2 - Edexcel A-Level Maths Paper 3 June 2019](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-9.png)

## Question 5

### Q2 - Edexcel A-Level Maths Paper 3 June 2020

![Q2 - Edexcel A-Level Maths Paper 3 June 2020](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-18.png)

## Question 6

### Q3 - Edexcel A-Level Maths Paper 3 June 202

![Q3 - Edexcel A-Level Maths Paper 3 June 2020](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-19.png)

## Question 7

### Q1 - Edexcel A-Level Maths Paper 3 June 2021

![Q1 - Edexcel A-Level Maths Paper 3 June 2021](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-24.png)

## Question 8

### Q5 - Edexcel A-Level Maths Paper 3 June 2021

![Q5 - Edexcel A-Level Maths Paper 3 June 2021](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-33.png)

## Question 9

### Q1 - Edexcel A-Level Maths Paper 3 June 2022

![Q1 - Edexcel A-Level Maths Paper 3 June 2022](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-34.png)

## Question 10

### Q3 - Edexcel A-Level Maths Paper 3 June 2022

![Q3 - Edexcel A-Level Maths Paper 3 June 2022](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-37.png)

## Question 11

### Q3 - Edexcel A-Level Maths Paper 3 June 2023

![Q3 - Edexcel A-Level Maths Paper 3 June 2023](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-45.png)

## Question 12

### Q4 - Edexcel A-Level Maths Paper 3 June 2023

![Q4 - Edexcel A-Level Maths Paper 3 June 2023](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-46.png)

## Question 13

### Q4 - Edexcel A-Level Maths Paper 3 June 2024

![Q4 - Edexcel A-Level Maths Paper 3 June 2024](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-57.png)

![Q4 - Edexcel A-Level Maths Paper 3 June 2024](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-58.png)

## Question 14

### Q3 - Edexcel A-Level Maths Paper 3 June 2025

![Q3 - Edexcel A-Level Maths Paper 3 June 2025](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-68.png)

## Question 15

### Q4 - Edexcel A-Level Maths Paper 3 June 2025

![Q4 - Edexcel A-Level Maths Paper 3 June 2025](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-69.png)

---

### A-Level Maths Tutoring

I offer one-to-one and small group A-Level Maths tutoring for students across the UK and internationally. With 94+ five-star Google reviews and tutoring experience since 2017, I specialise in helping students understand difficult concepts and improve their exam technique.

[A-Level Maths Tutoring](https://www.a-level-maths-tutor.com/a-level-maths-tutor/)

[94+ 5-star Google Reviews](https://www.a-level-maths-tutor.com/reviews/)

[Contact Me](https://www.a-level-maths-tutor.com/contact/)

[Back to A-Level Maths Revision](https://www.a-level-maths-tutor.com/a-level-maths-revision/)
### Edexcel A-Level Maths | Forces
URL: https://www.a-level-maths-tutor.com/edexcel-a-level-maths-forces/
Last updated: 2026-06-12T12:04:04.000Z
## Question 1

### Q7 - Edexcel A-Level Maths Paper 3 June 2018

![Q7 - Edexcel A-Level Maths Paper 3 June 2018](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-1.png)

![Q7 - Edexcel A-Level Maths Paper 3 June 2018](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-2.png)

## Question 2

### Q3 - Edexcel A-Level Maths Paper 3 June 2019

![Q3 - Edexcel A-Level Maths Paper 3 June 2019](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-10.png)

## Question 3

### Q1 - Edexcel A-Level Maths Paper 3 June 2020

![Q1 - Edexcel A-Level Maths Paper 3 June 2020](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-16.png)

![Q1 - Edexcel A-Level Maths Paper 3 June 2020](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-17.png)

## Question 4

### Q2 - Edexcel A-Level Maths Paper 3 June 2021

![Q2 - Edexcel A-Level Maths Paper 3 June 2021](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-25.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-26.png)

Q2 - Edexcel A-Level Maths Paper 3 June 2021

![Q2 - Edexcel A-Level Maths Paper 3 June 2021](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-27.png)

## Question 5

### Edexcel A-Level Maths Paper 3 June 2022

![Q2 - Edexcel A-Level Maths Paper 3 June 2022](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-35.png)

![Q2 - Edexcel A-Level Maths Paper 3 June 2022](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-36.png)

## Question 6

### Q2 - Edexcel A-Level Maths Paper 3 June 2023

![Q2 - Edexcel A-Level Maths Paper 3 June 2023](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-43.png)

![Q2 - Edexcel A-Level Maths Paper 3 June 2023](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-44.png)

## Question 7

### Q1 - Edexcel A-Level Maths Paper 3 June 2024

![Q1 - Edexcel A-Level Maths Paper 3 June 2024](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-52.png)

## Question 8

### Q3 - Edexcel A-Level Maths Paper 3 June 2024

![Q3 - Edexcel A-Level Maths Paper 3 June 2024](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-55.png)

![Q3 - Edexcel A-Level Maths Paper 3 June 2024](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-56.png)

## Question 9

### Q1 - Edexcel A-Level Maths Paper 3 June 2025

![Q1 - Edexcel A-Level Maths Paper 3 June 2025](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-64.png)

![Q1 - Edexcel A-Level Maths Paper 3 June 2025](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-65.png)

## Question 10

### Q2 - Edexcel A-Level Maths Paper 3 June 2025

![Q2 - Edexcel A-Level Maths Paper 3 June 2025](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-66.png)

![Q2 - Edexcel A-Level Maths Paper 3 June 2025](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-67.png)

---

### A-Level Maths Tutoring

I offer one-to-one and small group A-Level Maths tutoring for students across the UK and internationally. With 94+ five-star Google reviews and tutoring experience since 2017, I specialise in helping students understand difficult concepts and improve their exam technique.

[A-Level Maths Tutoring](https://www.a-level-maths-tutor.com/a-level-maths-tutor/)

[94+ 5-star Google Reviews](https://www.a-level-maths-tutor.com/reviews/)

[Contact Me](https://www.a-level-maths-tutor.com/contact/)

[Back to A-Level Maths Revision](https://www.a-level-maths-tutor.com/a-level-maths-revision/)
### Edexcel A-Level Maths | Projectiles
URL: https://www.a-level-maths-tutor.com/edexcel-a-level-maths-projectiles/
Last updated: 2026-06-12T11:57:57.000Z
## Question 1

### Q10 - Edexcel A-Level Maths Paper 3 June 2018

![Q10 - Edexcel A-Level Maths Paper 3 June 2018](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-6.png)

![Q10 - Edexcel A-Level Maths Paper 3 June 2018](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-7.png)

## Question 2

### Q5 - Edexcel A-Level Maths Paper 3 June 2019

![Q5 - Edexcel A-Level Maths Paper 3 June 2019](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-14.png)

![Q5 - Edexcel A-Level Maths Paper 3 June 2019](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-15.png)

## Question 3

### Q5 - Edexcel A-Level Maths Paper 3 June 2020

![Q5 - Edexcel A-Level Maths Paper 3 June 2020](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-22.png)

![Q5 - Edexcel A-Level Maths Paper 3 June 2020](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-23.png)

## Question 4

### Q4 - Edexcel A-Level Maths Paper 3 June 2021

![Q4 - Edexcel A-Level Maths Paper 3 June 2021](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-31.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-32.png)

Q4 - Edexcel A-Level Maths Paper 3 June 2021

## Question 5

### Q5 - Edexcel A-Level Maths Paper 3 June 2022

![Q5 - Edexcel A-Level Maths Paper 3 June 2022](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-40.png)

![Q5 - Edexcel A-Level Maths Paper 3 June 2022](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-41.png)

## Question 6

### Q5 - Edexcel A-Level Maths Paper 3 June 2023

![Q5 - Edexcel A-Level Maths Paper 3 June 2023](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-47.png)

![Q5 - Edexcel A-Level Maths Paper 3 June 2023](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-48.png)

![Q5 - Edexcel A-Level Maths Paper 3 June 2023](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-49.png)

## Question 7

### Q5 - Edexcel A-Level Maths Paper 3 June 2024

![Q5 - Edexcel A-Level Maths Paper 3 June 2024](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-59.png)

![Q5 - Edexcel A-Level Maths Paper 3 June 2024](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-60.png)

![Q5 - Edexcel A-Level Maths Paper 3 June 2024](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-61.png)

## Question 8

### Q5 - Edexcel A-Level Maths Paper 3 June 2025

![Q5 - Edexcel A-Level Maths Paper 3 June 2025](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-70.png)

![Q5 - Edexcel A-Level Maths Paper 3 June 2025](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-71.png)

---

### A-Level Maths Tutoring

I offer one-to-one and small group A-Level Maths tutoring for students across the UK and internationally. With 94+ five-star Google reviews and tutoring experience since 2017, I specialise in helping students understand difficult concepts and improve their exam technique.

[A-Level Maths Tutoring](https://www.a-level-maths-tutor.com/a-level-maths-tutor/)

[94+ 5-star Google Reviews](https://www.a-level-maths-tutor.com/reviews/)

[Contact Me](https://www.a-level-maths-tutor.com/contact/)

[Back to A-Level Maths Revision](https://www.a-level-maths-tutor.com/a-level-maths-revision/)
### Edexcel A-Level Maths | Moments
URL: https://www.a-level-maths-tutor.com/edexcel-a-level-maths-moments/
Last updated: 2026-06-13T14:50:44.000Z
## Question 1

### Q9 - Edexcel A-Level Maths Paper 3 June 2018

![Q9 - Edexcel A-Level Maths Paper 3 June 2018](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-4.png)

![Q9 - Edexcel A-Level Maths Paper 3 June 2018](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-5.png)

## Question 2

### Q4 - Edexcel A-Level Maths Paper 3 June 2019

![Q4 - Edexcel A-Level Maths Paper 3 June 2019](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-12.png)

![Q4 - Edexcel A-Level Maths Paper 3 June 2019](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-13.png)

[Video Solution](https://www.youtube.com/watch?v=yBkAkdP4jtA&list=PLNbnUZLQafHG3lClyZQriV8tQX7EPCUYv&index=3&pp=iAQBsAgC&ref=a-level-maths-tutor.com)

## Question 3

### Q4 - Edexcel A-Level Maths Paper 3 June 2020

![Q4 - Edexcel A-Level Maths Paper 3 June 2020](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-20.png)

![Q4 - Edexcel A-Level Maths Paper 3 June 2020](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-21.png)

[Video Solution](https://www.youtube.com/watch?v=XRKIWxfGEFw&list=PLNbnUZLQafHG3lClyZQriV8tQX7EPCUYv&index=1&pp=iAQBsAgC&ref=a-level-maths-tutor.com)

## Question 4

### Q3 - Edexcel A-Level Maths Paper 3 June 2021

![Q3 - Edexcel A-Level Maths Paper 3 June 2021](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-28.png)

![Q3 - Edexcel A-Level Maths Paper 3 June 2021](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-29.png)

![Q3 - Edexcel A-Level Maths Paper 3 June 2021](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-30.png)

## Question 5

### Edexcel A-Level Maths Paper 3 June 2022

![Q4 - Edexcel A-Level Maths Paper 3 June 2022](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-38.png)

![Q4 - Edexcel A-Level Maths Paper 3 June 2022](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-39.png)

[Video Solution](https://www.youtube.com/watch?v=8-eu5ADkBco&list=PLNbnUZLQafHG3lClyZQriV8tQX7EPCUYv&index=2&pp=iAQBsAgC&ref=a-level-maths-tutor.com)

## Question 6

### Edexcel A-Level Maths Paper 3 June 2023

![Q6 - Edexcel A-Level Maths Paper 3 June 2023](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-50.png)

![Q6 - Edexcel A-Level Maths Paper 3 June 2023](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-51.png)

## Question 7

### Q6 - Edexcel A-Level Maths Paper 3 June 2024

![Q6 - Edexcel A-Level Maths Paper 3 June 2024](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-62.png)

![Q6 - Edexcel A-Level Maths Paper 3 June 2024](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-63.png)

## Question 8

### Q6 - Edexcel A-Level Maths Paper 3 June 2025

![Q6 - Edexcel A-Level Maths Paper 3 June 2025](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-72.png)

![Q6 - Edexcel A-Level Maths Paper 3 June 2025](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-73.png)

![Q6 - Edexcel A-Level Maths Paper 3 June 2025](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-74.png)

![Q6 - Edexcel A-Level Maths Paper 3 June 2025](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/06/image-75.png)

---

### A-Level Maths Tutoring

I offer one-to-one and small group A-Level Maths tutoring for students across the UK and internationally. With 94+ five-star Google reviews and tutoring experience since 2017, I specialise in helping students understand difficult concepts and improve their exam technique.

[A-Level Maths Tutoring](https://www.a-level-maths-tutor.com/a-level-maths-tutor/)

[94+ 5-star Google Reviews](https://www.a-level-maths-tutor.com/reviews/)

[Contact Me](https://www.a-level-maths-tutor.com/contact/)

[Back to A-Level Maths Revision](https://www.a-level-maths-tutor.com/a-level-maths-revision/)
### Probability Tree Diagrams | GCSE Maths
URL: https://www.a-level-maths-tutor.com/probability-tree-diagrams-gcse-maths/
Last updated: 2026-05-12T16:31:14.000Z
### Question 1

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/05/CleanShot-2026-05-12-at-17.20.13@2x.png)

### Question 2

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/05/CleanShot-2026-05-12-at-17.22.07@2x.png)

### Question 3

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/05/CleanShot-2026-05-12-at-17.26.33@2x-1.png)

### Question 4

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/05/CleanShot-2026-05-12-at-17.26.10@2x-1-1.png)

### Question 5

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/05/CleanShot-2026-05-12-at-17.29.12@2x-1.png)

### Question 6

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/05/CleanShot-2026-05-12-at-17.29.17@2x-1.png)

---

### GCSE Maths Tutoring

I offer one-to-one and small group GCSE Maths tutoring for students across the UK and internationally. With 94+ five-star Google reviews and tutoring experience since 2017, I specialise in helping students understand difficult concepts and improve their exam technique.

[A-Level Maths Tutoring](https://www.a-level-maths-tutor.com/a-level-maths-tutor/)

[94+ 5-star Google Reviews](https://www.a-level-maths-tutor.com/reviews/)

[Contact Me](https://www.a-level-maths-tutor.com/contact/)

[Back to A-Level Maths Revision](https://www.a-level-maths-tutor.com/a-level-maths-revision/)
### PDF Files - Edexcel iGCSE Maths Past Papers
URL: https://www.a-level-maths-tutor.com/pdf-files-edexcel-igcse-maths-past-papers/
Last updated: 2026-05-06T14:46:06.000Z
Paper 1 QP

[Edexcel iGCSE Maths Paper 1 January 2019Edexcel iGCSE Maths Paper 1 January 2019.pdf724 KBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/05/Edexcel-iGCSE-Maths-Paper-1-January-2019-1.pdf "Download")

[Edexcel iGCSE Maths Paper 1 January 2020Edexcel iGCSE Maths Paper 1 January 2020.pdf1 MBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/05/Edexcel-iGCSE-Maths-Paper-1-January-2020-1.pdf "Download")

[Edexcel iGCSE Maths Paper 1 January 2021Edexcel iGCSE Maths Paper 1 January 2021.pdf1 MBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/05/Edexcel-iGCSE-Maths-Paper-1-January-2021-1.pdf "Download")

[Edexcel iGCSE Maths Paper 1 January 2022Edexcel iGCSE Maths Paper 1 January 2022.pdf1 MBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/05/Edexcel-iGCSE-Maths-Paper-1-January-2022-1.pdf "Download")

[Edexcel iGCSE Maths Paper 1 January 2023Edexcel iGCSE Maths Paper 1 January 2023.pdf1 MBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/05/Edexcel-iGCSE-Maths-Paper-1-January-2023-1.pdf "Download")

[Edexcel iGCSE Maths Paper 1 June 2018Edexcel iGCSE Maths Paper 1 June 2018.pdf270 KBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/05/Edexcel-iGCSE-Maths-Paper-1-June-2018-1.pdf "Download")

[Edexcel iGCSE Maths Paper 1 June 2019Edexcel iGCSE Maths Paper 1 June 2019.pdf347 KBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/05/Edexcel-iGCSE-Maths-Paper-1-June-2019-1.pdf "Download")

[Edexcel iGCSE Maths Paper 1 June 2021Edexcel iGCSE Maths Paper 1 June 2021.pdf1 MBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/05/Edexcel-iGCSE-Maths-Paper-1-June-2021-1.pdf "Download")

[Edexcel iGCSE Maths Paper 1 June 2022Edexcel iGCSE Maths Paper 1 June 2022.pdf1 MBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/05/Edexcel-iGCSE-Maths-Paper-1-June-2022-1.pdf "Download")

[Edexcel iGCSE Maths Paper 1 June 2023Edexcel iGCSE Maths Paper 1 June 2023.pdf1 MBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/05/Edexcel-iGCSE-Maths-Paper-1-June-2023-1.pdf "Download")

[Edexcel iGCSE Maths Paper 1 June 2024Edexcel iGCSE Maths Paper 1 June 2024.pdf1 MBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/05/Edexcel-iGCSE-Maths-Paper-1-June-2024.pdf "Download")

[Edexcel iGCSE Maths Paper 1 November 2020Edexcel iGCSE Maths Paper 1 November 2020.pdf941 KBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/05/Edexcel-iGCSE-Maths-Paper-1-November-2020-1.pdf "Download")

[Edexcel iGCSE Maths Paper 1 November 2021Edexcel iGCSE Maths Paper 1 November 2021.pdf1 MBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/05/Edexcel-iGCSE-Maths-Paper-1-November-2021-1.pdf "Download")

[Edexcel iGCSE Maths Paper 1 November 2023Edexcel iGCSE Maths Paper 1 November 2023.pdf1 MBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/05/Edexcel-iGCSE-Maths-Paper-1-November-2023.pdf "Download")

[Edexcel iGCSE Maths Paper 1 November 2024Edexcel iGCSE Maths Paper 1 November 2024.pdf1 MBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/05/Edexcel-iGCSE-Maths-Paper-1-November-2024.pdf "Download")

[Edexcel iGCSE Maths Paper 1R January 2019Edexcel iGCSE Maths Paper 1R January 2019.pdf655 KBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/05/Edexcel-iGCSE-Maths-Paper-1R-January-2019.pdf "Download")

[Edexcel iGCSE Maths Paper 1R January 2020Edexcel iGCSE Maths Paper 1R January 2020.pdf1 MBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/05/Edexcel-iGCSE-Maths-Paper-1R-January-2020.pdf "Download")

[Edexcel iGCSE Maths Paper 1R January 2021Edexcel iGCSE Maths Paper 1R January 2021.pdf1 MBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/05/Edexcel-iGCSE-Maths-Paper-1R-January-2021.pdf "Download")

[Edexcel iGCSE Maths Paper 1R January 2022Edexcel iGCSE Maths Paper 1R January 2022.pdf1 MBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/05/Edexcel-iGCSE-Maths-Paper-1R-January-2022.pdf "Download")

[Edexcel iGCSE Maths Paper 1R January 2023Edexcel iGCSE Maths Paper 1R January 2023.pdf1 MBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/05/Edexcel-iGCSE-Maths-Paper-1R-January-2023.pdf "Download")

[Edexcel iGCSE Maths Paper 1R June 2018Edexcel iGCSE Maths Paper 1R June 2018.pdf283 KBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/05/Edexcel-iGCSE-Maths-Paper-1R-June-2018.pdf "Download")

[Edexcel iGCSE Maths Paper 1R June 2019Edexcel iGCSE Maths Paper 1R June 2019.pdf349 KBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/05/Edexcel-iGCSE-Maths-Paper-1R-June-2019.pdf "Download")

[Edexcel iGCSE Maths Paper 1R June 2022Edexcel iGCSE Maths Paper 1R June 2022.pdf1 MBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/05/Edexcel-iGCSE-Maths-Paper-1R-June-2022.pdf "Download")

[Edexcel iGCSE Maths Paper 1R June 2023Edexcel iGCSE Maths Paper 1R June 2023.pdf1 MBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/05/Edexcel-iGCSE-Maths-Paper-1R-June-2023.pdf "Download")

[Edexcel iGCSE Maths Paper 1R June 2024Edexcel iGCSE Maths Paper 1R June 2024.pdf865 KBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/05/Edexcel-iGCSE-Maths-Paper-1R-June-2024.pdf "Download")

[Edexcel iGCSE Maths Paper 1R November 2020Edexcel iGCSE Maths Paper 1R November 2020.pdf1 MBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/05/Edexcel-iGCSE-Maths-Paper-1R-November-2020.pdf "Download")

Paper 2 QP

[Edexcel iGCSE Maths Paper 2 November 2024Edexcel iGCSE Maths Paper 2 November 2024.pdf1 MBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/05/Edexcel-iGCSE-Maths-Paper-2-November-2024.pdf "Download")

[Edexcel iGCSE Maths Paper 2 November 2023Edexcel iGCSE Maths Paper 2 November 2023.pdf1 MBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/05/Edexcel-iGCSE-Maths-Paper-2-November-2023.pdf "Download")

[Edexcel iGCSE Maths Paper 2 November 2021Edexcel iGCSE Maths Paper 2 November 2021.pdf1 MBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/05/Edexcel-iGCSE-Maths-Paper-2-November-2021.pdf "Download")

[Edexcel iGCSE Maths Paper 2 November 2020Edexcel iGCSE Maths Paper 2 November 2020.pdf929 KBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/05/Edexcel-iGCSE-Maths-Paper-2-November-2020.pdf "Download")

[Edexcel iGCSE Maths Paper 2 June 2024Edexcel iGCSE Maths Paper 2 June 2024.pdf996 KBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/05/Edexcel-iGCSE-Maths-Paper-2-June-2024.pdf "Download")

[Edexcel iGCSE Maths Paper 2 June 2023Edexcel iGCSE Maths Paper 2 June 2023.pdf2 MBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/05/Edexcel-iGCSE-Maths-Paper-2-June-2023.pdf "Download")

[Edexcel iGCSE Maths Paper 2 June 2022Edexcel iGCSE Maths Paper 2 June 2022.pdf1 MBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/05/Edexcel-iGCSE-Maths-Paper-2-June-2022.pdf "Download")

[Edexcel iGCSE Maths Paper 2 June 2021Edexcel iGCSE Maths Paper 2 June 2021.pdf1 MBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/05/Edexcel-iGCSE-Maths-Paper-2-June-2021.pdf "Download")

[Edexcel iGCSE Maths Paper 2 June 2019Edexcel iGCSE Maths Paper 2 June 2019.pdf350 KBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/05/Edexcel-iGCSE-Maths-Paper-2-June-2019.pdf "Download")

[Edexcel iGCSE Maths Paper 2 June 2018Edexcel iGCSE Maths Paper 2 June 2018.pdf253 KBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/05/Edexcel-iGCSE-Maths-Paper-2-June-2018.pdf "Download")

[Edexcel iGCSE Maths Paper 2 January 2023Edexcel iGCSE Maths Paper 2 January 2023.pdf2 MBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/05/Edexcel-iGCSE-Maths-Paper-2-January-2023.pdf "Download")

[Edexcel iGCSE Maths Paper 2 January 2022Edexcel iGCSE Maths Paper 2 January 2022.pdf1 MBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/05/Edexcel-iGCSE-Maths-Paper-2-January-2022.pdf "Download")

[Edexcel iGCSE Maths Paper 2 January 2021Edexcel iGCSE Maths Paper 2 January 2021.pdf1 MBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/05/Edexcel-iGCSE-Maths-Paper-2-January-2021.pdf "Download")

[Edexcel iGCSE Maths Paper 2 January 2020Edexcel iGCSE Maths Paper 2 January 2020.pdf1 MBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/05/Edexcel-iGCSE-Maths-Paper-2-January-2020.pdf "Download")

[Edexcel iGCSE Maths Paper 2 January 2019Edexcel iGCSE Maths Paper 2 January 2019.pdf450 KBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/05/Edexcel-iGCSE-Maths-Paper-2-January-2019.pdf "Download")

[Edexcel iGCSE Maths Paper 2R January 2023Edexcel iGCSE Maths Paper 2R January 2023.pdf2 MBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/05/Edexcel-iGCSE-Maths-Paper-2R-January-2023.pdf "Download")

[Edexcel iGCSE Maths Paper 2R January 2022Edexcel iGCSE Maths Paper 2R January 2022.pdf1 MBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/05/Edexcel-iGCSE-Maths-Paper-2R-January-2022.pdf "Download")

[Edexcel iGCSE Maths Paper 2R January 2021Edexcel iGCSE Maths Paper 2R January 2021.pdf1 MBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/05/Edexcel-iGCSE-Maths-Paper-2R-January-2021.pdf "Download")

[Edexcel iGCSE Maths Paper 2R January 2020Edexcel iGCSE Maths Paper 2R January 2020.pdf958 KBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/05/Edexcel-iGCSE-Maths-Paper-2R-January-2020.pdf "Download")

[Edexcel iGCSE Maths Paper 2R January 2019Edexcel iGCSE Maths Paper 2R January 2019.pdf502 KBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/05/Edexcel-iGCSE-Maths-Paper-2R-January-2019.pdf "Download")

[Edexcel iGCSE Maths Paper 2R November 2020Edexcel iGCSE Maths Paper 2R November 2020.pdf1 MBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/05/Edexcel-iGCSE-Maths-Paper-2R-November-2020.pdf "Download")

[Edexcel iGCSE Maths Paper 2R June 2024Edexcel iGCSE Maths Paper 2R June 2024.pdf1 MBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/05/Edexcel-iGCSE-Maths-Paper-2R-June-2024.pdf "Download")

[Edexcel iGCSE Maths Paper 2R June 2023Edexcel iGCSE Maths Paper 2R June 2023.pdf1 MBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/05/Edexcel-iGCSE-Maths-Paper-2R-June-2023.pdf "Download")

[Edexcel iGCSE Maths Paper 2R June 2022Edexcel iGCSE Maths Paper 2R June 2022.pdf2 MBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/05/Edexcel-iGCSE-Maths-Paper-2R-June-2022.pdf "Download")

[Edexcel iGCSE Maths Paper 2R June 2019Edexcel iGCSE Maths Paper 2R June 2019.pdf338 KBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/05/Edexcel-iGCSE-Maths-Paper-2R-June-2019-1.pdf "Download")

[Edexcel iGCSE Maths Paper 2R June 2018Edexcel iGCSE Maths Paper 2R June 2018.pdf257 KBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/05/Edexcel-iGCSE-Maths-Paper-2R-June-2018.pdf "Download")

Paper 1 MS

[Edexcel iGCSE Maths Paper 1 January 2019 MSEdexcel iGCSE Maths Paper 1 January 2019 MS.pdf745 KBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/05/Edexcel-iGCSE-Maths-Paper-1-January-2019-MS.pdf "Download")

[Edexcel iGCSE Maths Paper 1 January 2020 MSEdexcel iGCSE Maths Paper 1 January 2020 MS.pdf247 KBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/05/Edexcel-iGCSE-Maths-Paper-1-January-2020-MS.pdf "Download")

[Edexcel iGCSE Maths Paper 1 January 2021 MSEdexcel iGCSE Maths Paper 1 January 2021 MS.pdf552 KBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/05/Edexcel-iGCSE-Maths-Paper-1-January-2021-MS.pdf "Download")

[Edexcel iGCSE Maths Paper 1 January 2022 MSEdexcel iGCSE Maths Paper 1 January 2022 MS.pdf527 KBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/05/Edexcel-iGCSE-Maths-Paper-1-January-2022-MS.pdf "Download")

[Edexcel iGCSE Maths Paper 1 January 2023 MSEdexcel iGCSE Maths Paper 1 January 2023 MS.pdf432 KBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/05/Edexcel-iGCSE-Maths-Paper-1-January-2023-MS.pdf "Download")

[Edexcel iGCSE Maths Paper 1 June 2018 MSEdexcel iGCSE Maths Paper 1 June 2018 MS.pdf669 KBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/05/Edexcel-iGCSE-Maths-Paper-1-June-2018-MS.pdf "Download")

[Edexcel iGCSE Maths Paper 1 June 2019 MSEdexcel iGCSE Maths Paper 1 June 2019 MS.pdf503 KBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/05/Edexcel-iGCSE-Maths-Paper-1-June-2019-MS.pdf "Download")

[Edexcel iGCSE Maths Paper 1 June 2021 MSEdexcel iGCSE Maths Paper 1 June 2021 MS.pdf624 KBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/05/Edexcel-iGCSE-Maths-Paper-1-June-2021-MS.pdf "Download")

[Edexcel iGCSE Maths Paper 1 June 2022 MSEdexcel iGCSE Maths Paper 1 June 2022 MS.pdf540 KBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/05/Edexcel-iGCSE-Maths-Paper-1-June-2022-MS.pdf "Download")

[Edexcel iGCSE Maths Paper 1 June 2023 MSEdexcel iGCSE Maths Paper 1 June 2023 MS.pdf421 KBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/05/Edexcel-iGCSE-Maths-Paper-1-June-2023-MS-1.pdf "Download")

[Edexcel iGCSE Maths Paper 1 June 2024 MSEdexcel iGCSE Maths Paper 1 June 2024 MS.pdf565 KBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/05/Edexcel-iGCSE-Maths-Paper-1-June-2024-MS.pdf "Download")

[Edexcel iGCSE Maths Paper 1 November 2020 MSEdexcel iGCSE Maths Paper 1 November 2020 MS.pdf449 KBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/05/Edexcel-iGCSE-Maths-Paper-1-November-2020-MS.pdf "Download")

[Edexcel iGCSE Maths Paper 1 November 2021 MSEdexcel iGCSE Maths Paper 1 November 2021 MS.pdf764 KBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/05/Edexcel-iGCSE-Maths-Paper-1-November-2021-MS.pdf "Download")

[Edexcel iGCSE Maths Paper 1 November 2023 MSEdexcel iGCSE Maths Paper 1 November 2023 MS.pdf347 KBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/05/Edexcel-iGCSE-Maths-Paper-1-November-2023-MS.pdf "Download")

[Edexcel iGCSE Maths Paper 1 November 2024 MSEdexcel iGCSE Maths Paper 1 November 2024 MS.pdf668 KBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/05/Edexcel-iGCSE-Maths-Paper-1-November-2024-MS.pdf "Download")

[Edexcel iGCSE Maths Paper 1R January 2019 MSEdexcel iGCSE Maths Paper 1R January 2019 MS.pdf669 KBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/05/Edexcel-iGCSE-Maths-Paper-1R-January-2019-MS.pdf "Download")

[Edexcel iGCSE Maths Paper 1R January 2020 MSEdexcel iGCSE Maths Paper 1R January 2020 MS.pdf220 KBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/05/Edexcel-iGCSE-Maths-Paper-1R-January-2020-MS.pdf "Download")

[Edexcel iGCSE Maths Paper 1R January 2021 MSEdexcel iGCSE Maths Paper 1R January 2021 MS.pdf464 KBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/05/Edexcel-iGCSE-Maths-Paper-1R-January-2021-MS.pdf "Download")

[Edexcel iGCSE Maths Paper 1R January 2022 MSEdexcel iGCSE Maths Paper 1R January 2022 MS.pdf444 KBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/05/Edexcel-iGCSE-Maths-Paper-1R-January-2022-MS.pdf "Download")

[Edexcel iGCSE Maths Paper 1R January 2023 MSEdexcel iGCSE Maths Paper 1R January 2023 MS.pdf548 KBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/05/Edexcel-iGCSE-Maths-Paper-1R-January-2023-MS.pdf "Download")

[Edexcel iGCSE Maths Paper 1R June 2018 MSEdexcel iGCSE Maths Paper 1R June 2018 MS.pdf737 KBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/05/Edexcel-iGCSE-Maths-Paper-1R-June-2018-MS.pdf "Download")

[Edexcel iGCSE Maths Paper 1R June 2019 MSEdexcel iGCSE Maths Paper 1R June 2019 MS.pdf592 KBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/05/Edexcel-iGCSE-Maths-Paper-1R-June-2019-MS.pdf "Download")

[Edexcel iGCSE Maths Paper 1R June 2022 MSEdexcel iGCSE Maths Paper 1R June 2022 MS.pdf471 KBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/05/Edexcel-iGCSE-Maths-Paper-1R-June-2022-MS.pdf "Download")

[Edexcel iGCSE Maths Paper 1R June 2023 MSEdexcel iGCSE Maths Paper 1R June 2023 MS.pdf422 KBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/05/Edexcel-iGCSE-Maths-Paper-1R-June-2023-MS.pdf "Download")

[Edexcel iGCSE Maths Paper 1R June 2024 MSEdexcel iGCSE Maths Paper 1R June 2024 MS.pdf535 KBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/05/Edexcel-iGCSE-Maths-Paper-1R-June-2024-MS.pdf "Download")

[Edexcel iGCSE Maths Paper 1R November 2020 MSEdexcel iGCSE Maths Paper 1R November 2020 MS.pdf446 KBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/05/Edexcel-iGCSE-Maths-Paper-1R-November-2020-MS.pdf "Download")

Paper 2 MS

[Edexcel iGCSE Maths Paper 2R November 2020 MSEdexcel iGCSE Maths Paper 2R November 2020 MS.pdf540 KBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/05/Edexcel-iGCSE-Maths-Paper-2R-November-2020-MS.pdf "Download")

[Edexcel iGCSE Maths Paper 2R June 2024 MSEdexcel iGCSE Maths Paper 2R June 2024 MS.pdf608 KBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/05/Edexcel-iGCSE-Maths-Paper-2R-June-2024-MS.pdf "Download")

[Edexcel iGCSE Maths Paper 2R June 2023 MSEdexcel iGCSE Maths Paper 2R June 2023 MS.pdf577 KBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/05/Edexcel-iGCSE-Maths-Paper-2R-June-2023-MS.pdf "Download")

[Edexcel iGCSE Maths Paper 2R June 2022 MSEdexcel iGCSE Maths Paper 2R June 2022 MS.pdf622 KBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/05/Edexcel-iGCSE-Maths-Paper-2R-June-2022-MS.pdf "Download")

[Edexcel iGCSE Maths Paper 2R June 2019 MSEdexcel iGCSE Maths Paper 2R June 2019 MS.pdf633 KBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/05/Edexcel-iGCSE-Maths-Paper-2R-June-2019-MS.pdf "Download")

[Edexcel iGCSE Maths Paper 2R June 2018 MSEdexcel iGCSE Maths Paper 2R June 2018 MS.pdf467 KBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/05/Edexcel-iGCSE-Maths-Paper-2R-June-2018-MS.pdf "Download")

[Edexcel iGCSE Maths Paper 2R January 2023 MSEdexcel iGCSE Maths Paper 2R January 2023 MS.pdf550 KBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/05/Edexcel-iGCSE-Maths-Paper-2R-January-2023-MS.pdf "Download")

[Edexcel iGCSE Maths Paper 2R January 2022 MSEdexcel iGCSE Maths Paper 2R January 2022 MS.pdf565 KBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/05/Edexcel-iGCSE-Maths-Paper-2R-January-2022-MS.pdf "Download")

[Edexcel iGCSE Maths Paper 2R January 2021 MSEdexcel iGCSE Maths Paper 2R January 2021 MS.pdf543 KBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/05/Edexcel-iGCSE-Maths-Paper-2R-January-2021-MS.pdf "Download")

[Edexcel iGCSE Maths Paper 2R January 2020 MSEdexcel iGCSE Maths Paper 2R January 2020 MS.pdf306 KBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/05/Edexcel-iGCSE-Maths-Paper-2R-January-2020-MS.pdf "Download")

[Edexcel iGCSE Maths Paper 2R January 2019 MSEdexcel iGCSE Maths Paper 2R January 2019 MS.pdf711 KBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/05/Edexcel-iGCSE-Maths-Paper-2R-January-2019-MS.pdf "Download")

[Edexcel iGCSE Maths Paper 2 November 2024 MSEdexcel iGCSE Maths Paper 2 November 2024 MS.pdf593 KBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/05/Edexcel-iGCSE-Maths-Paper-2-November-2024-MS.pdf "Download")

[Edexcel iGCSE Maths Paper 2 November 2023 MSEdexcel iGCSE Maths Paper 2 November 2023 MS.pdf455 KBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/05/Edexcel-iGCSE-Maths-Paper-2-November-2023-MS.pdf "Download")

[Edexcel iGCSE Maths Paper 2 November 2021 MSEdexcel iGCSE Maths Paper 2 November 2021 MS.pdf418 KBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/05/Edexcel-iGCSE-Maths-Paper-2-November-2021-MS.pdf "Download")

[Edexcel iGCSE Maths Paper 2 November 2020 MSEdexcel iGCSE Maths Paper 2 November 2020 MS.pdf462 KBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/05/Edexcel-iGCSE-Maths-Paper-2-November-2020-MS.pdf "Download")

[Edexcel iGCSE Maths Paper 2 June 2024 MSEdexcel iGCSE Maths Paper 2 June 2024 MS.pdf643 KBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/05/Edexcel-iGCSE-Maths-Paper-2-June-2024-MS.pdf "Download")

[Edexcel iGCSE Maths Paper 2 June 2023 MSEdexcel iGCSE Maths Paper 2 June 2023 MS.pdf575 KBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/05/Edexcel-iGCSE-Maths-Paper-2-June-2023-MS.pdf "Download")

[Edexcel iGCSE Maths Paper 2 June 2022 MSEdexcel iGCSE Maths Paper 2 June 2022 MS.pdf557 KBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/05/Edexcel-iGCSE-Maths-Paper-2-June-2022-MS.pdf "Download")

[Edexcel iGCSE Maths Paper 2 June 2021 MSEdexcel iGCSE Maths Paper 2 June 2021 MS.pdf629 KBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/05/Edexcel-iGCSE-Maths-Paper-2-June-2021-MS.pdf "Download")

[Edexcel iGCSE Maths Paper 2 June 2019 MSEdexcel iGCSE Maths Paper 2 June 2019 MS.pdf636 KBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/05/Edexcel-iGCSE-Maths-Paper-2-June-2019-MS.pdf "Download")

[Edexcel iGCSE Maths Paper 2 June 2018 MSEdexcel iGCSE Maths Paper 2 June 2018 MS.pdf560 KBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/05/Edexcel-iGCSE-Maths-Paper-2-June-2018-MS.pdf "Download")

[Edexcel iGCSE Maths Paper 2 January 2023 MSEdexcel iGCSE Maths Paper 2 January 2023 MS.pdf917 KBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/05/Edexcel-iGCSE-Maths-Paper-2-January-2023-MS.pdf "Download")

[Edexcel iGCSE Maths Paper 2 January 2022 MSEdexcel iGCSE Maths Paper 2 January 2022 MS.pdf498 KBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/05/Edexcel-iGCSE-Maths-Paper-2-January-2022-MS.pdf "Download")

[Edexcel iGCSE Maths Paper 2 January 2021 MSEdexcel iGCSE Maths Paper 2 January 2021 MS.pdf413 KBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/05/Edexcel-iGCSE-Maths-Paper-2-January-2021-MS.pdf "Download")

[Edexcel iGCSE Maths Paper 2 January 2020 MSEdexcel iGCSE Maths Paper 2 January 2020 MS.pdf294 KBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/05/Edexcel-iGCSE-Maths-Paper-2-January-2020-MS.pdf "Download")

[Edexcel iGCSE Maths Paper 2 January 2019 MSEdexcel iGCSE Maths Paper 2 January 2019 MS.pdf648 KBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/05/Edexcel-iGCSE-Maths-Paper-2-January-2019-MS.pdf "Download")
### Edexcel A-Level Maths | Quadratics
URL: https://www.a-level-maths-tutor.com/edexcel-a-level-maths-quadratics/
Last updated: 2026-06-24T14:26:01.000Z
### Question 1

### Edexcel A-Level Maths Paper 1 June 2018

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-35.png)

### Question 2

### Edexcel A-Level Maths Paper 2 June 2018

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/05/image.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/05/image-1.png)

### Question 3

### Edexcel A-Level Maths Paper 1 June 2020

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/05/image-2.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/05/image-3.png)

### Question 4

### Edexcel A-Level Maths Paper 1 June 2020

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/05/image-4.png)

### Question 5

### Edexcel A-Level Maths Paper 2 June 2020

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/05/image-5.png)

### Question 6

### Edexcel A-Level Maths Paper 1 June 2021

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/05/image-7.png)

### Question 7

### Edexcel A-Level Maths Paper 1 June 2021

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/05/image-8.png)

### Question 8

### Edexcel A-Level Maths Paper 1 June 2021

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/05/image-9.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/05/image-10.png)

### Question 9

### Edexcel A-Level Maths Paper 2 June 2022

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/05/image-11-1.png)

### Question 10

### Edexcel A-Level Maths Paper 1 June 2023

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/05/image-12.png)

### Question 11

### Edexcel A-Level Maths Paper 1 June 2023

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/05/image-13.png)

### Question 12

### Edexcel A-Level Maths Paper 1 June 2024

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/05/image-17-1.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/05/image-18.png)

### Question 13

### Edexcel A-Level Maths Paper 2 June 2024

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/05/image-15.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/05/image-16.png)

### Question 14

### Edexcel A-Level Maths Paper 1 June 2025

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/05/image-20.png)

### Question 15

### Edexcel A-Level Maths Paper 2 June 2025

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/05/image-19.png)

---

### A-Level Maths Tutoring

I offer one-to-one and small group A-Level Maths tutoring for students across the UK and internationally. With 94+ five-star Google reviews and tutoring experience since 2017, I specialise in helping students understand difficult concepts and improve their exam technique.

[A-Level Maths Tutoring](https://www.a-level-maths-tutor.com/a-level-maths-tutor/)

[94+ 5-star Google Reviews](https://www.a-level-maths-tutor.com/reviews/)

[Contact Me](https://www.a-level-maths-tutor.com/contact/)

[Back to A-Level Maths Revision](https://www.a-level-maths-tutor.com/a-level-maths-revision/)
### AS-Level Maths | Differentiation
URL: https://www.a-level-maths-tutor.com/as-level-maths-differentiation/
Last updated: 2026-07-08T16:10:54.000Z
To differentiate $y = ax^n$: multiply the coefficient by the power and subtract one from the power, giving $\\displaystyle\\frac{dy}{dx} = nax^{n-1}$.

## Question 1

Differentiate the following expressions with respect to $x$.

**a)** $y = x^6 - 7x^2$

**b)** $y = 1 - 6x^{\\frac{5}{2}}$

**c)** $y = 2x + 8x^{-2}$

**d)** $y = x^2 - 4x^6$

**e)** $y = 5x^3 - 6x^{\\frac{3}{2}}$

**f)** $y = 9x^{-3} + 7x^{-2}$

**g)** $y = 5 - 5x^{-1}$

Show Answers 

**a)** $\\displaystyle\\frac{dy}{dx} = 6x^5 - 14x$

**b)** $\\displaystyle\\frac{dy}{dx} = -15x^{\\frac{3}{2}}$

**c)** $\\displaystyle\\frac{dy}{dx} = 2 - 16x^{-3}$

**d)** $\\displaystyle\\frac{dy}{dx} = 2x - 24x^5$

**e)** $\\displaystyle\\frac{dy}{dx} = 15x^2 - 9x^{\\frac{1}{2}}$

**f)** $\\displaystyle\\frac{dy}{dx} = -27x^{-4} - 14x^{-3}$

**g)** $\\displaystyle\\frac{dy}{dx} = 5x^{-2}$

To find the **gradient** of a curve at a specific point: differentiate to find $\\displaystyle\\frac{dy}{dx}$, then substitute the given value of $x$.

## Question 2

For each curve, find the gradient at the given value of $x$.

**a)** $y = x^3 - 5x^2 + 2$, where $x = 3$

**b)** $\\displaystyle y = 4x^2 + \\frac{3}{x}$, where $x = 1$

**c)** $y = 2x^4 - 8x$, where $x = 1$

**d)** $y = x^3 + 2x^2 - 5x + 1$, where $x = 2$

**e)** $y = 4x^2 - 3x + 7$, where $x = -2$

Show Answers 

**a)** gradient $= -3$

**b)** gradient $= 5$

**c)** gradient $= 0$

**d)** gradient $= 15$

**e)** gradient $= -19$

To find the **x-coordinate** of a stationary point: solve $\\displaystyle\\frac{dy}{dx} = 0$ for $x$.

To find the **y-coordinate** of a stationary point: substitute $x$ into the equation of the curve.

To determine the **nature** of a stationary point: substitute $x$ into $\\displaystyle\\frac{d^2y}{dx^2}$.

If $\\displaystyle\\frac{d^2y}{dx^2} < 0$ it is a maximum. If $\\displaystyle\\frac{d^2y}{dx^2} > 0$ it is a minimum.

If $\\displaystyle\\frac{d^2y}{dx^2} = 0$ check the gradient on either side.

## Question 3

For each of the following cubic equations find the coordinates of the stationary points and determine their nature.

**a)** $y = x^3 - 3x^2 - 9x + 3$

**b)** $y = x^3 + 12x^2 + 45x + 50$

**c)** $y = 2x^3 - 6x^2 + 12$

**d)** $y = 25 - 24x + 9x^2 - x^3$

Show Answers 

**a)** min$(3,\\,-24)$, max$(-1,\\,8)$

**b)** min$(-3,\\,-4)$, max$(-5,\\,0)$

**c)** min$(2,\\,4)$, max$(0,\\,12)$

**d)** min$(2,\\,5)$, max$(4,\\,9)$

## Question 4

For each of the following equations find the coordinates of the stationary points and determine their nature.

**a)** $\\displaystyle y = x + \\frac{4}{x},\\quad x \\neq 0$

**b)** $\\displaystyle y = x^2 + \\frac{16}{x},\\quad x \\neq 0$

**c)** $y = x - 4\\sqrt{x},\\quad x > 0$

**d)** $\\displaystyle y = 4x^2 + \\frac{1}{x},\\quad x \\neq 0$

Show Answers 

**a)** min$(2,\\,4)$, max$(-2,\\,-4)$

**b)** min$(2,\\,12)$

**c)** min$(4,\\,-4)$

**d)** min$\\!\\left(\\tfrac{1}{2},\\,3\\right)$

A function is **increasing** where $\\displaystyle\\frac{dy}{dx} > 0$, and **decreasing** where $\\displaystyle\\frac{dy}{dx} < 0$.

## Question 5

For each of the following equations find the range of values of $x$ for which $y$ is increasing or decreasing.

**a)** $y = 2x^3 - 3x^2 - 12x + 2$, increasing

**b)** $y = x^3 - 6x^2 + 12$, decreasing

**c)** $y = x^3 - 3x + 8$, increasing

**d)** $y = 1 - 3x^2 - x^3$, decreasing

Show Answers 

**a)** $x < -1$ or $x > 2$

**b)** $0 < x < 4$

**c)** $x < -1$ or $x > 1$

**d)** $x < -2$ or $x > 0$

To find the equation of a **tangent** at a point: use $\\displaystyle\\frac{dy}{dx}$ to find the gradient, substitute $x$ into the curve to find the $y$-coordinate, then use $y = mx + c$.

## Question 6

For each of the following curves find an equation of the tangent at the point whose $x$-coordinate is given.

**a)** $y = x^2 - 9x + 13$, where $x = 6$

**b)** $y = x^4 + x + 1$, where $x = 1$

**c)** $y = 2x^2 + 6x + 7$, where $x = -1$

**d)** $y = 2x^3 - 4x + 5$, where $x = 1$

**e)** $y = 2x^3 - 4x^2 - 3$, where $x = 2$

Show Answers 

**a)** $y = 3x - 23$

**b)** $y = 5x - 2$

**c)** $y = 2x + 5$

**d)** $y = 2x + 1$

**e)** $y = 8x - 19$

To find the equation of a **normal** at a point: use $\\displaystyle\\frac{dy}{dx}$ to find the gradient, take the negative reciprocal, substitute $x$ into the curve to find the $y$-coordinate, then use $y = mx + c$.

## Question 7

For each of the following curves find an equation of the normal at the point whose $x$-coordinate is given.

**a)** $f(x) = x^3 - 4x^2 + 1$, where $x = 2$

**b)** $f(x) = x^3 - 7x^2 + 11x$, where $x = 3$

**c)** $f(x) = 3x^4 - 7x^3 + 5$, where $x = 2$

**d)** $f(x) = \\tfrac{1}{4}x^5 - 18x + 11$, where $x = 2$

Show Answers 

**a)** $4y = x - 30$

**b)** $4y = x - 15$

**c)** $12y + x + 34 = 0$

**d)** $2y + x + 32 = 0$

## Question 8

Find the rate of change of each quantity with respect to the stated variable.

**a)** If $A = \\pi x^2 - 20x$, find the rate of change of $A$ with respect to $x$.

**b)** If $V = x - 2\\pi x^3$, find the rate of change of $V$ with respect to $x$.

**c)** If $P = at^2 - bt$, find the rate of change of $P$ with respect to $t$.

**d)** If $W = 6kh^{\\frac{1}{2}} - h$, find the rate of change of $W$ with respect to $h$.

**e)** If $N = (at + b)^2$, find the rate of change of $N$ with respect to $t$.

Show Answers 

**a)** $\\displaystyle\\frac{dA}{dx} = 2\\pi x - 20$

**b)** $\\displaystyle\\frac{dV}{dx} = 1 - 6\\pi x^2$

**c)** $\\displaystyle\\frac{dP}{dt} = 2at - b$

**d)** $\\displaystyle\\frac{dW}{dh} = 3kh^{-\\frac{1}{2}} - 1$

**e)** $\\displaystyle\\frac{dN}{dt} = 2a^2t + 2ab$

## Question 9

For each of the following equations find the coordinates of the stationary points and determine their nature.

**a)** $\\displaystyle y = \\frac{1}{x} - \\frac{1}{\\sqrt{x}},\\quad x > 0$

**b)** $\\displaystyle y = \\frac{3\\sqrt{x} - 2}{x^{\\frac{3}{2}}},\\quad x > 0$

**c)** $\\displaystyle y = \\sqrt\[3\]{x} + \\frac{27}{x},\\quad x > 0$

**d)** $\\displaystyle y = \\frac{1}{3\\sqrt{x}}\\!\\left(\\frac{2}{x} - 3\\right),\\quad x > 0$

Show Answers 

**a)** min$\\!\\left(4,\\,-\\tfrac{1}{4}\\right)$

**b)** max$(1,\\,1)$

**c)** min$(27,\\,4)$

**d)** min$\\!\\left(2,\\,-\\displaystyle\\frac{\\sqrt{2}}{3}\\right)$

The derivative from first principles is $\\displaystyle f'(x) = \\lim\_{h \\to 0} \\frac{f(x+h) - f(x)}{h}$.

## Question 10

Prove each of the following from first principles.

**a)** The derivative of $4x$ is $4$.

**b)** The derivative of $5x^2$ is $10x$.

**c)** The derivative of $3x^2$ is $6x$.

**d)** The derivative of $x^3$ is $3x^2$.

**e)** The derivative of $2x^3$ is $6x^2$.

---

### A-Level Maths Tutoring

I offer one-to-one and small group A-Level Maths tutoring for students across the UK and internationally. With 94+ five-star Google reviews and tutoring experience since 2017, I specialise in helping students understand difficult concepts and improve their exam technique.

[A-Level Maths Tutoring](https://www.a-level-maths-tutor.com/a-level-maths-tutor/)

[94+ 5-star Google Reviews](https://www.a-level-maths-tutor.com/reviews/)

[Contact Me](https://www.a-level-maths-tutor.com/contact/)

[Back to A-Level Maths Revision](https://www.a-level-maths-tutor.com/a-level-maths-revision/)
### AS-Level Maths | Binomial Expansion
URL: https://www.a-level-maths-tutor.com/as-level-maths-binomial-expansion/
Last updated: 2026-04-28T14:53:48.000Z
## Question 1

$(a + b)^n = a^n + \\dbinom{n}{1}a^{n-1}b + \\cdots + \\dbinom{n}{r}a^{n-r}b^r + \\cdots + b^n$

Find the first four terms in the expansion in ascending powers of $x$ of

(a) $(1 + x)^{10}$

(b) $(1 + 2x)^8$

(c) $\\left(1 - \\tfrac{1}{2}x\\right)^7$

(d) $(2 + 5x)^6$

**Answers**

(a) $1 + 10x + 45x^2 + 120x^3 + \\cdots$

(b) $1 + 16x + 112x^2 + 448x^3 + \\cdots$

(c) $1 - \\tfrac{7}{2}x + \\tfrac{21}{4}x^2 - \\tfrac{35}{8}x^3 + \\cdots$

(d) $1024 + 25600x + 288000x^2 + 1920000x^3 + \\cdots$

## Question 2

Find the coefficient indicated in the following expansions.

(a) $(1 + x)^{20}$, coefficient of $x^3$

(b) $(1 - x)^{14}$, coefficient of $x^4$

(c) $(1 + 4x)^9$, coefficient of $x^2$

(d) $(1 - 3y)^{14}$, coefficient of $y^3$

**Answers**

(a) $1140$ (b) $1001$ (c) $576$ (d) $-9828$

## Question 3

Expand each of the following in ascending powers of $x$ up to and including the term in $x^2$.

(a) $(1 + x^2)(1 - 3x)^{10}$

(b) $(1 - 2x)(1 + x)^8$

(c) $(1 + x + x^2)(1 - x)^6$

(d) $(1 + 3x - x^2)(1 + 2x)^7$

**Answers**

(a) $1 - 30x + 406x^2 + \\cdots$

(b) $1 + 6x + 12x^2 + \\cdots$

(c) $1 - 5x + 10x^2 + \\cdots$

(d) $1 + 17x + 125x^2 + \\cdots$

## Question 4

Find the term independent of $y$ in each of the following expansions.

(a) $\\left(y + \\dfrac{1}{y}\\right)^8$

(b) $\\left(2y - \\dfrac{1}{2y}\\right)^{12}$

(c) $\\left(\\dfrac{1}{y} + y^2\\right)^6$

(d) $\\left(3y - \\dfrac{1}{y^2}\\right)^9$

**Answers**

(a) $70$ (b) $924$ (c) $15$ (d) $-61236$

## Question 5

(a) Expand $(1 + x)^6$ in ascending powers of $x$ up to and including the term in $x^3$, simplifying each coefficient.

(b) By substituting a suitable value of $x$ into your answer to part (a), obtain an estimate for

 (i) $1.02^6$

 (ii) $0.99^6$

giving your answers to 4 decimal places.

**Answers**

(a) $1 + 6x + 15x^2 + 20x^3 + \\cdots$

(b)(i) $1.02^6 \\approx 1.1262$

(b)(ii) $0.99^6 \\approx 0.9415$

## Question 6

(a) Expand $(1 + 2y)^8$ in ascending powers of $y$ up to and including the term in $y^3$, simplifying each coefficient.

(b) By substituting a suitable value of $y$ into your answer to part (a), obtain an estimate for

 (i) $0.98^8$

 (ii) $1.01^8$

giving your answers to 4 decimal places.

**Answers**

(a) $1 + 16y + 112y^2 + 448y^3 + \\cdots$

(b)(i) $0.98^8 \\approx 0.8508$

(b)(ii) $1.01^8 \\approx 1.0829$

---

### A-Level Maths Tutoring

I offer one-to-one and small group A-Level Maths tutoring for students across the UK and internationally. With 94+ five-star Google reviews and tutoring experience since 2017, I specialise in helping students understand difficult concepts and improve their exam technique.

[A-Level Maths Tutoring](https://www.a-level-maths-tutor.com/a-level-maths-tutor/)

[94+ 5-star Google Reviews](https://www.a-level-maths-tutor.com/reviews/)

[Contact Me](https://www.a-level-maths-tutor.com/contact/)

[Back to A-Level Maths Revision](https://www.a-level-maths-tutor.com/a-level-maths-revision/)
### A-Level Maths | Cubics
URL: https://www.a-level-maths-tutor.com/a-level-maths-cubics/
Last updated: 2026-08-15T10:17:52.000Z
Question 1

Divide the cubic by the linear factor, and fully factorise the cubic if possible.

(a) $x^3+2x^2-x-2$ by $x+1$

(b) $x^3+2x^2-9x+2$ by $x-2$

(c) $20+x+3x^2+x^3$ by $x+4$

(d) $2x^3-x^2-4x+3$ by $x-1$

(e) $6x^3-19x^2-73x+90$ by $x-5$

(f) $-x^3+5x^2+10x-8$ by $x+2$

(g) $x^3-2x+21$ by $x+3$

(h) $3x^3+16x^2+72$ by $x+6$

Show Answers 

(a) Quotient $x^2+x-2$; fully factorised: $(x-1)(x+1)(x+2)$

(b) Quotient $x^2+4x-1$ (does not factorise further over rationals)

(c) Quotient $x^2-x+5$ (does not factorise further — no real roots)

(d) Quotient $2x^2+x-3$; fully factorised: $(x-1)^2(2x+3)$

(e) Quotient $6x^2+11x-18$ (does not factorise further over rationals)

(f) Quotient $-x^2+7x-4$ (does not factorise further over rationals)

(g) Quotient $x^2-3x+7$ (does not factorise further — no real roots)

(h) Quotient $3x^2-2x+12$ (does not factorise further — no real roots)

Question 2

Use the factor theorem to determine whether or not

(a) $(x-1)$ is a factor of $x^3+2x^2-2x-1$

(b) $(x+2)$ is a factor of $x^3-5x^2-9x+2$

(c) $(x-3)$ is a factor of $x^3-x^2-14x+27$

(d) $(x+6)$ is a factor of $2x^3+13x^2+2x-24$

(e) $(2x+1)$ is a factor of $2x^3-5x^2+7x-14$

(f) $(3x-2)$ is a factor of $2-17x+25x^2-6x^3$

Show Answers 

(a) $f(1)=0$ — yes, a factor

(b) $f(-2)=-8$ — no, not a factor

(c) $f(3)=3$ — no, not a factor

(d) $f(-6)=0$ — yes, a factor

(e) $f(-\\frac{1}{2})=-19$ — no, not a factor

(f) $f(\\frac{2}{3})=0$ — yes, a factor

Question 3

Use the remainder theorem to find the remainder obtained in dividing

(a) $x^3+4x^2-x+6$ by $x-2$

(b) $x^3-2x^2+7x+1$ by $x+1$

(c) $2x^3+x^2-9x+17$ by $x+5$

(d) $8x^3+4x^2-6x-3$ by $2x-1$

(e) $2x^3-3x^2-20x-7$ by $2x+1$

(f) $3x^3-6x^2+2x-7$ by $3x-2$

Show Answers 

(a) $28$

(b) $-9$

(c) $-163$

(d) $-4$

(e) $2$

(f) $-\\frac{67}{9}$

Question 4

$$f(x) \\equiv x^3-2x^2-11x+12$$

(a) Show that $(x-1)$ is a factor of $f(x)$.

(b) Hence, express $f(x)$ as the product of three linear factors.

Show Answers 

(a) $f(1) = 1-2-11+12 = 0$, so $(x-1)$ is a factor.

(b) Dividing $f(x)$ by $(x-1)$ gives $x^2-x-12$, which factorises as $(x-4)(x+3)$.  
$$f(x) = (x-1)(x-4)(x+3)$$

Question 5

Given that $x=-2$ is a solution to the equation $$g(x)\\equiv x^3+7x^2+7x-6=0$$

(a) express $g(x)$ as the product of a linear factor and a quadratic factor,

(b) find, to 2 decimal places, the other two solutions to the equation $g(x)=0$.

Show Answers 

(a) Dividing $g(x)$ by $(x+2)$ gives $x^2+5x-3$.  
$$g(x) = (x+2)(x^2+5x-3)$$

(b) Solving $x^2+5x-3=0$ by the quadratic formula:  
$$x = \\frac{-5\\pm\\sqrt{25+12}}{2} = \\frac{-5\\pm\\sqrt{37}}{2}$$ $$x \\approx 0.54 \\text{ or } x \\approx -5.54$$

Question 6

By first finding a linear factor, fully factorise $$x^3-2x^2-5x+6$$

Show Answers 

Testing $x=1$: $1-2-5+6=0$, so $(x-1)$ is a factor.

Dividing by $(x-1)$ gives $x^2-x-6 = (x-3)(x+2)$.

$$x^3-2x^2-5x+6 = (x-1)(x-3)(x+2)$$

---

### A-Level Maths Tutoring

I offer one-to-one and small group A-Level Maths tutoring for students across the UK and internationally. With 94+ five-star Google reviews and tutoring experience since 2017, I specialise in helping students understand difficult concepts and improve their exam technique.

[A-Level Maths Tutoring](https://www.a-level-maths-tutor.com/a-level-maths-tutor/)

[94+ 5-star Google Reviews](https://www.a-level-maths-tutor.com/reviews/)

[Contact Me](https://www.a-level-maths-tutor.com/contact/)

[Back to A-Level Maths Revision](https://www.a-level-maths-tutor.com/a-level-maths-revision/)
### Edexcel A-Level Maths Past Papers 2025
URL: https://www.a-level-maths-tutor.com/edexcel-a-level-maths-past-papers/
Last updated: 2026-04-27T11:19:05.000Z
### Edexcel A-Level Maths June 2025

- [Edexcel A-Level Maths Paper 1 June 2025](https://www.a-level-maths-tutor.com/content/files/2026/04/Edexcel-A-Level-Maths-Paper-1-June-2025.pdf) | Mark Scheme | Video Answers
- [Edexcel A-Level Maths Paper 2 June 2025](https://www.a-level-maths-tutor.com/content/files/2026/04/Edexcel-A-Level-Maths-Paper-2-June-2025.pdf) | Mark Scheme | Video Answers
- [Edexcel A-Level Maths Paper 3a June 2025](https://www.a-level-maths-tutor.com/content/files/2026/04/Edexcel-A-Level-Maths-Paper-3a-June-2025.pdf) | Mark Scheme | Video Answers
- [Edexcel A-Level Maths Paper 3b June 2025](https://www.a-level-maths-tutor.com/content/files/2026/04/Edexcel-A-Level-Maths-Paper-3b-June-2025.pdf) | Mark Scheme | Video Answers

### Edexcel A-Level Maths June 2024

- [Edexcel A-Level Maths Paper 1 June 2024](https://www.tootingtutors.co.uk/content/files/2025/03/Edexcel-A-Level-Maths-Paper-1-June-2024-1.pdf?ref=a-level-maths-tutor.com) | Mark Scheme | Video Answers
- [Edexcel A-Level Maths Paper 2 June 2024](https://www.tootingtutors.co.uk/content/files/2025/03/Edexcel-A-Level-Maths-Paper-2-June-2024-1.pdf?ref=a-level-maths-tutor.com) | Mark Scheme | Video Answers
- [Edexcel A-Level Maths Paper 3a June 2024](https://www.tootingtutors.co.uk/content/files/2025/03/Edexcel-A-Level-Maths-Paper-3-Statistics-June-2024-1.pdf?ref=a-level-maths-tutor.com) | Mark Scheme | Video Answers
- [Edexcel A-Level Maths Paper 3b June 2024](https://www.tootingtutors.co.uk/content/files/2025/03/Edexcel-A-Level-Maths-Paper-3-Mechanics-June-2024.pdf?ref=a-level-maths-tutor.com) | Mark Scheme | Video Answers

### Edexcel A-Level Maths June 2023

- [Edexcel A-Level Maths Paper 1 June 2023](https://www.a-level-maths-tutor.com/content/files/2026/04/Edexcel-A-Level-Maths-Paper-1-June-2023.pdf) | Mark Scheme | Video Answers
- [Edexcel A-Level Maths Paper 2 June 2023](https://www.a-level-maths-tutor.com/content/files/2026/04/Edexcel-A-Level-Maths-Paper-2-June-2023.pdf) | Mark Scheme | Video Answers
- [Edexcel A-Level Maths Paper 3a June 2024](https://www.a-level-maths-tutor.com/content/files/2026/04/Edexcel-A-Level-Maths-Paper-3a-June-2023.pdf) | Mark Scheme | Video Answers
- [Edexcel A-Level Maths Paper 3b June 2024](https://www.a-level-maths-tutor.com/content/files/2026/04/Edexcel-A-Level-Maths-Paper-3b-June-2023.pdf) | Mark Scheme | Video Answers

### Edexcel A-Level Maths June 2022

- Edexcel A-Level Maths Paper 1 June 2022 | Mark Scheme | Video Answers
- Edexcel A-Level Maths Paper 2 June 2022 | Mark Scheme | Video Answers
- Edexcel A-Level Maths Paper 3 June 2022 | Mark Scheme | Video Answers

### Edexcel A-Level Maths June 2021

- Edexcel A-Level Maths Paper 1 June 2021 | Mark Scheme | Video Answers
- Edexcel A-Level Maths Paper 2 June 2021 | Mark Scheme | Video Answers
- Edexcel A-Level Maths Paper 3 June 2021 | Mark Scheme | Video Answers

### Edexcel A-Level Maths June 2020

- Edexcel A-Level Maths Paper 1 June 2020 | Mark Scheme | Video Answers
- Edexcel A-Level Maths Paper 2 June 2020 | Mark Scheme | Video Answers
- Edexcel A-Level Maths Paper 3 June 2020 | Mark Scheme | Video Answers

### Edexcel A-Level Maths June 2019

- Edexcel A-Level Maths Paper 1 June 2019 | Mark Scheme | Video Answers
- Edexcel A-Level Maths Paper 2 June 2019 | Mark Scheme | Video Answers
- Edexcel A-Level Maths Paper 3 June 2019 | Mark Scheme | Video Answers

### Edexcel A-Level Maths June 2018

- Edexcel A-Level Maths Paper 1 June 2018 | Mark Scheme | Video Answers
- Edexcel A-Level Maths Paper 2 June 2018 | Mark Scheme | Video Answers
- Edexcel A-Level Maths Paper 3 June 2018 | Mark Scheme | Video Answers

---

### A-Level Maths Tutoring

I offer one-to-one and small group A-Level Maths tutoring for students across the UK and internationally. With 94+ five-star Google reviews and tutoring experience since 2017, I specialise in helping students understand difficult concepts and improve their exam technique.

[A-Level Maths Tutoring](https://www.a-level-maths-tutor.com/a-level-maths-tutor/)

[94+ 5-star Google Reviews](https://www.a-level-maths-tutor.com/reviews/)

[Contact Me](https://www.a-level-maths-tutor.com/contact/)

[Back to A-Level Maths Revision](https://www.a-level-maths-tutor.com/a-level-maths-revision/)
### PDF Files - Edexcel A-Level Maths Past Papers
URL: https://www.a-level-maths-tutor.com/pdf-files/
Last updated: 2026-05-06T14:36:06.000Z
[Edexcel A-Level Maths Paper 1 June 2025Edexcel A-Level Maths Paper 1 June 2025.pdf1 MBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/04/Edexcel-A-Level-Maths-Paper-1-June-2025.pdf "Download")

[Edexcel A-Level Maths Paper 1 June 2025 MSEdexcel A-Level Maths Paper 1 June 2025 MS.pdf1 MBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/04/Edexcel-A-Level-Maths-Paper-1-June-2025-MS.pdf "Download")

[Edexcel A-Level Maths Paper 2 June 2025Edexcel A-Level Maths Paper 2 June 2025.pdf940 KBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/04/Edexcel-A-Level-Maths-Paper-2-June-2025.pdf "Download")

[Edexcel A-Level Maths Paper 2 June 2025 MSEdexcel A-Level Maths Paper 2 June 2025 MS.pdf2 MBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/04/Edexcel-A-Level-Maths-Paper-2-June-2025-MS.pdf "Download")

[Edexcel A-Level Maths Paper 3a June 2025Edexcel A-Level Maths Paper 3a June 2025.pdf302 KBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/04/Edexcel-A-Level-Maths-Paper-3a-June-2025.pdf "Download")

[Edexcel A-Level Maths Paper 3a June 2025 MSEdexcel A-Level Maths Paper 3a June 2025 MS.pdf571 KBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/04/Edexcel-A-Level-Maths-Paper-3a-June-2025-MS.pdf "Download")

[Edexcel A-Level Maths Paper 3b June 2025Edexcel A-Level Maths Paper 3b June 2025.pdf318 KBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/04/Edexcel-A-Level-Maths-Paper-3b-June-2025.pdf "Download")

[Edexcel A-Level Maths Paper 3b June 2025 MSEdexcel A-Level Maths Paper 3b June 2025 MS.pdf437 KBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/04/Edexcel-A-Level-Maths-Paper-3b-June-2025-MS.pdf "Download")

[Edexcel A-Level Maths Paper 1 June 2023 MSEdexcel A-Level Maths Paper 1 June 2023 MS.pdf797 KBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/04/Edexcel-A-Level-Maths-Paper-1-June-2023-MS.pdf "Download")

[Edexcel A-Level Maths Paper 1 June 2023Edexcel A-Level Maths Paper 1 June 2023.pdf710 KBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/04/Edexcel-A-Level-Maths-Paper-1-June-2023.pdf "Download")

[Edexcel A-Level Maths Paper 2 June 2023 MSEdexcel A-Level Maths Paper 2 June 2023 MS.pdf789 KBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/04/Edexcel-A-Level-Maths-Paper-2-June-2023-MS-1.pdf "Download")

[Edexcel A-Level Maths Paper 2 June 2023Edexcel A-Level Maths Paper 2 June 2023.pdf872 KBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/04/Edexcel-A-Level-Maths-Paper-2-June-2023.pdf "Download")

[Edexcel A-Level Maths Paper 3a June 2023 MSEdexcel A-Level Maths Paper 3a June 2023 MS.pdf422 KBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/04/Edexcel-A-Level-Maths-Paper-3a-June-2023-MS.pdf "Download")

[Edexcel A-Level Maths Paper 3a June 2023Edexcel A-Level Maths Paper 3a June 2023.pdf460 KBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/04/Edexcel-A-Level-Maths-Paper-3a-June-2023.pdf "Download")

[Edexcel A-Level Maths Paper 3b June 2023 MSEdexcel A-Level Maths Paper 3b June 2023 MS.pdf545 KBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/04/Edexcel-A-Level-Maths-Paper-3b-June-2023-MS.pdf "Download")

[Edexcel A-Level Maths Paper 3b June 2023Edexcel A-Level Maths Paper 3b June 2023.pdf571 KBdownload-circle](https://www.a-level-maths-tutor.com/content/files/2026/04/Edexcel-A-Level-Maths-Paper-3b-June-2023.pdf "Download")
### OCR MEI A-Level Maths | Moments
URL: https://www.a-level-maths-tutor.com/ocr-mei-a-level-maths-moments/
Last updated: 2026-04-24T16:25:30.000Z
### Question 1

### OCR MEI A-Level Maths Paper 1 June 2018

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/CleanShot-2026-04-24-at-17.25.00@2x.png)

### Question 2

### OCR MEI A-Level Maths Paper 1 June 2019

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/CleanShot-2026-04-24-at-17.23.42@2x.png)

### Question 3

### OCR MEI A-Level Maths Paper 1 June 2020

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/CleanShot-2026-04-24-at-17.23.11@2x.png)

### Question 4

### OCR MEI A-Level Maths Paper 1 June 2021

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/CleanShot-2026-04-24-at-17.22.30@2x.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/CleanShot-2026-04-24-at-17.22.34@2x.png)

### Question 5

### OCR MEI A-Level Maths Paper 1 June 2022

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/CleanShot-2026-04-24-at-17.21.24@2x.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/CleanShot-2026-04-24-at-17.21.28@2x.png)

### Question 6

### OCR MEI A-Level Maths Paper 1 June 2023

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/CleanShot-2026-04-24-at-17.19.24@2x.png)

### Question 7

### OCR MEI A-Level Maths Paper 1 June 2024

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/CleanShot-2026-04-24-at-17.18.26@2x.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/CleanShot-2026-04-24-at-17.18.31@2x.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/CleanShot-2026-04-24-at-17.18.35@2x.png)

### Question 8

### OCR MEI A-Level Maths Paper 1 June 2025
### AS-Level Maths | Trigonometry
URL: https://www.a-level-maths-tutor.com/as-level-maths-trigonometry/
Last updated: 2026-06-25T10:33:23.000Z
**Worked Example**

$\\sin x° = 0.4$, $0 \\leq x \\leq 360°$

$x = \\sin^{-1}(0.4)$

$x = 23.6°, 156.4°$

## Question 1

Solve each equation for $x$ in the interval $0 \\leq x \\leq 360°$. Give your answers to 1 decimal place where appropriate.

**a)** $\\sin x° = 0.27$

**b)** $\\sin x° = 0.813$

**c)** $\\sin x° = 0.6$

**d)** $\\sin x° = 0.95$

Show Answers 

**a)** $x = 15.7°, 164.3°$ **b)** $x = 54.4°, 125.6°$ **c)** $x = 36.9°, 143.1°$ **d)** $x = 71.8°, 108.2°$

**Worked Example**

$\\cos x° = 0.6$, $0 \\leq x \\leq 360°$

$x = \\cos^{-1}(0.6)$

$x = 53.1°, 306.9°$

## Question 2

Solve each equation for $x$ in the interval $0 \\leq x \\leq 360°$. Give your answers to 1 decimal place where appropriate.

**a)** $\\cos x° = 0.185$

**b)** $\\cos x° = 0.4$

**c)** $\\cos x° = 0.7$

**d)** $\\cos x° = 0.92$

Show Answers 

**a)** $x = 79.3°, 280.7°$ **b)** $x = 66.4°, 293.6°$ **c)** $x = 45.6°, 314.4°$ **d)** $x = 23.1°, 336.9°$

**Worked Example**

$\\tan x° = 0.8$, $0 \\leq x \\leq 360°$

$x = \\tan^{-1}(0.8)$

$x = 38.7°, 218.7°$

## Question 3

Solve each equation for $x$ in the interval $0 \\leq x \\leq 360°$. Give your answers to 1 decimal place where appropriate.

**a)** $\\tan x° = 0.1$

**b)** $\\tan x° = 1.6$

**c)** $\\tan x° = 0.7$

**d)** $\\tan x° = 3.4$

Show Answers 

**a)** $x = 5.7°, 185.7°$ **b)** $x = 58.0°, 238.0°$ **c)** $x = 35.0°, 215.0°$ **d)** $x = 73.6°, 253.6°$

After finding two consecutive solutions, keep adding or subtracting $360°$ to each solution to find more solutions.

e.g. $\\ldots, -330°, -210°, 30°, 150°, 390°, 510°, \\ldots$

## Question 4

Solve each equation for $x$ in the interval $0 \\leq x \\leq 720°$. Give your answers to 1 decimal place where appropriate.

**a)** $\\sin x° = 0.3$

**b)** $\\sin x° = 0.85$

**c)** $\\sin x° = -0.45$

**d)** $\\sin x° = -0.7$

Show Answers 

**a)** $x = 17.5°, 162.5°, 377.5°, 522.5°$

**b)** $x = 58.2°, 121.8°, 418.2°, 481.8°$

**c)** $x = 206.7°, 333.3°, 566.7°, 693.3°$

**d)** $x = 224.4°, 315.6°, 584.4°, 675.6°$

## Question 5

Solve each equation for $x$ in the interval $0 \\leq x \\leq 720°$. Give your answers to 1 decimal place where appropriate.

**a)** $\\cos x° = -0.39$

**b)** $\\cos x° = -0.636$

**c)** $\\cos x° = 0.55$

**d)** $\\cos x° = -0.8$

Show Answers 

**a)** $x = 113.0°, 247.1°, 473.0°, 607.1°$

**b)** $x = 129.5°, 230.5°, 489.5°, 590.5°$

**c)** $x = 56.6°, 303.4°, 416.6°, 663.4°$

**d)** $x = 143.1°, 216.9°, 503.1°, 576.9°$

## Question 6

Solve each equation for $x$ in the interval $0 \\leq x \\leq 720°$. Give your answers to 1 decimal place where appropriate.

**a)** $\\tan x° = -0.7$

**b)** $\\tan x° = -3.4$

**c)** $\\tan x° = 2.1$

**d)** $\\tan x° = -1.9$

Show Answers 

**a)** $x = 145.0°, 325.0°, 505.0°, 685.0°$

**b)** $x = 106.4°, 286.4°, 466.4°, 646.4°$

**c)** $x = 64.5°, 244.5°, 424.5°, 604.5°$

**d)** $x = 117.8°, 297.8°, 477.8°, 657.8°$

**Adjusting the Range**

If the original range is $0° \\leq x \\leq 360°$, this changes depending on what's inside the brackets:

$\\sin(x-30)°$: range becomes $-30° \\leq x-30 \\leq 330°$

$\\sin(x+45)°$: range becomes $45° \\leq x+45 \\leq 405°$

$\\sin 2x°$: range becomes $0° \\leq 2x \\leq 720°$

$\\sin 3x°$: range becomes $0° \\leq 3x \\leq 1080°$

**Worked Example**

$\\sin(x-30)° = 0.5$, $0 \\leq x \\leq 360°$

$x - 30 = \\sin^{-1}(0.5)$

$x - 30 = 30°, 150°$

$x = 60°, 180°$

## Question 7

Solve each equation for $x$ in the interval $0 \\leq x \\leq 360°$. Give your answers to 1 decimal place where appropriate.

**a)** $\\sin(x-30)° = 0.5$

**b)** $\\sin(x-45)° = 0.6$

**c)** $\\sin(x-60)° = -0.4$

**d)** $\\sin(x-20)° = -0.75$

Show Answers 

**a)** $x = 60°, 180°$ **b)** $x = 81.9°, 188.1°$ **c)** $x = 36.4°, 263.6°$ **d)** $x = 248.6°, 331.4°$

## Question 8

Solve each equation for $x$ in the interval $0 \\leq x \\leq 360°$. Give your answers to 1 decimal place where appropriate.

**a)** $\\sin(x+30)° = 0.7$

**b)** $\\sin(x+40)° = 0.3$

**c)** $\\sin(x+50)° = -0.6$

**d)** $\\sin(x+25)° = -0.45$

Show Answers 

**a)** $x = 14.4°, 105.6°$ **b)** $x = 122.5°, 337.5°$ **c)** $x = 166.9°, 273.1°$ **d)** $x = 181.7°, 308.3°$

## Question 9

Solve each equation for $x$ in the interval $0 \\leq x \\leq 360°$. Give your answers to 1 decimal place where appropriate.

**a)** $\\sin 2x° = 0.5$

**b)** $\\sin 2x° = -0.7$

**c)** $\\sin 3x° = 0.6$

**d)** $\\sin 3x° = -0.3$

Show Answers 

**a)** $x = 15°, 75°, 195°, 255°$

**b)** $x = 112.2°, 157.8°, 292.2°, 337.8°$

**c)** $x = 12.3°, 47.7°, 132.3°, 167.7°, 252.3°, 287.7°$

**d)** $x = 65.8°, 114.2°, 185.8°, 234.2°, 305.8°, 354.2°$

## Question 10

Solve each equation for $x$ in the interval $0 \\leq x \\leq 360°$. Give your answers to 1 decimal place where appropriate.

**a)** $\\sin \\tfrac{1}{2}x° = 0.5$

**b)** $\\sin \\tfrac{1}{2}x° = 0.8$

**c)** $\\sin \\tfrac{1}{3}x° = 0.6$

**d)** $\\sin \\tfrac{1}{3}x° = 0.85$

Show Answers 

**a)** $x = 60°, 300°$ **b)** $x = 106.3°, 253.7°$ **c)** $x = 110.6°$ **d)** $x = 174.6°$

$\\cos(x+30)° = 0.5$, $0 \\leq x \\leq 360°$

$x + 30 = 60°, 300°$

$x = 30°, 270°$

## Question 11

Solve each equation for $x$ in the interval $0 \\leq x \\leq 360°$. Give your answers to 1 decimal place where appropriate.

**a)** $\\cos(x-30)° = 0.5$

**b)** $\\cos(x-45)° = -0.6$

**c)** $\\cos(x-60)° = 0.4$

**d)** $\\cos(x-20)° = -0.75$

Show Answers 

**a)** $x = 90°, 330°$ **b)** $x = 171.9°, 278.1°$ **c)** $x = 126.4°, 353.6°$ **d)** $x = 158.6°, 241.4°$

## Question 12

Solve each equation for $x$ in the interval $0 \\leq x \\leq 360°$. Give your answers to 1 decimal place where appropriate.

**a)** $\\cos(x+30)° = 0.5$

**b)** $\\cos(x+40)° = -0.3$

**c)** $\\cos(x+50)° = 0.6$

**d)** $\\cos(x+25)° = -0.45$

Show Answers 

**a)** $x = 30°, 270°$ **b)** $x = 67.5°, 212.5°$ **c)** $x = 3.1°, 256.9°$ **d)** $x = 91.7°, 218.3°$

## Question 13

Solve each equation for $x$ in the interval $0 \\leq x \\leq 360°$. Give your answers to 1 decimal place where appropriate.

**a)** $\\cos 2x° = 0.64$

**b)** $\\cos 2x° = -0.415$

**c)** $\\cos 3x° = 0.5$

**d)** $\\cos 3x° = -0.2$

Show Answers 

**a)** $x = 25.1°, 154.9°, 205.1°, 334.9°$

**b)** $x = 57.3°, 122.7°, 237.3°, 302.7°$

**c)** $x = 20°, 100°, 140°, 220°, 260°, 340°$

**d)** $x = 33.9°, 86.2°, 153.9°, 206.2°, 273.9°, 326.2°$

## Question 14

Solve each equation for $x$ in the interval $0 \\leq x \\leq 360°$. Give your answers to 1 decimal place where appropriate.

**a)** $\\cos \\tfrac{1}{2}x° = 0.5$

**b)** $\\cos \\tfrac{1}{2}x° = -0.6$

**c)** $\\cos \\tfrac{1}{3}x° = 0.7$

**d)** $\\cos \\tfrac{1}{3}x° = -0.4$

Show Answers 

**a)** $x = 120°$ **b)** $x = 253.7°$ **c)** $x = 136.7°$ **d)** $x = 340.7°$

$\\tan(x-30)° = 1$, $0 \\leq x \\leq 360°$

$x - 30 = 45°, 225°$

$x = 75°, 255°$

## Question 15

Solve each equation for $x$ in the interval $0 \\leq x \\leq 360°$. Give your answers to 1 decimal place where appropriate.

**a)** $\\tan(x-30)° = 1$

**b)** $\\tan(x-45)° = -1.26$

**c)** $\\tan(x-60)° = 0.5$

**d)** $\\tan(x-20)° = -2.74$

Show Answers 

**a)** $x = 75°, 255°$ **b)** $x = 173.4°, 353.4°$ **c)** $x = 86.6°, 266.6°$ **d)** $x = 130.1°, 310.1°$

## Question 16

Solve each equation for $x$ in the interval $0 \\leq x \\leq 360°$. Give your answers to 1 decimal place where appropriate.

**a)** $\\tan(x+30)° = 1$

**b)** $\\tan(x+40)° = -1.26$

**c)** $\\tan(x+50)° = 0.591$

**d)** $\\tan(x+25)° = -2.74$

Show Answers 

**a)** $x = 15°, 195°$ **b)** $x = 88.4°, 268.4°$ **c)** $x = 160.6°, 340.6°$ **d)** $x = 85.1°, 265.1°$

## Question 17

Solve each equation for $x$ in the interval $0 \\leq x \\leq 360°$. Give your answers to 1 decimal place where appropriate.

**a)** $\\tan 2x° = -2.74$

**b)** $\\tan 2x° = 0.591$

**c)** $\\tan 3x° = 1$

**d)** $\\tan 3x° = -1.26$

Show Answers 

**a)** $x = 55.0°, 145.0°, 235.0°, 325.0°$

**b)** $x = 15.3°, 105.3°, 195.3°, 285.3°$

**c)** $x = 15°, 75°, 135°, 195°, 255°, 315°$

**d)** $x = 42.8°, 102.8°, 162.8°, 222.8°, 282.8°, 342.8°$

## Question 18

Solve each equation for $x$ in the interval $0 \\leq x \\leq 360°$. Give your answers to 1 decimal place where appropriate.

**a)** $\\tan \\tfrac{1}{2}x° = 1$

**b)** $\\tan \\tfrac{1}{2}x° = -1.26$

**c)** $\\tan \\tfrac{1}{3}x° = 0.591$

**d)** $\\tan \\tfrac{1}{3}x° = -2.74$

Show Answers 

**a)** $x = 90°$ **b)** $x = 256.9°$ **c)** $x = 91.7°$ **d)** $x = 330.2°$

$2\\sin^2\\theta° - 3\\sin\\theta° + 1 = 0$, $0 \\leq \\theta \\leq 360°$

$(2\\sin\\theta°-1)(\\sin\\theta°-1) = 0$

$\\sin\\theta° = \\tfrac{1}{2}, 1$

$\\theta = 30°, 90°, 150°$

## Question 19

Solve each equation for $\\theta$ in the interval $0 \\leq \\theta \\leq 360°$. Give your answers to 1 decimal place where appropriate.

**a)** $\\sin^2\\theta° = 0.75$

**b)** $1 - \\tan^2\\theta° = 0$

**c)** $2\\cos^2\\theta° + \\cos\\theta° = 0$

**d)** $\\sin\\theta°(4\\cos\\theta° - 1) = 0$

Show Answers 

**a)** $\\theta = 60°, 120°, 240°, 300°$ **b)** $\\theta = 45°, 135°, 225°, 315°$

**c)** $\\theta = 90°, 120°, 240°, 270°$ **d)** $\\theta = 0°, 75.5°, 180°, 284.5°, 360°$

$\\sin^2\\theta + \\cos^2\\theta = 1$

$\\tan\\theta = \\dfrac{\\sin\\theta}{\\cos\\theta}$

$2\\sin^2 x - 5\\cos x + 1 = 0$, $0 \\leq x \\leq 360°$

$2(1-\\cos^2 x) - 5\\cos x + 1 = 0$

$2\\cos^2 x + 5\\cos x - 3 = 0$

$(2\\cos x - 1)(\\cos x + 3) = 0$

$\\cos x = \\tfrac{1}{2}$

$x = 60°, 300°$

## Question 20

Solve each equation for $x$ in the interval $0 \\leq x \\leq 360°$. Give your answers to 1 decimal place where appropriate.

**a)** $2\\sin^2 x - 5\\cos x + 1 = 0$

**b)** $5\\sin^2 x = 19\\cos x + 1$

**c)** $3\\sin^2 x = 8 + 16\\cos x$

**d)** $\\tan^2 x - \\tan x = 6$

**e)** $6\\cos^2 x - \\cos x - 2 = 0$

Show Answers 

**a)** $x = 60°, 300°$ **b)** $x \\approx 78.5°, 281.5°$ **c)** $x \\approx 109.5°, 250.5°$

**d)** $x \\approx 71.6°, 116.6°, 251.6°, 296.6°$ **e)** $x \\approx 48.2°, 120°, 240°, 311.8°$

$3\\cos^2 x - \\sin^2 x = 2$, $0 \\leq x \\leq 360°$

$3\\cos^2 x - (1-\\cos^2 x) = 2$

$4\\cos^2 x = 3$

$\\cos x = \\pm\\dfrac{\\sqrt{3}}{2}$

$x = 30°, 150°, 210°, 330°$

## Question 21

Solve each equation for $x$ in the interval $0 \\leq x \\leq 360°$. Give your answers to 1 decimal place where appropriate.

**a)** $3\\cos x = 8\\tan x$

**b)** $2\\tan x \\sin x = 3$

**c)** $2\\cos x = 3\\tan x$

**d)** $3\\sin x - 2\\tan x = 0$

**e)** $\\cos x = 3\\tan x$

Show Answers 

**a)** $x \\approx 19.5°, 160.5°$ **b)** $x = 60°, 300°$ **c)** $x = 30°, 150°$

**d)** $x = 0°, 48.2°, 180°, 311.8°, 360°$ **e)** $x \\approx 17.6°, 162.4°$

## Question 22

Solve each of the following trigonometric equations in the range given.

**a)** $4\\tan^2\\theta\\cos\\theta = 15$ $0 \\leq \\theta < 360°$

**b)** $\\dfrac{3 + \\sin^2\\theta}{\\cos\\theta - 2} = 3\\cos\\theta$ $0 \\leq \\theta < 360°$

**c)** $2\\sin x = \\tan x$ $0 \\leq x < 360°$

**d)** $\\tfrac{1}{2}\\tan x - \\sin x = 0$ $0 \\leq x < 360°$

**e)** $\\dfrac{\\sin x - \\cos x}{\\cos x} = 2$ $0 \\leq x < 360°$

**f)** $4\\tan y\\sin y\\cos y + 4\\tan y\\cos y + 1 = 0$ $0 \\leq y < 360°$

Show Answers 

**a)** $\\theta \\approx 75.5°, 284.5°$ **b)** $\\theta = 120°, 240°$ **c)** $x = 0°, 60°, 180°, 300°$

**d)** $x = 0°, 60°, 180°, 300°$ **e)** $x \\approx 71.6°, 251.6°$ **f)** $y = 210°, 330°$

---

### A-Level Maths Tutoring

I offer one-to-one and small group A-Level Maths tutoring for students across the UK and internationally. With 94+ five-star Google reviews and tutoring experience since 2017, I specialise in helping students understand difficult concepts and improve their exam technique.

[A-Level Maths Tutoring](https://www.a-level-maths-tutor.com/a-level-maths-tutor/)

[94+ 5-star Google Reviews](https://www.a-level-maths-tutor.com/reviews/)

[Contact Me](https://www.a-level-maths-tutor.com/contact/)

[Back to A-Level Maths Revision](https://www.a-level-maths-tutor.com/a-level-maths-revision/)
### A-Level Maths | Integration
URL: https://www.a-level-maths-tutor.com/a-level-maths-integration/
Last updated: 2026-04-23T11:46:16.000Z
## Key Formulae

$\\displaystyle\\int e^{kx}\\,dx = \\frac{1}{k}e^{kx} + c$

$\\displaystyle\\int \\sin(kx)\\,dx = -\\frac{1}{k}\\cos(kx) + c$

$\\displaystyle\\int \\cos(kx)\\,dx = \\frac{1}{k}\\sin(kx) + c$

$\\displaystyle\\int \\frac{1}{kx+c}\\,dx = \\frac{1}{k}\\ln|kx+c| + C$

## Question 1 — Integrating Trig Functions

(a) $\\displaystyle\\int 5\\sin 2x\\,dx$

(b) $\\displaystyle\\int 3\\cos 6x\\,dx$

(c) $\\displaystyle\\int 5\\sin x - 4\\cos 2x\\,dx$

(d) $\\displaystyle\\int 5\\cos 2x - 3\\sin 5x\\,dx$

(e) $\\displaystyle\\int 15\\cos 3x - 15\\sin 5x\\,dx$

(f) $\\displaystyle\\int \\sin 8x - \\tfrac{1}{2}\\cos 3x\\,dx$

(g) $\\displaystyle\\int 2\\cos\\tfrac{1}{3}x + 3\\sin\\tfrac{1}{2}x\\,dx$

(h) $\\displaystyle\\int 7\\cos 3x - 3\\cos 7x\\,dx$

(i) $\\displaystyle\\int \\tfrac{1}{2}\\sin 5x - \\tfrac{1}{2}\\sin\\tfrac{1}{4}x\\,dx$

(j) $\\displaystyle\\int 10\\cos 2x - \\sin\\tfrac{x}{4} + 9\\sin\\tfrac{3x}{2}\\,dx$

## Question 2 — Integrating Exponential Functions

(a) $\\displaystyle\\int e^x + e^{2x} + e^{-x}\\,dx$

(b) $\\displaystyle\\int 4e^{2x} - e^{-2x} + 3e^{3x}\\,dx$

(c) $\\displaystyle\\int 2e^{4x} - e^{-3x} + \\tfrac{1}{2}e^{2x}\\,dx$

(d) $\\displaystyle\\int 4e^{-2x} - 2e^{-4x} + \\tfrac{1}{2}e^{3x}\\,dx$

(e) $\\displaystyle\\int 5e^{\\frac{1}{2}x} - \\tfrac{1}{2}e^{-\\frac{1}{2}x} + \\tfrac{3}{4}e^{\\frac{1}{4}x}\\,dx$

(f) $\\displaystyle\\int e^x + e^{2x} + e^{3x}\\,dx$

(g) $\\displaystyle\\int 6e^{2x} + e^{-2x} - 3e^{-x}\\,dx$

(h) $\\displaystyle\\int 3e^{2x} - 2e^{-2x} + \\tfrac{1}{2}e^{4x}\\,dx$

(i) $\\displaystyle\\int 6e^{-3x} - 2e^{-2x} + \\tfrac{1}{3}e^{2x}\\,dx$

(j) $\\displaystyle\\int 3e^{\\frac{1}{2}x} - \\tfrac{1}{2}e^{-\\frac{1}{4}x} + 3e^{\\frac{3}{2}x}\\,dx$

## Question 3 — Integrating Logarithmic Forms

(a) $\\displaystyle\\int \\frac{1}{x+1} + \\frac{1}{2x-1} + \\frac{1}{2-x}\\,dx$

(b) $\\displaystyle\\int \\frac{4}{2x+1} + \\frac{2}{2x-1} + \\frac{1}{1-3x}\\,dx$

(c) $\\displaystyle\\int \\frac{6}{2x-1} + \\frac{4}{3x-1} - \\frac{2}{1-4x} + \\frac{1}{2x}\\,dx$

(d) $\\displaystyle\\int \\frac{2}{3x-2} + \\frac{2}{5x-1} - \\frac{2}{1-x} + \\frac{4}{3x}\\,dx$

(e) $\\displaystyle\\int \\frac{4}{2x-3} - \\frac{2}{1-2x} - \\frac{1}{1+2x} + \\frac{1}{2x}\\,dx$

(f) $\\displaystyle\\int \\frac{1}{x+2} + \\frac{1}{3x-1} + \\frac{1}{1-x}\\,dx$

(g) $\\displaystyle\\int \\frac{6}{3x+1} + \\frac{4}{2x-1} + \\frac{1}{1-4x}\\,dx$

(h) $\\displaystyle\\int \\frac{8}{4x-1} + \\frac{5}{2x-1} - \\frac{2}{1-3x} + \\frac{4}{x}\\,dx$

(i) $\\displaystyle\\int \\frac{9}{3x-1} + \\frac{2}{6x-1} - \\frac{2}{1-2x} + \\frac{1}{2x}\\,dx$

(j) $\\displaystyle\\int \\frac{3}{5x-3} - \\frac{2}{x} - \\frac{1}{1+3x} + \\frac{9}{2x}\\,dx$

## Question 4 — Reverse Chain Rule

Integrate with respect to $x$:

(a) $(x-2)^7$

(b) $(2x+5)^3$

(c) $6(1+3x)^4$

(d) $\\left(\\tfrac{1}{4}x-2\\right)^5$

(e) $(8-5x)^4$

(f) $\\dfrac{1}{(x+7)^2}$

(g) $\\dfrac{8}{(4x-3)^5}$

(h) $\\dfrac{1}{2(5-3x)^3}$

## Question 5 — Integration by Substitution (1 step)

Showing your working in full, use the given substitution to find:

(a) $\\displaystyle\\int 2x(x^2-1)^3\\,dx$ $u = x^2-1$

(b) $\\displaystyle\\int \\sin^4 x\\cos x\\,dx$ $u = \\sin x$

(c) $\\displaystyle\\int 3x^2(2+x^3)^2\\,dx$ $u = 2+x^3$

(d) $\\displaystyle\\int 2xe^{x^2}\\,dx$ $u = x^2$

(e) $\\displaystyle\\int \\frac{x}{(x^2+3)^4}\\,dx$ $u = x^2+3$

(f) $\\displaystyle\\int \\sin 2x\\cos^3 2x\\,dx$ $u = \\cos 2x$

(g) $\\displaystyle\\int \\frac{3x}{x^2-2}\\,dx$ $u = x^2-2$

(h) $\\displaystyle\\int x\\sqrt{1-x^2}\\,dx$ $u = 1-x^2$

(i) $\\displaystyle\\int \\sec^3 x\\tan x\\,dx$ $u = \\sec x$

(j) $\\displaystyle\\int (x+1)(x^2+2x)^3\\,dx$ $u = x^2+2x$

## Question 6 — Integration by Substitution (2 steps)

Using the given substitution, find:

(a) $\\displaystyle\\int x(2x-1)^4\\,dx$ $u = 2x-1$

(b) $\\displaystyle\\int x\\sqrt{1-x}\\,dx$ $u^2 = 1-x$

(c) $\\displaystyle\\int \\frac{1}{(1-x^2)^{3/2}}\\,dx$ $x = \\sin u$

(d) $\\displaystyle\\int \\frac{1}{\\sqrt{x}-1}\\,dx$ $x = u^2$

(e) $\\displaystyle\\int (x+1)(2x+3)^3\\,dx$ $u = 2x+3$

(f) $\\displaystyle\\int \\frac{x^2}{\\sqrt{x-2}}\\,dx$ $u^2 = x-2$

## Question 7 — Integration by Substitution (with Limits)

Using the given substitution, evaluate:

(a) $\\displaystyle\\int\_1^2 x(x^2-3)^3\\,dx$ $u = x^2-3$

(b) $\\displaystyle\\int\_0^{\\pi/6} \\sin^3 x\\cos x\\,dx$ $u = \\sin x$

## Question 8 — Integrating with Partial Fractions

1\. $\\displaystyle\\int \\frac{17-4x}{(x-2)(x+1)}\\,dx$

2\. $\\displaystyle\\int \\frac{2-x}{(x+1)(2x-1)}\\,dx$

3\. $\\displaystyle\\int \\frac{4}{(x-2)(2-3x)}\\,dx$

4\. $\\displaystyle\\int \\frac{5x-7}{(x-1)(5x-3)}\\,dx$

5\. $\\displaystyle\\int \\frac{18x-1}{(2x+1)(3x-1)}\\,dx$

## Question 9 — Integration by Parts

$$\\int u\\,v' = uv - \\int v\\,u'$$

Use the **LATE** rule: Logarithmic → Algebraic → Trigonometric → Exponential. Whatever comes first is $u$; whatever comes last is $v'$.

Use integration by parts to find:

(a) $\\displaystyle\\int xe^x\\,dx$

(b) $\\displaystyle\\int 4x\\sin x\\,dx$

(c) $\\displaystyle\\int x\\cos 2x\\,dx$

(d) $\\displaystyle\\int x\\sqrt{x+1}\\,dx$

(e) $\\displaystyle\\int \\frac{x}{e^{3x}}\\,dx$

(f) $\\displaystyle\\int x\\sec^2 x\\,dx$

## Question 10 — Integration by Parts Twice

Find:

(a) $\\displaystyle\\int x^2\\sin x\\,dx$

(b) $\\displaystyle\\int x^2 e^{3x}\\,dx$

(c) $\\displaystyle\\int e^{-x}\\cos 2x\\,dx$

## Question 11 — Integration by Parts with Logarithms

Find:

(a) $\\displaystyle\\int \\ln 2x\\,dx$

(b) $\\displaystyle\\int 3x\\ln x\\,dx$

(c) $\\displaystyle\\int (\\ln x)^2\\,dx$

## Question 12 — Integration by Trigonometric Identities

(a) $\\displaystyle\\int 3\\sin^2 x\\,dx$

(b) $\\displaystyle\\int 4\\cos^2 x\\,dx$

(c) $\\displaystyle\\int 3\\sin x\\cos x\\,dx$

(d) $\\displaystyle\\int (2-3\\sin x)^2\\,dx$

(e) $\\displaystyle\\int (1-\\cos 2x)^2\\,dx$

(f) $\\displaystyle\\int 2\\tan^2 x\\,dx$

(g) $\\displaystyle\\int 5\\cot^2 x\\,dx$

(h) $\\displaystyle\\int (2\\tan x - \\cot x)^2\\,dx$

(i) $\\displaystyle\\int \\frac{4\\sin x}{\\cos^2 x}\\,dx$

(j) $\\displaystyle\\int \\frac{\\cos x}{3\\sin^2 x}\\,dx$

## All Integration Methods — Mixed Practice

Integrate with respect to $x$ unless stated otherwise.

1\. $(4x+5)^{\\frac{1}{2}}$

2\. $\\dfrac{1}{4x+5}$

3\. $\\left(1-\\dfrac{1}{x}\\right)^2$

4\. $\\cos x\\sin x$

5\. $\\tan 3x$

6\. $x\\sin 3x$

7\. $\\dfrac{1+x}{x^{\\frac{1}{2}}}$

8\. $\\dfrac{x}{1+x}$

9\. $\\sin x\\cos^4 x$

10\. $3\\ln x$

11\. $\\dfrac{x+2}{x(x-1)}$

12\. $\\dfrac{\\sec^2 x}{(1+\\tan x)^3}$

13\. $\\sin^2 2x$

14\. $\\dfrac{x^2}{x-2}$

15\. $(\\sin x + 2\\cos x)^2$

16\. $x^2 e^{4x}$

17\. $\\dfrac{1}{x^2-4}$

18\. $\\dfrac{x}{9x^2+1}$

19\. $(1-x^{-2})^2$

20\. $(2-3x)^{-2}$

21\. $(4-5x)^{-\\frac{1}{2}}$

22\. $\\cot 3x$

23\. $\\text{cosec}\\,2x\\cot 2x$

24\. $\\cot^2 3x$

25\. $x\\cos 5x$

26\. $\\dfrac{x}{(x-1)^{\\frac{1}{2}}}$

27\. $x^2 e^{-x}$

28\. $\\cos 2x\\sin x$

29\. $\\sin 2x\\cos x$

30\. $\\tan 2x\\sec 2x$

31\. $\\dfrac{(x+1)^2}{x^2+1}$

32\. $\\dfrac{2}{(x-2)(x-4)}$

33\. $\\dfrac{1}{x^2(x-1)}$

34\. $\\text{cosec}^2 2x + 1$

35\. $\\dfrac{x+4}{x-4}$

36\. $\\dfrac{1}{x(x^2-1)}$

37\. $\\dfrac{x^2}{x^3+1}$

38\. $(e^x + x)^2$

39\. $x^3\\ln x$

40\. $x^3 e^{x^2}$

41\. Use the identity $\\cos^2 x + \\sin^2 x \\equiv 1$ and the substitution $\\cos x = u$ to find $\\displaystyle\\int \\sin^3 x\\,dx$.

42\. Find $\\displaystyle\\int \\cos^3 x\\,dx$ and $\\displaystyle\\int \\sin^5 x\\,dx$.

43\. Use the identity $\\sec^2 x \\equiv \\tan^2 x + 1$ and the substitution $\\tan x = u$ to find $\\displaystyle\\int \\tan^4 x\\,dx$.

44\. Find (a) $\\displaystyle\\int \\sec^4 x\\,dx$ and (b) $\\displaystyle\\int \\cot^4 x\\,dx$.

45\. Use the identity $\\sin(A+B) + \\sin(A-B) \\equiv 2\\sin A\\cos B$ to find: (a) $\\displaystyle\\int 2\\sin 6x\\cos 4x\\,dx$ (b) $\\displaystyle\\int \\sin x\\cos\\tfrac{1}{2}x\\,dx$

46\. Evaluate $\\displaystyle\\int\_0^1 \\frac{x+9}{(x+2)(3-2x)}\\,dx$.

47\. Use the substitution $x = 3\\sin t$ to show that $\\displaystyle\\int\_0^3 x^2(9-x^2)^{\\frac{1}{2}}\\,dx = \\tfrac{81}{16}\\pi$.

48\. Evaluate $\\displaystyle\\int\_{\\pi/6}^{\\pi} \\sec^3 x\\tan x\\,dx$.

49\. Evaluate $\\displaystyle\\int\_3^4 \\frac{2x+4}{(x-2)(x^2+4)}\\,dx$.

50\. Evaluate $\\displaystyle\\int\_1^2 \\frac{x}{(1+x^2)}\\,dx$.
### Edexcel AS-Level Maths | Logs
URL: https://www.a-level-maths-tutor.com/logs-edexcel-as-level-maths/
Last updated: 2026-08-07T14:35:07.000Z
### Question 1

### Edexcel AS-Level Maths Paper 1 June 2018

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-182.png)

### Question 2

### Edexcel AS-Level Maths Paper 1 June 2018

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-185.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/08/image-186.png)

### Question 3

### Edexcel AS-Level Maths Paper 1 June 2020

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-192.png)

### Question 4

### Edexcel AS-Level Maths Paper 1 June 2021

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-194.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-195.png)

### Question 5

### Edexcel AS-Level Maths Paper 1 June 2022

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-199.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-200.png)

### Question 6

### Edexcel AS-Level Maths Paper 1 June 2022

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-196.png)

### Question 7

### Edexcel AS-Level Maths Paper 1 June 2023

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-201.png)

### Question 8

### Edexcel AS-Level Maths Paper 1 June 2024

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-203.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-204.png)

### Question 9

### Edexcel AS-Level Maths Paper 1 June 2024

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-205-1.png)

### Question 10

### Edexcel A-Level Maths Paper 2 June 2025

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-207.png)

---

### A-Level Maths Tutoring

I offer one-to-one and small group A-Level Maths tutoring for students across the UK and internationally. With 94+ five-star Google reviews and tutoring experience since 2017, I specialise in helping students understand difficult concepts and improve their exam technique.

[A-Level Maths Tutoring](https://www.a-level-maths-tutor.com/a-level-maths-tutor/)

[94+ 5-star Google Reviews](https://www.a-level-maths-tutor.com/reviews/)

[Contact Me](https://www.a-level-maths-tutor.com/contact/)

[Back to A-Level Maths Revision](https://www.a-level-maths-tutor.com/a-level-maths-revision/)
### Edexcel AS-Level Maths |  Exponential Modelling
URL: https://www.a-level-maths-tutor.com/exponential-modelling-edexcel-as-level-maths/
Last updated: 2026-04-23T12:56:35.000Z
### Question 1

### Edexcel AS-Level Maths Paper 1 June 2019

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-187.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-188.png)

### Question 2

### Edexcel AS-Level Maths Paper 1 June 2020

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-189.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-190.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-191.png)

### Question 3

### Edexcel AS-Level Maths Paper 1 June 2021

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-193.png)

### Question 4

### Edexcel AS-Level Maths Paper 1 June 2022

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-197.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-198.png)

### Question 5

### Edexcel AS-Level Maths Paper 1 June 2023

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-202.png)

### Question 6

### Edexcel AS-Level Maths Paper 1 June 2024

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-206.png)

### Question 7

### Edexcel A-Level Maths Paper 2 June 2025

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-208.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-210.png)

---

### A-Level Maths Tutoring

I offer one-to-one and small group A-Level Maths tutoring for students across the UK and internationally. With 94+ five-star Google reviews and tutoring experience since 2017, I specialise in helping students understand difficult concepts and improve their exam technique.

[A-Level Maths Tutoring](https://www.a-level-maths-tutor.com/a-level-maths-tutor/)

[94+ 5-star Google Reviews](https://www.a-level-maths-tutor.com/reviews/)

[Contact Me](https://www.a-level-maths-tutor.com/contact/)

[Back to A-Level Maths Revision](https://www.a-level-maths-tutor.com/a-level-maths-revision/)
### Edexcel AS-Level Maths | Trigonometry of Any Triangle
URL: https://www.a-level-maths-tutor.com/edexcel-as-level-maths-trigonometry-any-triangle/
Last updated: 2026-04-23T12:57:44.000Z
### Question 1

### Edexcel AS-Level Maths Paper 1 June 2018

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-163.png)

### Question 2

### Edexcel AS-Level Maths Paper 1 June 2019

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-164.png)

### Question 3

### Edexcel AS-Level Maths Paper 1 June 2020

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-166.png)

### Question 4

### Edexcel AS-Level Maths Paper 1 June 2021

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-167.png)

### Question 5

### Edexcel AS-Level Maths Paper 1 June 2022

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-168.png)

### Question 6

### Edexcel AS-Level Maths Paper 1 June 2023

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-169.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-170.png)

### Question 7

### Edexcel AS-Level Maths Paper 1 June 2024

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-171.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-172.png)

### Question 8

### Edexcel A-Level Maths Paper 2 June 2026

---

### A-Level Maths Tutoring

I offer one-to-one and small group A-Level Maths tutoring for students across the UK and internationally. With 94+ five-star Google reviews and tutoring experience since 2017, I specialise in helping students understand difficult concepts and improve their exam technique.

[A-Level Maths Tutoring](https://www.a-level-maths-tutor.com/a-level-maths-tutor/)

[94+ 5-star Google Reviews](https://www.a-level-maths-tutor.com/reviews/)

[Contact Me](https://www.a-level-maths-tutor.com/contact/)

[Back to A-Level Maths Revision](https://www.a-level-maths-tutor.com/a-level-maths-revision/)
### Edexcel AS-Level Maths | Graphs & Transformations
URL: https://www.a-level-maths-tutor.com/edexcel-as-level-maths-graphs-transformations/
Last updated: 2026-04-23T12:58:02.000Z
### Question 1

### Edexcel AS-Level Maths Paper 1 June 2018

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-126.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-127.png)

### Question 2

### Edexcel AS-Level Maths Paper 1 June 2019

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-128.png)

### Question 3

### Edexcel AS-Level Maths Paper 1 June 2019

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-129.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-130.png)

### Question 4

### Edexcel AS-Level Maths Paper 1 June 2020

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-131.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-132-1.png)

### Question 5

### Edexcel AS-Level Maths Paper 1 June 2021

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-136.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-137.png)

### Question 6

### Edexcel AS-Level Maths Paper 1 June 2022

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-138.png)

### Question 7

### Edexcel AS-Level Maths Paper 1 June 2023

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-141.png)

### Question 8

### Edexcel AS-Level Maths Paper 1 June 2023

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-144.png)

### Question 9

### Edexcel AS-Level Maths Paper 1 June 2024

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-145.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-146.png)

### Question 10

### Edexcel AS-Level Maths Paper 1 June 2024

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-147.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-148.png)

### Question 11

### Edexcel AS-Level Maths Paper 1 June 2025

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-149.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-150.png)
### Edexcel AS-Level Maths | Quadratics
URL: https://www.a-level-maths-tutor.com/edexcel-as-level-maths-quadratics/
Last updated: 2026-04-23T12:58:21.000Z
### Question 1

### Edexcel AS-Level Maths Paper 1 June 2018

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-125.png)

### Question 2

### Edexcel AS-Level Maths Paper 1 June 2018

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-96.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-97.png)

### Question 3

### Edexcel AS-Level Maths Paper 1 June 2019

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-99.png)

### Question 4

### Edexcel AS-Level Maths Paper 1 June 2021

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-133.png)

### Question 5

### Edexcel AS-Level Maths Paper 1 June 2021

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-134.png)

### Question 6

### Edexcel AS-Level Maths Paper 1 June 2021

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-135.png)

### Question 7

### Edexcel AS-Level Maths Paper 1 June 2022

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-139.png)

### Question 8

### Edexcel AS-Level Maths Paper 1 June 2023

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-140.png)

### Question 9

### Edexcel AS-Level Maths Paper 1 June 2024

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-142.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-143.png)

### Question 10

### Edexcel AS-Level Maths Paper 1 June 2025

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-151.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-152.png)

### Question 11

### Edexcel AS-Level Maths Paper 1 June 2025

### 

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-153.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-154.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-155.png)

### Question 12

### Edexcel AS-Level Maths Paper 1 June 2025

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-156.png)
### Edexcel AS-Level Maths | Co-ordinate Geometry
URL: https://www.a-level-maths-tutor.com/edexcel-as-level-maths-coordinate-geometry/
Last updated: 2026-04-23T12:59:44.000Z
### Question 1

### Edexcel AS-Level Maths Paper 1 June 2018

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-110.png)

### Question 2

### Edexcel AS-Level Maths Paper 1 June 2019

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-112.png)

### Question 3

### Edexcel AS-Level Maths Paper 1 June 2019

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-111.png)

### Question 4

### Edexcel AS-Level Maths Paper 1 June 2019

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-113.png)

### Question 5

### Edexcel AS-Level Maths Paper 1 June 2020

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-114.png)

### Question 6

### Edexcel AS-Level Maths Paper 1 June 2021

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-115.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-116.png)

### Question 7

### Edexcel AS-Level Maths Paper 1 June 2022

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-117.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-118.png)

### Question 8

### Edexcel AS-Level Maths Paper 1 June 2023

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-119.png)

### Question 9

### Edexcel AS-Level Maths Paper 1 June 2023

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-120.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-121.png)

### Question 10

### Edexcel AS-Level Maths Paper 1 June 2024

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-122.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-123.png)

### Question 11

### Edexcel AS-Level Maths Paper 1 June 2025

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-124.png)
### GCSE Maths | Indices
URL: https://www.a-level-maths-tutor.com/gcse-maths-indices/
Last updated: 2026-07-29T14:36:02.000Z
$a^m \\times a^n = a^{m+n}$

When the base is the same, add the powers.

**Worked Example**

$m^4 \\times m^3 = m^{4+3} = m^7$

## Question 1

**a)** $m^2 \\times m^3$

**b)** $m^3 \\times m^3$

**c)** $m^6 \\times m^2$

**d)** $m^7 \\times m^3$

**e)** $m^6 \\times m^8$

**f)** $m^2 \\times m$

**g)** $m \\times m^3$

**h)** $m^7 \\times m^8$

**i)** $m^9 \\times m^2$

**j)** $m \\times m^8$

**k)** $m^6 \\times m^5$

**l)** $m^2 \\times m^2 \\times m^2 \\times m^2$

Show Answers 

**a)** $m^5$ **b)** $m^6$ **c)** $m^8$ **d)** $m^{10}$ **e)** $m^{14}$ **f)** $m^3$

**g)** $m^4$ **h)** $m^{15}$ **i)** $m^{11}$ **j)** $m^9$ **k)** $m^{11}$ **l)** $m^8$

$a^m \\div a^n = a^{m-n}$

When the base is the same, subtract the powers.

**Worked Example**

$n^7 \\div n^2 = n^{7-2} = n^5$

## Question 2

**a)** $n^5 \\div n^2$

**b)** $n^8 \\div n^3$

**c)** $n^9 \\div n^2$

**d)** $n^7 \\div n^5$

**e)** $n^3 \\div n$

**f)** $n^8 \\div n$

**g)** $n^7 \\div n^4$

**h)** $n^9 \\div n^3$

**i)** $n^4 \\div n^8$

**j)** $n \\div n^3$

**k)** $n^{45} \\div n^5$

**l)** $n^3 \\div n^3$

Show Answers 

**a)** $n^3$ **b)** $n^5$ **c)** $n^7$ **d)** $n^2$ **e)** $n^2$ **f)** $n^7$

**g)** $n^3$ **h)** $n^6$ **i)** $n^{-4}$ **j)** $n^{-2}$ **k)** $n^{40}$ **l)** $1$

$(a^m)^n = a^{m \\times n}$

When a power is raised to another power, multiply the powers.

**Worked Example**

$(y^4)^3 = y^{4 \\times 3} = y^{12}$

## Question 3

**a)** $(y^5)^2$

**b)** $(y^3)^2$

**c)** $(y^4)^3$

**d)** $(y^5)^4$

**e)** $(y^3)^6$

**f)** $(y^7)^3$

**g)** $(y^6)^6$

**h)** $(y^9)^2$

**i)** $(y^4)^8$

**j)** $(y^3)^{-5}$

**k)** $(y^{-5})^2$

Show Answers 

**a)** $y^{10}$ **b)** $y^6$ **c)** $y^{12}$ **d)** $y^{20}$ **e)** $y^{18}$ **f)** $y^{21}$

**g)** $y^{36}$ **h)** $y^{18}$ **i)** $y^{32}$ **j)** $y^{-15}$ **k)** $y^{-10}$

$(ka^m)^n = k^n \\times a^{m \\times n}$

Apply the outer power to both the number and the letter.

**Worked Example**

$(3x^2)^3 = 3^3 \\times x^{2 \\times 3} = 27x^6$

## Question 4

**a)** $(2x^3)^2$

**b)** $(5x^6)^2$

**c)** $(5x^5)^3$

**d)** $(2x^3)^4$

**e)** $(7x^5)^2$

**f)** $(4x^7)^3$

**g)** $(2x^6)^6$

**h)** $(10x^9)^3$

**i)** $(3x^4)^4$

Show Answers 

**a)** $4x^6$ **b)** $25x^{12}$ **c)** $125x^{15}$ **d)** $16x^{12}$ **e)** $49x^{10}$

**f)** $64x^{21}$ **g)** $64x^{36}$ **h)** $1000x^{27}$ **i)** $81x^{16}$

$a^0 = 1$ (for any non-zero $a$)

Anything to the power of $0$ equals $1$.

**Worked Example**

$6^0 = 1$

## Question 5

**a)** $5^0$

**b)** $12^0$

**c)** $x^0$

**d)** $100^0$

**e)** $(-3)^0$

**f)** $y^0$

**g)** $7^0$

**h)** $(2x)^0$

**i)** $\\left(\\dfrac{1}{2}\\right)^0$

**j)** $m^0$

**k)** $(4xy)^0$

**l)** $1^0$

Show Answers 

All answers $= 1$

$a^{-1} = \\dfrac{1}{a}$

A power of $-1$ means the reciprocal — flip the number.

**Worked Example**

$8^{-1} = \\dfrac{1}{8}$

## Question 6

**a)** $5^{-1}$

**b)** $2^{-1}$

**c)** $10^{-1}$

**d)** $3^{-1}$

**e)** $7^{-1}$

**f)** $4^{-1}$

**g)** $x^{-1}$

**h)** $12^{-1}$

**i)** $100^{-1}$

**j)** $\\left(\\dfrac{1}{2}\\right)^{-1}$

**k)** $\\left(\\dfrac{2}{3}\\right)^{-1}$

**l)** $\\left(\\dfrac{3}{5}\\right)^{-1}$

Show Answers 

**a)** $\\dfrac{1}{5}$ **b)** $\\dfrac{1}{2}$ **c)** $\\dfrac{1}{10}$ **d)** $\\dfrac{1}{3}$ **e)** $\\dfrac{1}{7}$ **f)** $\\dfrac{1}{4}$

**g)** $\\dfrac{1}{x}$ **h)** $\\dfrac{1}{12}$ **i)** $\\dfrac{1}{100}$ **j)** $2$ **k)** $\\dfrac{3}{2}$ **l)** $\\dfrac{5}{3}$

$a^{\\frac{1}{2}} = \\sqrt{a}$

A power of $\\frac{1}{2}$ means the square root.

**Worked Example**

$25^{\\frac{1}{2}} = \\sqrt{25} = 5$

## Question 7

**a)** $64^{\\frac{1}{2}}$

**b)** $9^{\\frac{1}{2}}$

**c)** $144^{\\frac{1}{2}}$

**d)** $25^{\\frac{1}{2}}$

**e)** $4^{\\frac{1}{2}}$

**f)** $100^{\\frac{1}{2}}$

**g)** $49^{\\frac{1}{2}}$

**h)** $16^{\\frac{1}{2}}$

**i)** $400^{\\frac{1}{2}}$

**j)** $81^{\\frac{1}{2}}$

**k)** $36^{\\frac{1}{2}}$

**l)** $121^{\\frac{1}{2}}$

Show Answers 

**a)** $8$ **b)** $3$ **c)** $12$ **d)** $5$ **e)** $2$ **f)** $10$

**g)** $7$ **h)** $4$ **i)** $20$ **j)** $9$ **k)** $6$ **l)** $11$

$a^{\\frac{1}{3}} = \\sqrt\[3\]{a}$

A power of $\\frac{1}{3}$ means the cube root.

**Worked Example**

$64^{\\frac{1}{3}} = \\sqrt\[3\]{64} = 4$

## Question 8

**a)** $216^{\\frac{1}{3}}$

**b)** $8^{\\frac{1}{3}}$

**c)** $729^{\\frac{1}{3}}$

**d)** $1^{\\frac{1}{3}}$

**e)** $64^{\\frac{1}{3}}$

**f)** $\\left(\\dfrac{1}{8}\\right)^{\\frac{1}{3}}$

**g)** $343^{\\frac{1}{3}}$

**h)** $27^{\\frac{1}{3}}$

**i)** $1000^{\\frac{1}{3}}$

**j)** $512^{\\frac{1}{3}}$

**k)** $\\left(\\dfrac{1}{27}\\right)^{\\frac{1}{3}}$

**l)** $125^{\\frac{1}{3}}$

Show Answers 

**a)** $6$ **b)** $2$ **c)** $9$ **d)** $1$ **e)** $4$ **f)** $\\dfrac{1}{2}$

**g)** $7$ **h)** $3$ **i)** $10$ **j)** $8$ **k)** $\\dfrac{1}{3}$ **l)** $5$

$a^{\\frac{m}{n}} = \\left(\\sqrt\[n\]{a}\\right)^m$

Do the root first (from the denominator), then the power (from the numerator). Rooting first keeps the numbers small.

**Worked Example**

$8^{2/3} \\rightarrow 2$ (cube root) $\\rightarrow 4$ (squared)

## Question 9

Part 1 — powers of $\\frac{3}{2}$:

**a)** $25^{\\frac{3}{2}}$

**b)** $4^{\\frac{3}{2}}$

**c)** $100^{\\frac{3}{2}}$

**d)** $9^{\\frac{3}{2}}$

**e)** $36^{\\frac{3}{2}}$

**f)** $16^{\\frac{3}{2}}$

Part 2 — powers of $\\frac{2}{3}$:

**g)** $125^{\\frac{2}{3}}$

**h)** $8^{\\frac{2}{3}}$

**i)** $1000^{\\frac{2}{3}}$

**j)** $27^{\\frac{2}{3}}$

**k)** $216^{\\frac{2}{3}}$

**l)** $64^{\\frac{2}{3}}$

Show Answers 

**a)** $125$ **b)** $8$ **c)** $1000$ **d)** $27$ **e)** $216$ **f)** $64$

**g)** $25$ **h)** $4$ **i)** $100$ **j)** $9$ **k)** $36$ **l)** $16$

$a^{-\\frac{m}{n}} = \\dfrac{1}{a^{\\frac{m}{n}}}$

The minus sign makes it a reciprocal. Then evaluate the fractional power as before: root first, then power.

**Worked Example**

$9^{-3/2} \\rightarrow \\dfrac{1}{9^{3/2}} \\rightarrow \\dfrac{1}{3}$ (square root) $\\rightarrow \\dfrac{1}{27}$ (cubed)

## Question 10

**a)** $4^{-\\frac{3}{2}}$

**b)** $9^{-\\frac{3}{2}}$

**c)** $8^{-\\frac{2}{3}}$

**d)** $27^{-\\frac{2}{3}}$

**e)** $16^{-\\frac{3}{2}}$

**f)** $4^{-\\frac{5}{2}}$

**g)** $8^{-\\frac{4}{3}}$

**h)** $27^{-\\frac{4}{3}}$

**i)** $16^{-\\frac{3}{4}}$

**j)** $32^{-\\frac{2}{5}}$

Show Answers 

**a)** $\\dfrac{1}{8}$ **b)** $\\dfrac{1}{27}$ **c)** $\\dfrac{1}{4}$ **d)** $\\dfrac{1}{9}$ **e)** $\\dfrac{1}{64}$

**f)** $\\dfrac{1}{32}$ **g)** $\\dfrac{1}{16}$ **h)** $\\dfrac{1}{81}$ **i)** $\\dfrac{1}{8}$ **j)** $\\dfrac{1}{4}$

---

### GCSE Maths Tutoring

I offer one-to-one and small group GCSE Maths tutoring for students across the UK and internationally. With 94+ five-star Google reviews and tutoring experience since 2017, I specialise in helping students understand difficult concepts and improve their exam technique.

[GCSE Maths Tutoring](https://www.a-level-maths-tutor.com/gcse-maths-tutor/)

[94+ 5-star Google Reviews](https://www.a-level-maths-tutor.com/reviews/)

[Contact Me](https://www.a-level-maths-tutor.com/contact/)

[Back to A-Level Maths Revision](https://www.a-level-maths-tutor.com/a-level-maths-revision/)
### Edexcel AS-Level Maths | Variable Acceleration
URL: https://www.a-level-maths-tutor.com/edexcel-as-level-maths-variable-acceleration/
Last updated: 2026-08-17T16:24:55.000Z
### Question 1

### Edexcel AS-Level Maths Paper 2 May 2018

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-83.png)

### Question 2

### Edexcel AS-Level Maths Paper 2 May 2019

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-84.png)

### Question 3

### Edexcel AS-Level Maths Paper 2 May 2020

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-85.png)

### Question 4

### Edexcel AS-Level Maths Paper 2 May 2021

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-86.png)

### Question 5

### Edexcel AS-Level Maths Paper 2 May 2022

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-87.png)

### Question 6

### Edexcel AS-Level Maths Paper 2 May 2023

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-88.png)

### Question 7

### Edexcel AS-Level Maths Paper 2 May 2024

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-90.png)

### Question 8

### Edexcel AS-Level Maths Paper 2 May 2025

###
### A-Level Maths | Moments
URL: https://www.a-level-maths-tutor.com/a-level-maths-moments/
Last updated: 2026-04-23T12:59:12.000Z
### Question 1

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/CleanShot-2026-04-16-at-10.31.34@2x.png)

### Question 2

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/CleanShot-2026-04-16-at-10.31.47@2x.png)
### GCSE Maths | Quadratic Simultaneous Equations
URL: https://www.a-level-maths-tutor.com/gcse-maths-quadratic-simultaneous-equations/
Last updated: 2026-04-21T16:18:57.000Z
### Question 1

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/CleanShot-2026-04-21-at-17.17.08@2x.png)

### Question 2

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/CleanShot-2026-04-21-at-17.18.46@2x.png)
### Revision
URL: https://www.a-level-maths-tutor.com/maths-revision-and-practice-questions/
Last updated: 2026-04-14T15:57:11.000Z
[A-Level Maths](https://www.a-level-maths-tutor.com/a-level-maths-revision/)

[GCSE Maths](https://www.a-level-maths-tutor.com/gcse-maths-revision/)
### GCSE Maths
URL: https://www.a-level-maths-tutor.com/gcse-maths-revision/
Last updated: 2026-08-05T15:31:14.000Z
## Algebra

1. Algebra | [Revision](https://www.a-level-maths-tutor.com/gcse-maths-algebra/)
2. Quadratics | [Revision](https://www.a-level-maths-tutor.com/gcse-maths-quadratics/)
3. Quadratic simultaneous equations | [Revision](https://www.a-level-maths-tutor.com/gcse-maths-quadratic-simultaneous-equations/)

## Number

1. Percentages | [Revision](https://www.a-level-maths-tutor.com/gcse-maths-percentages/)
2. Compound interest | [Revision](https://www.a-level-maths-tutor.com/gcse-maths-compound-interest/)
3. Ratios | [Revision](https://www.a-level-maths-tutor.com/gcse-maths-ratios/)
4. Indices | [Revision](https://www.a-level-maths-tutor.com/gcse-maths-indices/)
5. Surds | [Revision](https://www.a-level-maths-tutor.com/gcse-maths-surds/)

## Geometry

1. Trigonometry | [Revision](https://www.a-level-maths-tutor.com/gcse-maths-trigonometry/)

## Statistics

1. Probability Tree Diagrams | Revision

---

### A-Level Maths Tutoring

I offer one-to-one and small group A-Level Maths tutoring for students across the UK and internationally. With 94+ five-star Google reviews and tutoring experience since 2017, I specialise in helping students understand difficult concepts and improve their exam technique.

[A-Level Maths Tutoring](https://www.a-level-maths-tutor.com/a-level-maths-tutor/)

[94+ 5-star Google Reviews](https://www.a-level-maths-tutor.com/reviews/)

[Contact Me](https://www.a-level-maths-tutor.com/contact/)

[Back to A-Level Maths Revision](https://www.a-level-maths-tutor.com/a-level-maths-revision/)
### GCSE Maths | Quadratics
URL: https://www.a-level-maths-tutor.com/gcse-maths-quadratics/
Last updated: 2026-08-26T15:18:49.000Z
Factorising quadratics

$$x^2+7x+12 = (x+3)(x+4)$$ 

### Question 1

Factorise the following quadratics.

(a) $x^2+7x+12$

(b) $x^2+6x+8$

(c) $x^2+5x+6$

(d) $x^2+8x+7$

(e) $x^2+4x+4$

(f) $x^2+8x+15$

(g) $x^2+6x+9$

(h) $x^2+11x+28$

Show Answers 

(a) $(x+3)(x+4)$

(b) $(x+2)(x+4)$

(c) $(x+2)(x+3)$

(d) $(x+1)(x+7)$

(e) $(x+2)^2$

(f) $(x+3)(x+5)$

(g) $(x+3)^2$

(h) $(x+4)(x+7)$

### Question 2

Factorise the following quadratics.

(a) $x^2+x-12$

(b) $x^2+5x-6$

(c) $x^2+3x-10$

(d) $x^2+3x-4$

(e) $x^2+2x-48$

(f) $x^2+4x-32$

(g) $x^2+2x-35$

(h) $x^2+8x-33$

Show Answers 

(a) $(x-3)(x+4)$

(b) $(x-1)(x+6)$

(c) $(x-2)(x+5)$

(d) $(x-1)(x+4)$

(e) $(x-6)(x+8)$

(f) $(x-4)(x+8)$

(g) $(x-5)(x+7)$

(h) $(x-3)(x+11)$

### Question 3

Factorise the following quadratics.

(a) $x^2-3x-10$

(b) $x^2-x-20$

(c) $x^2-6x-27$

(d) $x^2-2x-3$

(e) $x^2-x-12$

(f) $x^2-4x-12$

(g) $x^2-4x-21$

(h) $x^2-6x-55$

Show Answers 

(a) $(x-5)(x+2)$

(b) $(x-5)(x+4)$

(c) $(x-9)(x+3)$

(d) $(x-3)(x+1)$

(e) $(x-4)(x+3)$

(f) $(x-6)(x+2)$

(g) $(x-7)(x+3)$

(h) $(x-11)(x+5)$

### Question 4

Factorise the following quadratics.

(a) $x^2-6x+9$

(b) $x^2-9x+20$

(c) $x^2-9x+14$

(d) $x^2-13x+22$

(e) $x^2-9x+8$

(f) $x^2-12x+32$

(g) $x^2-15x+36$

(h) $x^2-14x+48$

Show Answers 

(a) $(x-3)^2$

(b) $(x-4)(x-5)$

(c) $(x-2)(x-7)$

(d) $(x-2)(x-11)$

(e) $(x-1)(x-8)$

(f) $(x-4)(x-8)$

(g) $(x-3)(x-12)$

(h) $(x-6)(x-8)$

### Question 5

Factorise the following quadratics.

(a) $x^2-9x+8$

(b) $x^2+24x+23$

(c) $x^2-5x-14$

(d) $x^2-7x+12$

(e) $x^2+12x+36$

(f) $x^2-2x-63$

(g) $x^2+14x+24$

(h) $x^2+17x+60$

(i) $x^2-11x+30$

(j) $x^2-4x-32$

(k) $x^2-2x-63$

(l) $x^2-16x-17$

Show Answers 

(a) $(x-1)(x-8)$

(b) $(x+1)(x+23)$

(c) $(x-7)(x+2)$

(d) $(x-3)(x-4)$

(e) $(x+6)^2$

(f) $(x-9)(x+7)$

(g) $(x+2)(x+12)$

(h) $(x+5)(x+12)$

(i) $(x-5)(x-6)$

(j) $(x-8)(x+4)$

(k) $(x-9)(x+7)$

(l) $(x-17)(x+1)$

$$a^2-b^2 = (a-b)(a+b)$$ 

$$x^2-25 = (x-5)(x+5)$$ 

### Question 6

Factorise the following quadratics using the difference of two squares.

(a) $x^2-25$

(b) $y^2-49$

(c) $w^2-100$

(d) $x^2-4$

(e) $c^2-64$

(f) $x^2-1$

(g) $x^2-900$

(h) $y^2-9$

(i) $16-x^2$

(j) $1-y^2$

(k) $81-x^2$

(l) $144-h^2$

(m) $x^2-y^2$

(n) $a^2-c^2$

(o) $9x^2-25$

(p) $4y^2-1$

Show Answers 

(a) $(x-5)(x+5)$

(b) $(y-7)(y+7)$

(c) $(w-10)(w+10)$

(d) $(x-2)(x+2)$

(e) $(c-8)(c+8)$

(f) $(x-1)(x+1)$

(g) $(x-30)(x+30)$

(h) $(y-3)(y+3)$

(i) $(4-x)(4+x)$

(j) $(1-y)(1+y)$

(k) $(9-x)(9+x)$

(l) $(12-h)(12+h)$

(m) $(x-y)(x+y)$

(n) $(a-c)(a+c)$

(o) $(3x-5)(3x+5)$

(p) $(2y-1)(2y+1)$

Solving quadratics by factorising

$$(x-1)(x-3)=0 \\implies x=1 \\text{ or } x=3$$ 

### Question 7

Solve the following quadratics.

(a) $(x-1)(x-3)=0$

(b) $(y-4)(y-9)=0$

(c) $(m+1)(m+6)=0$

(d) $(x-3)(x+2)=0$

(e) $(t+7)(t-3)=0$

(f) $(k-10)(k+9)=0$

(g) $(w+5)(w+11)=0$

(h) $(y-8)(y-2)=0$

(i) $(x+3)(x-9)=0$

Show Answers 

(a) $x=1$ or $x=3$

(b) $y=4$ or $y=9$

(c) $m=-1$ or $m=-6$

(d) $x=3$ or $x=-2$

(e) $t=-7$ or $t=3$

(f) $k=10$ or $k=-9$

(g) $w=-5$ or $w=-11$

(h) $y=8$ or $y=2$

(i) $x=-3$ or $x=9$

Solving quadratics with the quadratic formula

$$x = \\frac{-b\\pm\\sqrt{b^2-4ac}}{2a}$$ 

$$x^2+5x+1=0$$ $$x = \\frac{-5\\pm\\sqrt{21}}{2}$$ 

### Question 8

Solve the following quadratics using the quadratic formula.

(a) $x^2+5x+1=0$

(b) $2x^2+7x+2=0$

(c) $4x^2+8x+3=0$

(d) $x^2+2x-4=0$

(e) $3x^2+4x-5=0$

(f) $2x^2+5x-10=0$

(g) $x^2-4x+2=0$

(h) $7x^2-6x+1=0$

(i) $3x^2-10x+4=0$

(j) $x^2-x-11=0$

(k) $x^2-6x-20=0$

(l) $2x^2-x-9=0$

Show Answers 

(a) $x=\\dfrac{-5\\pm\\sqrt{21}}{2}$

(b) $x=\\dfrac{-7\\pm\\sqrt{33}}{4}$

(c) $x=-\\dfrac{1}{2}$ or $x=-\\dfrac{3}{2}$

(d) $x=-1\\pm\\sqrt{5}$

(e) $x=\\dfrac{-2\\pm\\sqrt{19}}{3}$

(f) $x=\\dfrac{-5\\pm\\sqrt{105}}{4}$

(g) $x=2\\pm\\sqrt{2}$

(h) $x=\\dfrac{3\\pm\\sqrt{2}}{7}$

(i) $x=\\dfrac{5\\pm\\sqrt{13}}{3}$

(j) $x=\\dfrac{1\\pm3\\sqrt{5}}{2}$

(k) $x=3\\pm\\sqrt{29}$

(l) $x=\\dfrac{1\\pm\\sqrt{73}}{4}$

Completing the square

$$x^2+bx+c = \\left(x+\\frac{b}{2}\\right)^2 - \\left(\\frac{b}{2}\\right)^2 + c$$ 

$$y = x^2-8x-2$$ $$y = (x-4)^2-18$$ Minimum point: $(4,-18)$ 

### Question 9

Complete the square in the following quadratics, then state the coordinates of the maximum or minimum point.

(a) $y=x^2-8x-2$

(b) $y=x^2+6x+10$

(c) $y=x^2-4x+1$

(d) $y=x^2+4x+9$

(e) $y=x^2+8x+20$

Show Answers 

(a) $(x-4)^2-18$; minimum point $(4,-18)$

(b) $(x+3)^2+1$; minimum point $(-3,1)$

(c) $(x-2)^2-3$; minimum point $(2,-3)$

(d) $(x+2)^2+5$; minimum point $(-2,5)$

(e) $(x+4)^2+4$; minimum point $(-4,4)$

$$y = 4x^2-8x+28$$ Factor out the leading coefficient first: $$y = 4\\left(x^2-2x\\right)+28 = 4(x-1)^2+24$$ Minimum point: $(1,24)$ 

### Question 10

Complete the square in the following quadratics, then state the coordinates of the maximum or minimum point.

(a) $y=4x^2-8x+28$

(b) $y=5x^2+20x+15$

(c) $y=3x^2+24x+45$

(d) $y=4x^2-8x+16$

(e) $y=5x^2+10x$

Show Answers 

(a) $4(x-1)^2+24$; minimum point $(1,24)$

(b) $5(x+2)^2-5$; minimum point $(-2,-5)$

(c) $3(x+4)^2-3$; minimum point $(-4,-3)$

(d) $4(x-1)^2+12$; minimum point $(1,12)$

(e) $5(x+1)^2-5$; minimum point $(-1,-5)$

Factorising harder quadratics

$$2x^2+7x+5 = (x+1)(2x+5)$$ 

### Question 11

Factorise the following quadratics.

(a) $2x^2+7x+5$

(b) $2x^2+11x+15$

(c) $2x^2+9x+10$

(d) $3x^2+13x+4$

(e) $3x^2+4x+1$

(f) $3x^2+8x+4$

(g) $5x^2+13x+6$

(h) $5x^2+26x+5$

(i) $7x^2+10x+3$

(j) $11x^2+47x+12$

(k) $2x^2+17x+36$

(l) $5x^2+62x+24$

Show Answers 

(a) $(x+1)(2x+5)$

(b) $(x+3)(2x+5)$

(c) $(x+2)(2x+5)$

(d) $(x+4)(3x+1)$

(e) $(x+1)(3x+1)$

(f) $(x+2)(3x+2)$

(g) $(x+2)(5x+3)$

(h) $(x+5)(5x+1)$

(i) $(x+1)(7x+3)$

(j) $(x+4)(11x+3)$

(k) $(x+4)(2x+9)$

(l) $(x+12)(5x+2)$

Solving quadratic inequalities

$$(x-4)(x-1)<0$$ The critical values are $x=1$ and $x=4$. Since the graph is a positive $u$-shape, it's below zero between the roots: $$1<x<4$$ 

### Question 12

Solve the following quadratic inequalities.

(a) $(x-4)(x-1)<0$

(b) $(x-2)(x+1)<0$

(c) $(x+7)(x+3)\\leq 0$

(d) $(x-5)(x+4)\\leq 0$

(e) $x(x-9)>0$

(f) $(x+6)(x-5)>0$

(g) $(x+10)(x+1)\\geq 0$

(h) $(x-7)(x+7)\\geq 0$

(i) $(x+8)(x+2)<0$

(j) $(x-4)(x+7)\\geq 0$

(k) $(x+1)(x-5)\\leq 0$

(l) $(x-12)(x-11)>0$

Show Answers 

(a) $1<x<4$

(b) $-1<x<2$

(c) $-7\\leq x\\leq -3$

(d) $-4\\leq x\\leq 5$

(e) $x<0$ or $x>9$

(f) $x<-6$ or $x>5$

(g) $x\\leq -10$ or $x\\geq -1$

(h) $x\\leq -7$ or $x\\geq 7$

(i) $-8<x<-2$

(j) $x\\leq -7$ or $x\\geq 4$

(k) $-1\\leq x\\leq 5$

(l) $x<11$ or $x>12$

---

### GCSE Maths Tutoring

I offer one-to-one and small group GCSE Maths tutoring for students across the UK and internationally. With 94+ five-star Google reviews and tutoring experience since 2017, I specialise in helping students understand difficult concepts and improve their exam technique.

[GCSE Maths Tutoring](https://www.a-level-maths-tutor.com/gcse-maths-tutor/)

[94+ 5-star Google Reviews](https://www.a-level-maths-tutor.com/reviews/)

[Contact Me](https://www.a-level-maths-tutor.com/contact/)

[Back to A-Level Maths Revision](https://www.a-level-maths-tutor.com/a-level-maths-revision/)
### A-Level Maths | Probability Distribution
URL: https://www.a-level-maths-tutor.com/a-level-maths-probability-distribution/
Last updated: 2026-07-22T15:46:04.000Z
### Question 1

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/CleanShot-2026-04-14-at-14.57.05@2x.png)

### Question 2

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/CleanShot-2026-04-14-at-14.57.25@2x.png)

### Question 3

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/CleanShot-2026-04-14-at-14.57.11@2x.png)

### Question 4

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/CleanShot-2026-04-14-at-14.57.14@2x.png)

### Question 5

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/07/CleanShot-2026-07-22-at-16.20.36@2x.png)

### Question 5

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/07/CleanShot-2026-07-22-at-16.28.18@2x.png)

### Question 6

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/CleanShot-2026-04-14-at-15.03.21@2x.png)

### Question 7

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/CleanShot-2026-04-14-at-15.03.26@2x.png)

---

### A-Level Maths Tutoring

I offer one-to-one and small group A-Level Maths tutoring for students across the UK and internationally. With 94+ five-star Google reviews and tutoring experience since 2017, I specialise in helping students understand difficult concepts and improve their exam technique.

[A-Level Maths Tutoring](https://www.a-level-maths-tutor.com/a-level-maths-tutor/)

[94+ 5-star Google Reviews](https://www.a-level-maths-tutor.com/reviews/)

[Contact Me](https://www.a-level-maths-tutor.com/contact/)

[Back to A-Level Maths Revision](https://www.a-level-maths-tutor.com/a-level-maths-revision/)
### AS-Level Maths | Probability
URL: https://www.a-level-maths-tutor.com/as-level-maths-probability/
Last updated: 2026-04-23T13:00:03.000Z
###   
What does P(A) mean?

P(A) is the probability of A happening

### What does P(A') mean?

P(A') is the probability of A not happening

### What does P(A∩B) mean?

P(A∩B) is the probability of A and B happening

### What does P(AUB) mean?

P(AUB) is the probability of only A happening, or only B happening, or both A and B happening

### What does P(A|B) mean?

P(A|B) is the probability of A happening given that we know B is also happening.

### What does independent mean?

A and B are independent if **P(A∩B) = P(A) x P(B)**

### What does mutually exclusive mean?

A and B are mutually exclusive if **P(A∩B) = 0**

## Venn Diagrams

### Question 1

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/02/CleanShot-2026-02-13-at-13.40.36@2x.png)

### Question 2

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/02/CleanShot-2026-02-13-at-13.41.17@2x.png)

### Question 3

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/02/CleanShot-2026-02-13-at-13.41.45@2x.png)

## Probability Tree Diagrams

### Question 8

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/02/CleanShot-2026-02-13-at-13.53.53@2x.png)

### Question 9

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/02/CleanShot-2026-02-13-at-13.55.38@2x.png)

### Question 10

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/02/CleanShot-2026-02-13-at-13.56.19@2x.png)
### A-Level Maths | Quadratics
URL: https://www.a-level-maths-tutor.com/a-level-maths-quadratics/
Last updated: 2026-08-26T15:23:18.000Z
Sketching Quadratics

### Question 1

Sketch each curve showing the coordinates of any points of intersection with the coordinate axes.

(a) $y=x^2-3x+2$

(b) $y=x^2+5x+6$

(c) $y=x^2-9$

(d) $y=x^2-2x$

(e) $y=x^2-10x+25$

(f) $y=2x^2-14x+20$

(g) $y=-x^2+5x-4$

(h) $y=2+x-x^2$

(i) $y=2x^2-3x+1$

(j) $y=2x^2+13x+6$

(k) $y=3-8x+4x^2$

(l) $y=2+7x-4x^2$

(m) $y=5x^2-17x+6$

(n) $y=-6x^2+7x-2$

(o) $y=6x^2+x-5$

Show Answers 

(a) $(1,0)$, $(2,0)$, $(0,2)$

(b) $(-3,0)$, $(-2,0)$, $(0,6)$

(c) $(-3,0)$, $(3,0)$, $(0,-9)$

(d) $(0,0)$, $(2,0)$

(e) $(5,0)$, $(0,25)$

(f) $(2,0)$, $(5,0)$, $(0,20)$

(g) $(1,0)$, $(4,0)$, $(0,-4)$

(h) $(-1,0)$, $(2,0)$, $(0,2)$

(i) $\\left(\\frac{1}{2},0\\right)$, $(1,0)$, $(0,1)$

(j) $(-6,0)$, $\\left(-\\frac{1}{2},0\\right)$, $(0,6)$

(k) $\\left(\\frac{1}{2},0\\right)$, $\\left(\\frac{3}{2},0\\right)$, $(0,3)$

(l) $\\left(-\\frac{1}{4},0\\right)$, $(2,0)$, $(0,2)$

(m) $\\left(\\frac{2}{5},0\\right)$, $(3,0)$, $(0,6)$

(n) $\\left(\\frac{1}{2},0\\right)$, $\\left(\\frac{2}{3},0\\right)$, $(0,-2)$

(o) $(-1,0)$, $\\left(\\frac{5}{6},0\\right)$, $(0,-5)$

### Question 2

Sketch each curve showing the exact coordinates of its turning point and the point where it crosses the $y$-axis.

(a) $y=x^2-4x+3$

(b) $y=x^2+2x-24$

(c) $y=x^2-2x+5$

(d) $y=30+8x+x^2$

(e) $y=x^2+2x+1$

(f) $y=8+2x-x^2$

(g) $y=-x^2+8x-7$

(h) $y=-x^2-4x-7$

(i) $y=x^2-5x+4$

Show Answers 

(a) $(2,-1)$, $(0,3)$

(b) $(-1,-25)$, $(0,-24)$

(c) $(1,4)$, $(0,5)$

(d) $(-4,14)$, $(0,30)$

(e) $(-1,0)$, $(0,1)$

(f) $(1,9)$, $(0,8)$

(g) $(4,9)$, $(0,-7)$

(h) $(-2,-3)$, $(0,-7)$

(i) $\\left(\\frac{5}{2},-\\frac{9}{4}\\right)$, $(0,4)$

The Discriminant

### Question 3

By evaluating the discriminant, determine whether the roots of each equation are real and distinct, real and equal, or not real.

(a) $x^2+2x-7=0$

(b) $x^2+x+3=0$

(c) $x^2-4x+5=0$

(d) $x^2-6x+3=0$

(e) $x^2+14x+49=0$

(f) $x^2-9x+17=0$

(g) $x^2+3x=11$

(h) $2+3x+2x^2=0$

(i) $5x^2+8x+3=0$

(j) $3x^2-7x+5=0$

(k) $9x^2-12x+4=0$

(l) $13x^2+19x+7=0$

Show Answers 

(a) $\\Delta=32$ — real and distinct

(b) $\\Delta=-11$ — not real

(c) $\\Delta=-4$ — not real

(d) $\\Delta=24$ — real and distinct

(e) $\\Delta=0$ — real and equal

(f) $\\Delta=13$ — real and distinct

(g) $\\Delta=53$ — real and distinct

(h) $\\Delta=-7$ — not real

(i) $\\Delta=4$ — real and distinct

(j) $\\Delta=-11$ — not real

(k) $\\Delta=0$ — real and equal

(l) $\\Delta=-3$ — not real

### Question 4

The quadratic equation $x^2+10x+k=0$, where $k$ is a constant, has no real roots.

Find the range of possible values of $k$.

Show Answers 

$k>25$

### Question 5

$f(x)\\equiv 25x^2+20x+p$, where $p$ is a non-zero constant.

The quadratic equation $f(x)=0$ has equal roots.

Find the value of $p$.

Show Answers 

$p=4$

### Question 6

The quadratic equation $mx^2+12x+m=0$, where $m$ is a constant, has repeated roots.

Find the possible values of $m$.

Show Answers 

$m=\\pm 6$

### Question 7

Find the range of values of the non-zero constant $k$, given that the quadratic equation $3kx^2-2kx-4x+3=0$ has two different real roots.

Show Answers 

$k<1$ or $k>4$, $k\\neq 0$

### Question 8

It is given that $f(x)=x^2+2x-m(x^2-2x+2)-2$, where $m$ is a constant such that $m\\neq 1$.

The equation $f(x)=0$ has distinct real roots.

Determine the range of values of $m$.

Show Answers 

$-1<m<3$, $m\\neq 1$

---

### A-Level Maths Tutoring

I offer one-to-one and small group A-Level Maths tutoring for students across the UK and internationally. With 94+ five-star Google reviews and tutoring experience since 2017, I specialise in helping students understand difficult concepts and improve their exam technique.

[A-Level Maths Tutoring](https://www.a-level-maths-tutor.com/a-level-maths-tutor/)

[94+ 5-star Google Reviews](https://www.a-level-maths-tutor.com/reviews/)

[Contact Me](https://www.a-level-maths-tutor.com/contact/)

[Back to A-Level Maths Revision](https://www.a-level-maths-tutor.com/a-level-maths-revision/)
### A-Level Maths | Co-ordinate Geometry
URL: https://www.a-level-maths-tutor.com/a-level-maths-coordinate-geometry/
Last updated: 2026-07-25T10:15:25.000Z
# Co-ordinates

Gradient $\\displaystyle m = \\frac{y\_2 - y\_1}{x\_2 - x\_1}$

**Worked Example**

Find the gradient of the line segment joining $(2,3)$ and $(6,11)$.

$m = \\dfrac{11-3}{6-2} = \\dfrac{8}{4} = 2$

## Question 1

Find the gradient of the line segment joining each pair of points.

**a)** $(3, 1)$ and $(5, 5)$

**b)** $(4, 7)$ and $(10, 9)$

**c)** $(6, 1)$ and $(2, 5)$

**d)** $(-2, 2)$ and $(2, 8)$

**e)** $(1, 3)$ and $(7, -1)$

**f)** $(4, 5)$ and $(-5, -7)$

**g)** $(-2, 0)$ and $(0, -8)$

**h)** $(8, 6)$ and $(-7, -2)$

Show Answers 

**a)** $2$ **b)** $\\tfrac{1}{3}$ **c)** $-1$ **d)** $\\tfrac{3}{2}$ **e)** $-\\tfrac{2}{3}$ **f)** $\\tfrac{4}{3}$ **g)** $-4$ **h)** $\\tfrac{8}{15}$

Midpoint $\\displaystyle\\left(\\frac{x\_1 + x\_2}{2},\\ \\frac{y\_1 + y\_2}{2}\\right)$

**Worked Example**

Find the midpoint of $(2,4)$ and $(8,10)$.

Midpoint $= \\left(\\dfrac{2+8}{2}, \\dfrac{4+10}{2}\\right) = (5, 7)$

## Question 2

Find the coordinates of the mid-point of the line segment joining each pair of points.

**a)** $(0, 2)$ and $(8, 4)$

**b)** $(1, 9)$ and $(7, 5)$

**c)** $(-5, 1)$ and $(3, -7)$

**d)** $(-5, -7)$ and $(7, -5)$

**e)** $(1, 0)$ and $(2, 9)$

**f)** $(-1, -2)$ and $(4, -5)$

**g)** $(2.4, 3.1)$ and $(0.6, 4.5)$

**h)** $(0, 3)$ and $\\left(\\tfrac{1}{2}, \\tfrac{3}{2}\\right)$

**i)** $\\left(-\\tfrac{5}{4}, 2\\right)$ and $\\left(-1, -\\tfrac{3}{5}\\right)$

Show Answers 

**a)** $(4, 3)$ **b)** $(4, 7)$ **c)** $(-1, -3)$ **d)** $(1, -6)$ **e)** $\\left(\\tfrac{3}{2}, \\tfrac{9}{2}\\right)$ **f)** $\\left(\\tfrac{3}{2}, -\\tfrac{7}{2}\\right)$

**g)** $(1.5, 3.8)$ **h)** $\\left(\\tfrac{1}{4}, \\tfrac{9}{4}\\right)$ **i)** $\\left(-\\tfrac{9}{8}, \\tfrac{7}{10}\\right)$

Length $\\displaystyle l^2 = (x\_2 - x\_1)^2 + (y\_2 - y\_1)^2$

**Worked Example**

Find the length of the line segment joining $(0,0)$ and $(6,8)$.

$l^2 = 6^2 + 8^2 = 36 + 64 = 100$

$l = 10$

## Question 3

Find the exact length of the line segment joining each pair of points, giving your answers in terms of surds where appropriate.

**a)** $(1, 1)$ and $(4, 5)$

**b)** $(0, 0)$ and $(3, 1)$

**c)** $(1, -4)$ and $(9, 11)$

**d)** $(7, -8)$ and $(-9, 4)$

**e)** $(3, 12)$ and $(1, 7)$

**f)** $(-6, -3)$ and $(2, -7)$

Show Answers 

**a)** $5$ **b)** $\\sqrt{10}$ **c)** $17$ **d)** $20$ **e)** $\\sqrt{29}$ **f)** $4\\sqrt{5}$

# Equation of a Line

Equation of a line $y = mx + c$ or $y - y\_1 = m(x - x\_1)$

Parallel lines: same gradient Perpendicular lines: gradient is the negative reciprocal

**Worked Example**

Find the gradient and $y$-intercept of $2x - 4y + 8 = 0$

$4y = 2x + 8$

$y = \\tfrac{1}{2}x + 2$

gradient $= \\tfrac{1}{2}$, $y$-intercept $= 2$

## Question 4

Find the gradient and $y$-intercept of each line.

**a)** $x + y + 3 = 0$

**b)** $x - 2y - 6 = 0$

**c)** $3x + 3y - 2 = 0$

**d)** $4x - 5y + 1 = 0$

Show Answers 

**a)** gradient $= -1$, $y$-intercept $= -3$

**b)** gradient $= \\tfrac{1}{2}$, $y$-intercept $= -3$

**c)** gradient $= -1$, $y$-intercept $= \\tfrac{2}{3}$

**d)** gradient $= \\tfrac{4}{5}$, $y$-intercept $= \\tfrac{1}{5}$

**Worked Example**

Find where $2x - y + 4 = 0$ crosses the coordinate axes.

$x = 0: \\; -y+4=0 \\Rightarrow y=4 \\;\\Rightarrow (0,4)$

$y = 0: \\; 2x+4=0 \\Rightarrow x=-2 \\;\\Rightarrow (-2,0)$

## Question 5

Find the coordinates of the points at which each straight line crosses the coordinate axes.

**a)** $y = 2x + 5$

**b)** $x - 3y + 6 = 0$

**c)** $2x + 4y - 3 = 0$

**d)** $5x - 3y = 10$

Show Answers 

**a)** $\\left(-\\tfrac{5}{2}, 0\\right)$ and $(0, 5)$

**b)** $(-6, 0)$ and $(0, 2)$

**c)** $\\left(0, \\tfrac{3}{4}\\right)$ and $\\left(\\tfrac{3}{2}, 0\\right)$

**d)** $\\left(0, -\\tfrac{10}{3}\\right)$ and $(2, 0)$

**Worked Example**

Find the equation of the line with gradient $3$ through $P(1, 2)$.

$y - 2 = 3(x - 1)$

$y = 3x - 1$

$3x - y - 1 = 0$

## Question 6

Find, in each case, the equation of the straight line with gradient $m$ which passes through the point $P$. Give your answers in the form $ax + by + c = 0$, where $a$, $b$ and $c$ are integers.

**a)** $m = 1$, $P(2, -4)$

**b)** $m = \\tfrac{1}{2}$, $P(6, 1)$

**c)** $m = -4$, $P(-1, 8)$

**d)** $m = \\tfrac{2}{5}$, $P(-3, 5)$

**e)** $m = -3$, $P\\!\\left(\\tfrac{3}{2}, -\\tfrac{1}{8}\\right)$

**f)** $m = -\\tfrac{3}{4}$, $P\\!\\left(\\tfrac{2}{3}, -7\\right)$

Show Answers 

**a)** $x - y - 6 = 0$ **b)** $x - 2y - 4 = 0$ **c)** $4x + y - 4 = 0$

**d)** $2x - 5y + 31 = 0$ **e)** $24x + 8y - 35 = 0$ **f)** $3x + 4y + 26 = 0$

**Worked Example**

Find where $y = x + 2$ and $y = 3x - 4$ intersect.

$x + 2 = 3x - 4$

$2x = 6 \\Rightarrow x = 3$

$y = 3 + 2 = 5$

Intersect at $(3, 5)$

## Question 7

Find the coordinates of the point of intersection of each pair of straight lines.

**a)** $y = 2x + 1$ and $y = 3x - 1$

**b)** $y = x + 7$ and $y = 4 - 2x$

**c)** $y = 5x - 4$ and $y = 3x - 1$

**d)** $x + 2y - 4 = 0$ and $3x - 2y + 4 = 0$

**e)** $2x + y - 2 = 0$ and $x + 3y + 9 = 0$

**f)** $3x + 2y = 0$ and $x + 4y - 2 = 0$

Show Answers 

**a)** $(2, 5)$ **b)** $(-1, 6)$ **c)** $\\left(\\tfrac{3}{2}, \\tfrac{7}{2}\\right)$ **d)** $(0, 2)$ **e)** $(3, -4)$ **f)** $\\left(-\\tfrac{2}{5}, \\tfrac{3}{5}\\right)$

# Equation of a Circle

Equation of a circle $(x - a)^2 + (y - b)^2 = r^2$ where $(a, b)$ is the centre and $r$ is the radius

Complete the square to find the centre and radius when the equation is expanded

**Worked Example**

Find the centre and radius of $(x-2)^2 + (y+3)^2 = 25$

Centre $= (2, -3)$, radius $= 5$

## Question 8

Write down the coordinates of the centre and the radius of each of the following circles.

**a)** $x^2 + y^2 = 16$

**b)** $(x - 6)^2 + (y - 1)^2 = 81$

**c)** $(x + 1)^2 + (y - 4)^2 = 121$

**d)** $(x - 7)^2 + y^2 = 0.09$

**e)** $(x + 2)^2 + (y + 5)^2 = 32$

**f)** $(x - 8)^2 + (y + 9)^2 = 108$

Show Answers 

**a)** centre $(0,0)$, radius $4$

**b)** centre $(6,1)$, radius $9$

**c)** centre $(-1,4)$, radius $11$

**d)** centre $(7,0)$, radius $0.3$

**e)** centre $(-2,-5)$, radius $4\\sqrt{2}$

**f)** centre $(8,-9)$, radius $6\\sqrt{3}$

**Worked Example**

Find the centre and radius of $x^2 + y^2 - 6x + 4y - 3 = 0$

$(x-3)^2 + (y+2)^2 = 3 + 9 + 4$

$(x-3)^2 + (y+2)^2 = 16$

Centre $= (3, -2)$, radius $= 4$

## Question 9

Find the coordinates of the centre and the radius of each of the following circles.

**a)** $x^2 + y^2 - 4y + 3 = 0$

**b)** $x^2 + y^2 - 2x - 10y - 23 = 0$

**c)** $x^2 + y^2 + 12x - 8y + 36 = 0$

**d)** $x^2 + y^2 - 2x + 16y = 35$

**e)** $x^2 + y^2 = 8x - 6y$

**f)** $x^2 + y^2 + 10x - 2y - 19 = 0$

Show Answers 

**a)** centre $(0,2)$, radius $1$

**b)** centre $(1,5)$, radius $7$

**c)** centre $(-6,4)$, radius $4$

**d)** centre $(1,-8)$, radius $10$

**e)** centre $(4,-3)$, radius $5$

**f)** centre $(-5,1)$, radius $3\\sqrt{5}$

**Worked Example**

Is $(1,1)$ inside, outside or on the circle $x^2 + y^2 = 4$?

Centre $(0,0)$, radius$^2 = 4$

distance$^2 = 1^2 + 1^2 = 2$

$2 < 4 \\;\\Rightarrow$ inside the circle

## Question 10

Find in each case whether the given point lies inside, outside or on the given circle.

**a)** $(0, -9)$ $x^2 + y^2 = 64$

**b)** $(4, 7)$ $x^2 + y^2 - 2x - 6y - 26 = 0$

**c)** $(7, -3)$ $x^2 + y^2 + 10x - 4y = 140$

**d)** $(-4, 1)$ $x^2 + y^2 + 2x + 8y - 13 = 0$

Show Answers 

**a)** outside (distance$^2=81$, radius$^2=64$)

**b)** inside (distance$^2=25$, radius$^2=36$)

**c)** on the circle (distance$^2=169=$ radius$^2$)

**d)** outside (distance$^2=34$, radius$^2=30$)

---

### A-Level Maths Tutoring

I offer one-to-one and small group A-Level Maths tutoring for students across the UK and internationally. With 94+ five-star Google reviews and tutoring experience since 2017, I specialise in helping students understand difficult concepts and improve their exam technique.

[A-Level Maths Tutoring](https://www.a-level-maths-tutor.com/a-level-maths-tutor/)

[94+ 5-star Google Reviews](https://www.a-level-maths-tutor.com/reviews/)

[Contact Me](https://www.a-level-maths-tutor.com/contact/)

[Back to A-Level Maths Revision](https://www.a-level-maths-tutor.com/a-level-maths-revision/)
### A-Level Maths | Binomial Expansion
URL: https://www.a-level-maths-tutor.com/a-level-maths-binomial-expansion/
Last updated: 2026-04-23T13:01:42.000Z
### Question 1

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/CleanShot-2026-04-13-at-16.27.27@2x.png)

### Question 2

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/CleanShot-2026-04-13-at-16.27.14@2x.png)

### Question 3

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/CleanShot-2026-04-13-at-16.27.38@2x.png)

### Question 4

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/CleanShot-2026-04-13-at-16.28.27@2x.png)

### Question 5

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/CleanShot-2026-04-13-at-16.28.38@2x.png)

### Question 6

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/CleanShot-2026-04-13-at-16.28.43@2x.png)

### Question 7

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/CleanShot-2026-04-13-at-16.28.47@2x.png)

Approximating values

### Question 8

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/CleanShot-2026-04-13-at-16.30.19@2x.png)

### Question 9

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/CleanShot-2026-04-13-at-16.30.31@2x.png)

### Question 10

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/CleanShot-2026-04-13-at-16.30.43@2x.png)

### Question 11

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/CleanShot-2026-04-13-at-16.30.49@2x.png)
### A-Level Maths | Partial Fractions
URL: https://www.a-level-maths-tutor.com/a-level-maths-partial-fractions/
Last updated: 2026-07-11T13:39:28.000Z
For distinct linear factors: $\\displaystyle\\frac{6x}{(x-1)(x+2)} = \\frac{A}{x-1} + \\frac{B}{x+2}$

Multiply both sides by $(x-1)(x+2)$, then substitute $x=1$ and $x=-2$ to solve for $A$ and $B$.

**Worked Example**

$\\displaystyle\\frac{6x}{(x-1)(x+2)} = \\frac{A}{x-1} + \\frac{B}{x+2}$

$6x = A(x+2) + B(x-1)$

$x=1: \\;\\; 6 = 3A \\;\\Rightarrow\\; A = 2$

$x=-2: \\;\\; -12 = -3B \\;\\Rightarrow\\; B = 4$

$\\displaystyle\\frac{6x}{(x-1)(x+2)} = \\frac{2}{x-1} + \\frac{4}{x+2}$

## Question 1

Express each of the following as partial fractions.

**a)** $\\displaystyle\\frac{6x}{(x-1)(x+2)}$

**b)** $\\displaystyle\\frac{7y-11}{(y+2)(y-3)}$

**c)** $\\displaystyle\\frac{19-4t}{(t+4)(t-3)}$

**d)** $\\displaystyle\\frac{w-22}{(w+2)(w-6)}$

**e)** $\\displaystyle\\frac{8z+7}{(z+2)(z-7)}$

Show Answers 

**a)** $\\displaystyle\\frac{2}{x-1} + \\frac{4}{x+2}$

**b)** $\\displaystyle\\frac{2}{y-3} + \\frac{5}{y+2}$

**c)** $\\displaystyle\\frac{1}{t-3} - \\frac{5}{t+4}$

**d)** $\\displaystyle\\frac{3}{w+2} - \\frac{2}{w-6}$

**e)** $\\displaystyle\\frac{1}{z+2} + \\frac{7}{z-7}$

For a repeated linear factor: $\\displaystyle\\frac{6x}{(x-2)(x+1)^2} = \\frac{A}{x-2} + \\frac{B}{x+1} + \\frac{C}{(x+1)^2}$

Multiply both sides by $(x-2)(x+1)^2$, substitute convenient values of $x$, then compare coefficients or substitute $x=0$ for any remaining unknown.

**Worked Example**

$\\displaystyle\\frac{4x+1}{(x-2)(x+1)^2} = \\frac{A}{x-2} + \\frac{B}{x+1} + \\frac{C}{(x+1)^2}$

$4x+1 = A(x+1)^2 + B(x-2)(x+1) + C(x-2)$

$x=2: \\;\\; 9 = 9A \\;\\Rightarrow\\; A = 1$

$x=-1: \\;\\; -3 = -3C \\;\\Rightarrow\\; C = 1$

$x=0: \\;\\; 1 = A - 2B - 2C \\;\\Rightarrow\\; 1 = 1 - 2B - 2 \\;\\Rightarrow\\; B = -1$

$\\displaystyle\\frac{4x+1}{(x-2)(x+1)^2} = \\frac{1}{x-2} - \\frac{1}{x+1} + \\frac{1}{(x+1)^2}$

## Question 2

Express each of the following as partial fractions.

**a)** $\\displaystyle\\frac{2x^2-x-3}{(x-2)(x-1)^2}$

**b)** $\\displaystyle\\frac{y^2-2y+8}{(y+2)(y-2)^2}$

**c)** $\\displaystyle\\frac{-3t^2+12t+7}{(t-3)(t+1)^2}$

**d)** $\\displaystyle\\frac{-3w^2+10w-11}{(w-2)(w-1)^2}$

Show Answers 

**a)** $\\displaystyle\\frac{3}{x-2} - \\frac{1}{x-1} + \\frac{2}{(x-1)^2}$

**b)** $\\displaystyle\\frac{1}{y+2} + \\frac{2}{(y-2)^2}$

**c)** $\\displaystyle\\frac{1}{t-3} - \\frac{4}{t+1} + \\frac{2}{(t+1)^2}$

**d)** $\\displaystyle\\frac{4}{(w-1)^2} - \\frac{3}{w-2}$

**Worked Example**

$\\displaystyle\\frac{2y+3}{y^2(y+1)} = \\frac{A}{y} + \\frac{B}{y^2} + \\frac{C}{y+1}$

$2y+3 = Ay(y+1) + B(y+1) + Cy^2$

$y=0: \\;\\; 3 = B \\;\\Rightarrow\\; B = 3$

$y=-1: \\;\\; 1 = C \\;\\Rightarrow\\; C = 1$

Compare $y^2$: $0 = A + C \\;\\Rightarrow\\; A = -1$

$\\displaystyle\\frac{2y+3}{y^2(y+1)} = -\\frac{1}{y} + \\frac{3}{y^2} + \\frac{1}{y+1}$

## Question 3

Express each of the following as partial fractions.

**a)** $\\displaystyle\\frac{2x^2-3}{(3-2x)(1-x)^2}$

**b)** $\\displaystyle\\frac{3y^2+17y+4}{y^2(y+4)}$

**c)** $\\displaystyle\\frac{t^2}{(t-2)(t-1)^2}$

**d)** $\\displaystyle\\frac{9w^2}{(2w+1)(w-1)^2}$

Show Answers 

**a)** $\\displaystyle\\frac{6}{3-2x} - \\frac{2}{1-x} - \\frac{1}{(1-x)^2}$

**b)** $\\displaystyle\\frac{1}{y^2} + \\frac{4}{y} - \\frac{1}{y+4}$

**c)** $\\displaystyle\\frac{4}{t-2} - \\frac{1}{(t-1)^2} - \\frac{3}{t-1}$

**d)** $\\displaystyle\\frac{4}{w-1} + \\frac{3}{(w-1)^2} + \\frac{1}{2w+1}$

If the degree of the numerator is $\\geq$ the degree of the denominator, first divide the numerator by the denominator: $\\displaystyle\\frac{f(x)}{g(x)} = Q(x) + \\frac{R(x)}{g(x)}$, where $Q(x)$ is the quotient and $R(x)$ the remainder.

**Worked Example**

$\\displaystyle\\frac{x^3+3x^2-5}{x+2}$

$x^3+3x^2-5 = (x+2)(x^2+x-2) - 1$

$\\displaystyle\\frac{x^3+3x^2-5}{x+2} = x^2+x-2 - \\frac{1}{x+2}$

## Question 4

For each of the following, find the constants $a$, $b$, $c$ and $d$ (or $a$, $b$, $c$ where only three appear).

**a)** $\\displaystyle\\frac{x^3+2x^2+3x-4}{x+1} \\equiv ax^2+bx+c+\\frac{d}{x+1}$

**b)** $\\displaystyle\\frac{2x^3+3x^2-4x+5}{x+3} \\equiv ax^2+bx+c+\\frac{d}{x+3}$

**c)** $\\displaystyle\\frac{2x^2+4x+5}{x^2-1} \\equiv a + \\frac{bx+c}{x^2-1}$

Show Answers 

**a)** $a=1,\\; b=1,\\; c=2,\\; d=-6$

**b)** $a=2,\\; b=-3,\\; c=5,\\; d=-10$

**c)** $a=2,\\; b=4,\\; c=7$

---

### A-Level Maths Tutoring

I offer one-to-one and small group A-Level Maths tutoring for students across the UK and internationally. With 94+ five-star Google reviews and tutoring experience since 2017, I specialise in helping students understand difficult concepts and improve their exam technique.

[A-Level Maths Tutoring](https://www.a-level-maths-tutor.com/a-level-maths-tutor/)

[94+ 5-star Google Reviews](https://www.a-level-maths-tutor.com/reviews/)

[Contact Me](https://www.a-level-maths-tutor.com/contact/)

[Back to A-Level Maths Revision](https://www.a-level-maths-tutor.com/a-level-maths-revision/)
### GCSE Maths | Transformations of Graphs
URL: https://www.a-level-maths-tutor.com/gcse-maths-transformations-graphs/
Last updated: 2026-09-10T10:35:13.000Z
### What are the three types of transformations

The three types of transformations are 

1. Enlargements (stretch)
2. Translations (movement)
3. Reflections

### How can we tell if a transformation affects the x-coordinates or the y-coordinates?

Transformations outside the bracket affect the y-coordinates

Transformations inside the bracket affect the x-coordinates

When it is inside the bracket, the transformation has the opposite effect to what you'd naturally expect.

### If f(x) is the original graph, what is the effect of the following transformations?

### f(x) + 21

vertical translation, up by 21

### f(x+21) 

horizontal translation, left by 21

### 2f(x) 

vertical stretch, scale factor 2

### f(2x)

horizontal stretch, scale factor 1/2

### \-f(x) 

vertical reflection

### f(-x)

horizontal reflection
### A-Level Maths | Graphs & Transformations
URL: https://www.a-level-maths-tutor.com/a-level-maths-graphs-transformations/
Last updated: 2026-09-10T11:17:45.000Z
### Straight-line graphs

**The equation of a straight line** is always in the form **y=mx+c**

**m**: the gradient

**c**: the y-intercept

To sketch a straight-line graph, draw a line through the y-intercept and the x-intercept.

### Circles

**The equation of a circle** is always in the form **(x-a)2+(y-b)2 \= r2** 

**Centre**: (a, b)

**Radius**: of the circle is r

You can find four of the points on the circle by using (a+r, b), (a-r, b) (a, b+r) and (a, b-r)

### Quadratics

**The equation of a quadratic** is always in the form **y = ax2 \+ bx + c**

A quadratic is always **U-shaped**

The equation of a quadratic can be written in the form **y = k(x-a)(x-b)** where (a, 0) and (b, 0) are the **x-intercepts**.

The equation of a quadratic can also be written in the form **y = k(x-a)2 \+ b** where (a, b) is the **turning point**.

### Question 1

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/CleanShot-2026-04-13-at-15.27.48@2x.png)

### Question 2

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/CleanShot-2026-04-13-at-15.27.59@2x.png)

### Question 3

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/CleanShot-2026-04-13-at-15.28.18@2x.png)

### Question 4

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/CleanShot-2026-04-13-at-15.28.24@2x.png)

### Question 5

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/CleanShot-2026-04-13-at-15.28.34@2x.png)

### Question 6

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/CleanShot-2026-04-13-at-15.28.52@2x.png)

### Cubics

**The equation of a cubic** can be written in the form **y= ax3+bx2+cx+d**.

A cubic graph is **N-shaped**.

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-62.png)

### Question 7

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/CleanShot-2026-04-13-at-15.30.40@2x.png)

### Question 8

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/CleanShot-2026-04-13-at-15.30.14@2x.png)

### Question 9

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/CleanShot-2026-04-13-at-15.31.12@2x.png)

### Question 10

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/CleanShot-2026-04-13-at-15.30.19@2x.png)

### Question 11

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/CleanShot-2026-04-13-at-15.30.09@2x.png)

### Quartics

The equation of a quartic is always in the form **y = ax4+bx3+cx2+dx+e**

A quartic graph is always **W-shaped**

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-63.png)

## 

### Reciprocal graphs

A reciprocal graph is written in the form **y = k/x** or **y = k/x2**

These graphs have **asymptotes** at y=0 and x=0.

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-64.png)

---

### A-Level Maths Tutoring

I offer one-to-one and small group A-Level Maths tutoring for students across the UK and internationally. With 94+ five-star Google reviews and tutoring experience since 2017, I specialise in helping students understand difficult concepts and improve their exam technique.

[A-Level Maths Tutoring](https://www.a-level-maths-tutor.com/a-level-maths-tutor/)

[94+ 5-star Google Reviews](https://www.a-level-maths-tutor.com/reviews/)

[Contact Me](https://www.a-level-maths-tutor.com/contact/)

[Back to A-Level Maths Revision](https://www.a-level-maths-tutor.com/a-level-maths-revision/)

##
### A-Level Maths | Functions
URL: https://www.a-level-maths-tutor.com/a-level-maths-functions/
Last updated: 2026-09-11T10:39:39.000Z
### Range of a Function

### Question 1

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/CleanShot-2026-04-13-at-15.06.35@2x.png)

### Question 2

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/CleanShot-2026-04-13-at-15.07.03@2x.png)

### Question 3

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/CleanShot-2026-04-13-at-15.07.31@2x.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/CleanShot-2026-04-13-at-15.07.47@2x.png)

### Question 4

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/CleanShot-2026-04-13-at-15.08.17@2x.png)

### Function Compositions

### Question 5

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/CleanShot-2026-04-13-at-15.09.17@2x.png)

### Question 6

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/CleanShot-2026-04-13-at-15.09.51@2x.png)

### Inverse Functions

### Question 7

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/CleanShot-2026-04-13-at-15.11.21@2x.png)

### Question 8

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/CleanShot-2026-04-13-at-15.11.27@2x.png)

### Range and Domain of Inverse Functions

### Question 9

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/CleanShot-2026-04-13-at-15.12.01@2x.png)

### Question 10

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/CleanShot-2026-04-13-at-15.12.48@2x.png)

### Question 11

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/CleanShot-2026-04-13-at-15.13.34@2x.png)

### Question 12

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/CleanShot-2026-04-13-at-15.14.10@2x.png)

### Question 13

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/CleanShot-2026-04-13-at-15.14.19@2x.png)

### Modulus

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/09/image.png)

---

### A-Level Maths Tutoring

I offer one-to-one and small group **A-Level Maths tutoring** for students across the UK and internationally. With 94+ five-star Google reviews and tutoring experience since 2017, I specialise in helping students understand difficult concepts and improve their exam technique.

[A-Level Maths Tutoring](https://www.a-level-maths-tutor.com/a-level-maths-tutor/)

[94+ 5-star Google Reviews](https://www.a-level-maths-tutor.com/reviews/)

[Contact Me](https://www.a-level-maths-tutor.com/contact/)

[Back to A-Level Maths Revision](https://www.a-level-maths-tutor.com/a-level-maths-revision/)
### A-Level Maths | Implicit Differentiation
URL: https://www.a-level-maths-tutor.com/a-level-maths-implicit-differentiation/
Last updated: 2026-04-13T14:01:46.000Z
### Question 1

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/CleanShot-2026-04-13-at-15.00.59@2x.png)

### Question 2

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/CleanShot-2026-04-13-at-15.01.25@2x.png)

### Question 3

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/CleanShot-2026-04-13-at-14.56.17@2x.png)

### Question 4

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/CleanShot-2026-04-13-at-14.57.31@2x.png)

### Question 5

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/CleanShot-2026-04-13-at-14.58.06@2x.png)
### Edexcel A-Level Maths | Functions
URL: https://www.a-level-maths-tutor.com/functions-edexcel-a-level-maths/
Last updated: 2026-04-23T10:59:10.000Z
### Question 1

### Edexcel A-Level Maths Paper 1 June 2018

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-35.png)

### Question 2

### Edexcel A-Level Maths Paper 2 June 2018

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-36.png)

[Answer](https://www.youtube.com/watch?v=2PHBnzOzUKE&t=15s&ref=a-level-maths-tutor.com)

### Question 3

### Edexcel A-Level Maths Paper 1 June 2019

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-37.png)

### Question 4

### Edexcel A-Level Maths Paper 1 June 2019

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-38.png)

### Question 5

### Edexcel A-Level Maths Paper 2 June 2019

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-39.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-40.png)

### Question 6

### Edexcel A-Level Maths Paper 1 June 2020

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-41.png)

### Question 7

### Edexcel A-Level Maths Paper 1 June 2020

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-42.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-43.png)

### Question 8

### Edexcel A-Level Maths Paper 2 June 2020

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-44.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-45.png)

### Question 9

### Edexcel A-Level Maths Paper 2 June 2020

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-46.png)

### Question 10

### Edexcel A-Level Maths Paper 2 June 2021

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-47.png)

### Question 11

### Edexcel A-Level Maths Paper 2 June 2021

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-48.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-49.png)

### Question 12

### Edexcel A-Level Maths Paper 2 June 2022

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-50.png)

### Question 13

### Edexcel A-Level Maths Paper 2 June 2022

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-51.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-52.png)

### Question 14

### Edexcel A-Level Maths Paper 1 June 2023

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-53.png)

### Question 15

### Edexcel A-Level Maths Paper 2 June 2023

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-54.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-55.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-56.png)

### Question 16

### Edexcel A-Level Maths Paper 1 June 2024

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-57.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-58.png)

### Question 17

### Edexcel A-Level Maths Paper 1 June 2024

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-59.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-60.png)

### Question 18

### Edexcel A-Level Maths Paper 1 June 2025

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-61.png)

---

### A-Level Maths Tutoring

I offer one-to-one and small group A-Level Maths tutoring for students across the UK and internationally. With 94+ five-star Google reviews and tutoring experience since 2017, I specialise in helping students understand difficult concepts and improving their exam results.

[A-Level Maths Tutoring](https://www.a-level-maths-tutor.com/a-level-maths-tutor/)

[94+ 5-star Google Reviews](https://www.a-level-maths-tutor.com/reviews/)

[Contact Me](https://www.a-level-maths-tutor.com/contact/)

[Back to A-Level Maths Revision](https://www.a-level-maths-tutor.com/a-level-maths-revision/)
### Edexcel A-Level Maths | Parametric Equations
URL: https://www.a-level-maths-tutor.com/edexcel-a-level-maths-parametric-equations/
Last updated: 2026-04-23T13:05:15.000Z
### Question 1

### Edexcel A-Level Maths Paper 1 June 2018

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-21.png)

[Answer](https://www.youtube.com/watch?v=-K7zg%5FO2gTs&ref=a-level-maths-tutor.com)

### Question 2

### Edexcel A-Level Maths Paper 2 June 2019

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-22.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-23.png)

[Answer](https://www.youtube.com/watch?v=nxy-KPASxwE&t=664s&ref=a-level-maths-tutor.com)

### Question 3

### Edexcel A-Level Maths Paper 2 June 2020

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-24.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-25.png)

[Answer](https://www.youtube.com/watch?v=fVgC1Kx960Y&ref=a-level-maths-tutor.com)

### Question 4

### Edexcel A-Level Maths Paper 1 June 2021

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-26.png)

### Question 5

### Edexcel A-Level Maths Paper 2 June 2021

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-27.png)

### Question 6

### Edexcel A-Level Maths Paper 1 June 2022

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-28.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-29.png)

### Question 7

### Edexcel A-Level Maths Paper 2 June 2022

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-30.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-31.png)

### Question 8

### Edexcel A-Level Maths Paper 2 June 2023

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-32-1.png)

### Question 9

### Edexcel A-Level Maths Paper 2 June 2024

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-33.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-34.png)

---

### A-Level Maths Tutoring

I offer one-to-one and small group A-Level Maths tutoring for students across the UK and internationally. With 94+ five-star Google reviews and tutoring experience since 2017, I specialise in helping students understand difficult concepts and improve their exam technique.

[A-Level Maths Tutoring](https://www.a-level-maths-tutor.com/a-level-maths-tutor/)

[94+ 5-star Google Reviews](https://www.a-level-maths-tutor.com/reviews/)

[Contact Me](https://www.a-level-maths-tutor.com/contact/)

[Back to A-Level Maths Revision](https://www.a-level-maths-tutor.com/a-level-maths-revision/)
### A-Level Maths | Parametric Equations
URL: https://www.a-level-maths-tutor.com/a-level-maths-parametric-equations/
Last updated: 2026-04-23T13:04:46.000Z
### Question 1

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/CleanShot-2026-03-25-at-18.13.52@2x.png)

### Question 2

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/CleanShot-2026-04-06-at-16.04.53@2x.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/CleanShot-2026-04-06-at-16.05.07@2x.png)

### Question 3

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/CleanShot-2026-04-06-at-16.21.46@2x.png)

### Question 4

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/CleanShot-2026-04-06-at-16.25.16@2x.png)

[**Answer (see q1**](https://www.physicsandmathstutor.com/pdf-pages/?pdf=https%3A%2F%2Fpmt.physicsandmathstutor.com%2Fdownload%2FMaths%2FA-level%2FC4%2FWorksheets-Notes%2FSolomon%2FC4%20Integration%20G%20-%20Answers.pdf&ref=a-level-maths-tutor.com)**)**

### Question 5

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-157.png)

[**Answer (see q2)**](https://www.physicsandmathstutor.com/pdf-pages/?pdf=https%3A%2F%2Fpmt.physicsandmathstutor.com%2Fdownload%2FMaths%2FA-level%2FC4%2FWorksheets-Notes%2FSolomon%2FC4%20Integration%20G%20-%20Answers.pdf&ref=a-level-maths-tutor.com)

### Question 6

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/CleanShot-2026-04-06-at-16.26.12@2x.png)

[**Answer (see q3)**](https://www.physicsandmathstutor.com/pdf-pages/?pdf=https%3A%2F%2Fpmt.physicsandmathstutor.com%2Fdownload%2FMaths%2FA-level%2FC4%2FWorksheets-Notes%2FSolomon%2FC4%20Integration%20G%20-%20Answers.pdf&ref=a-level-maths-tutor.com)
### Edexcel AS-Level Maths | Connected Particles
URL: https://www.a-level-maths-tutor.com/edexcel-as-level-maths-connected-particles/
Last updated: 2026-04-23T13:04:27.000Z
### Question 1

### Edexcel AS-Level Maths Paper 2 June 2018

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-4.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-5.png)

### Question 2

### Edexcel AS-Level Maths Paper 2 June 2019

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-6.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-7.png)

### Question 3

### Edexcel AS-Level Maths Paper 2 June 2020

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-8.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-9.png)

### Question 4

### Edexcel AS-Level Maths Paper 2 June 2021

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-11.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-12.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-13.png)

### Question 5

### Edexcel AS-Level Maths Paper 2 June 2022

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-14.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-15.png)

### Question 6

### Edexcel AS-Level Maths Paper 2 June 2023

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-16.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-17.png)

### Question 7

### Edexcel AS-Level Maths Paper 2 June 2024

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-18.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-19.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/image-20.png)

### Question 8

### Edexcel AS-Level Maths Paper 2 June 2025
### Edexcel A-Level Maths | Implicit Differentiation
URL: https://www.a-level-maths-tutor.com/edexcel-a-level-maths-implicit-differentiation/
Last updated: 2026-04-23T13:04:08.000Z
### Question 1

### Edexcel A-Level Maths Paper 1 June 2018

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-78.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-79.png)

### Question 2

### Edexcel A-Level Maths Paper 1 June 2020

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-100.png)

### Question 3

### Edexcel A-Level Maths Paper 2 June 2023

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-129-1.png)

### Question 4

### Edexcel A-Level Maths Paper 2 June 2024

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-145.png)

###
### Edexcel A-Level Maths | Differentiation
URL: https://www.a-level-maths-tutor.com/edexcel-a-level-maths-differentiation/
Last updated: 2026-04-23T13:11:15.000Z
### Question 1

### Edexcel A-Level Maths Paper 1 June 2018

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-76.png)

### Question 2

### Edexcel A-Level Maths Paper 1 June 2018

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-77.png)

### Question 3

### Edexcel A-Level Maths Paper 2 June 2018

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-81.png)

### Question 4

### Edexcel A-Level Maths Paper 2 June 2018

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-84.png)

### Question 5

### Edexcel A-Level Maths Paper 1 June 2019

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-85.png)

### Question 6

### Edexcel A-Level Maths Paper 1 June 2019

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-88.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-89.png)

### Question 7

### Edexcel A-Level Maths Paper 1 June 2019

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-92.png)

### Question 8

### Edexcel A-Level Maths Paper 2 June 2019

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-95.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-96.png)

### Question 9

### Edexcel A-Level Maths Paper 2 June 2020

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-104.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-105.png)

### Question 10

### Edexcel A-Level Maths Paper 2 June 2020

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-108.png)

### Question 11

### Edexcel A-Level Maths Paper 1 June 2021

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-109.png)

### Question 12

### Edexcel A-Level Maths Paper 1 June 2022

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-112.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-113.png)

### Question 13

### Edexcel A-Level Maths Paper 1 June 2022

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-114.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-115.png)

### Question 14

### Edexcel A-Level Maths Paper 2 June 2022

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-118.png)

### Question 15

### Edexcel A-Level Maths Paper 2 June 2022

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-122.png)

### Question 16

### Edexcel A-Level Maths Paper 1 June 2023

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-124.png)

### Question 17

### Edexcel A-Level Maths Paper 1 June 2023

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-125.png)

### Question 18

### Edexcel A-Level Maths Paper 2 June 2023

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-127.png)

### Question 19

### Edexcel A-Level Maths Paper 1 June 2024

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-133.png)

### Question 20

### Edexcel A-Level Maths Paper 1 June 2024

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-134.png)

### Question 21

### Edexcel A-Level Maths Paper 1 June 2024

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-135.png)

### Question 22

### Edexcel A-Level Maths Paper June 2024

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-139.png)

### Question 23

### Edexcel A-Level Maths Paper 2 June 2024

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-140.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-141-1.png)

### Question 24

### Edexcel A-Level Maths Paper 1 June 2025

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-147.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-148.png)

### Question 25

### Edexcel A-Level Maths Paper 1 June 2025

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-150-1-1.png)
### Edexcel A-Level Maths | Integration
URL: https://www.a-level-maths-tutor.com/integration-edexcel-a-level-maths/
Last updated: 2026-04-23T13:03:32.000Z
### Question 1

### Edexcel A-Level Maths Paper 1 June 2018

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-74.png)

### Question 2

### Edexcel A-Level Maths Paper 1 June 2018

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-75.png)

### Question 3

### Edexcel A-Level Maths Paper 2 June 2018

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-82.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-83.png)

### Question 4

### Edexcel A-Level Maths Paper 1 June 2019

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-86.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-87.png)

### Question 5

### Edexcel A-Level Maths Paper 1 June 2019

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-90.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-91.png)

### Question 6

### Edexcel A-Level Maths Paper 2 June 2019

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-93.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-94.png)

### Question 7

### Edexcel A-Level Maths Paper 2 June 2019

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-97.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-98.png)

### Question 8

### Edexcel A-Level Maths Paper 1 June 2020

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-99.png)

### Question 9

### Edexcel A-Level Maths Paper 2 June 2020

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-101.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-102.png)

### Question 10

### Edexcel A-Level Maths Paper 2 June 2020

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-103.png)

### Question 11

### Edexcel A-Level Maths Paper 2 June 2020

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-106.png)

### Question 12

### Edexcel A-Level Maths Paper 2 June 2021

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-110.png)

### Question 13

### Edexcel A-Level Maths Paper 1 June 2

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-111.png)

### Question 14

### Edexcel A-Level Maths Paper 1 June 2022

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-116.png)

### Question 15

### Edexcel A-Level Maths Paper 1 June 2022

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-117-1-1.png)

### Question 16

### Edexcel A-Level Maths Paper 2 June 2022

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-120.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-121.png)

### Question 17

### Edexcel A-Level Maths Paper 1 June 2023

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-123.png)

### Question 18

### Edexcel A-Level Maths Paper 2 June 2023

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-128.png)

### Question 19

### Edexcel A-Level Maths Paper 2 June 2023

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-130-1.png)

### Question 20

### Edexcel A-Level Maths Paper 2 June 2023

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-131.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-132.png)

### Question 21

### Edexcel A-Level Maths Paper 1 June 2024

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-136.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-137.png)

### Question 22

### Edexcel A-Level Maths Paper 1 June 2024

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-138.png)

### Question 23

### Edexcel A-Level Maths Paper 2 June 2024

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-143.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-144.png)

### Question 24

### Edexcel A-Level Maths Paper 1 June 2025

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-146.png)

### Question 25

### Edexcel A-Level Maths Paper 1 June 2025

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-149.png)

### Question 26

### Edexcel A-Level Maths Paper 1 June 2025

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-151.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-152.png)
### Edexcel A-Level Maths | Normal Distribution
URL: https://www.a-level-maths-tutor.com/edexcel-a-level-maths-normal-distribution/
Last updated: 2026-04-23T13:03:17.000Z
### Question 1

### Edexcel A-Level Maths Paper 3 June 2018

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-60.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-61.png)

### Question 2

### Edexcel A-Level Maths Paper 3 June 2019

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-62.png)

### Question 3

### Edexcel A-Level Maths Paper 3 June 2020

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-63.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-64.png)

### Question 4

### Edexcel A-Level Maths Paper 3 June 2021

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-65.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-66.png)

### Question 5

### Edexcel A-Level Maths Paper 3 June 2022

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-67.png)

### Question 6

### Edexcel A-Level Maths Paper 3 June 2022

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-68.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-69.png)

### Question 7

### Edexcel A-Level Maths Paper 3 June 2023

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-70.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-71.png)

### Question 8

### Edexcel A-Level Maths Paper 3 June 2024

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-72.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-73.png)

###
### Revision
URL: https://www.a-level-maths-tutor.com/revision/
Last updated: 2026-03-30T10:44:15.000Z
[GCSE Maths](www.a-level-maths-tutor.com/gcse-maths-revision/)

[A-Level Maths](www.a-level-maths-tutor.com/a-level-maths-revision/)
### Edexcel GCSE Maths | Vectors
URL: https://www.a-level-maths-tutor.com/edexcel-gcse-maths-vectors/
Last updated: 2026-04-23T13:02:40.000Z
### Question 1

![Edexcel GCSE Maths Paper 1 June 2017 (4 marks)](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/CleanShot-2026-03-28-at-11.12.35@2x.png)

Edexcel GCSE Maths Paper 1 June 2017 (4 marks)

### Question 2

![Edexcel GCSE Maths Paper 3 November 2017 (5 marks)](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/CleanShot-2026-03-28-at-11.25.26@2x.png)

Edexcel GCSE Maths Paper 3 November 2017 (5 marks)

### Question 3

![Edexcel GCSE Maths Paper 1 November 2018 (5 marks)](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/CleanShot-2026-03-28-at-11.44.26@2x.png)

Edexcel GCSE Maths Paper 1 November 2018 (5 marks)

### Question 4

![Edexcel GCSE Maths June 2019 Paper 2 (6 marks)](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/CleanShot-2026-03-30-at-11.02.14@2x.png)

Edexcel GCSE Maths June 2019 Paper 2 (6 marks)

![Edexcel GCSE Maths June 2019 Paper 2 (6 marks)](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/CleanShot-2026-03-30-at-11.02.18@2x.png)

Edexcel GCSE Maths Paper 2 June 2019 (6 marks)

### Question 5

### 

![Edexcel GCSE Maths Paper 3 November 2018 (5 marks)](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/CleanShot-2026-03-30-at-11.11.36@2x.png)

Edexcel GCSE Maths Paper 3 November 2018 (5 marks)

### Question 6

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/CleanShot-2026-03-30-at-11.26.05@2x.png)

Edexcel GCSE Maths Paper 1 June 2020 (4 marks)

### Question 7

![Edexcel GCSE Maths Paper 3 November 2021 (4 marks)](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/CleanShot-2026-03-30-at-11.27.39@2x.png)

Edexcel GCSE Maths Paper 3 November 2021 (4 marks)

### Question 8

![Edexcel GCSE Maths Paper 3 November 2022 (4 marks)](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/CleanShot-2026-03-30-at-11.28.58@2x.png)

Edexcel GCSE Maths Paper 3 November 2022 (4 marks)

### Question 9

![Edexcel GCSE Maths Paper 2 June 2023 (4 marks)](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/CleanShot-2026-03-30-at-11.30.48@2x.png)

Edexcel GCSE Maths Paper 2 June 2023 (4 marks)

### Question 10

![Edexcel GCSE Maths Paper 2 November 2023 (4 marks)](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/CleanShot-2026-03-30-at-11.32.55@2x.png)

Edexcel GCSE Maths Paper 2 November 2023 (4 marks)

### 

### Question 11

![Edexcel GCSE Maths Paper 2 June 2024 (5 marks)](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/CleanShot-2026-03-30-at-11.34.32@2x.png)

![Edexcel GCSE Maths Paper 2 June 2024 (5 marks)](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/CleanShot-2026-03-30-at-11.34.44@2x.png)

Edexcel GCSE Maths Paper 2 June 2024 (5 marks)
### Edexcel A-Level Maths | Radians
URL: https://www.a-level-maths-tutor.com/edexcel-a-level-maths-radians/
Last updated: 2026-04-23T13:02:22.000Z
## Trig Modelling

### Question 1

### Edexcel A-Level Maths Paper 1 June 2018

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-39.png)

### Question 2

### Edexcel A-Level Maths Paper 1 June 2018

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-57.png)

### Question 3

### Edexcel A-Level Maths Paper 2 June 2018

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-56.png)

### Question 4

### Edexcel A-Level Maths Paper 2 June 2019

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-41-1.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-42-1.png)

### Question 5

### Edexcel A-Level Maths Paper 1 June 2020

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-58.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-59.png)

### Question 6

### Edexcel A-Level Maths Paper 1 June 2021

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-55.png)

### Question 7

### Edexcel A-Level Maths Paper 2 June 2021

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-43.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-44.png)

### Question 8

### Edexcel A-Level Maths Paper 1 June 2022

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-45.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-46.png)

### Question 9

### Edexcel A-Level Maths Paper 1 June 2023

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-47.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-48.png)

### Question 10

### Edexcel A-Level Maths Paper 1 June 2023

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-54.png)

### Question 11

### Edexcel A-Level Maths Paper 1 June 2024

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-49.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-50.png)

### Question 12

### Edexcel A-Level Maths Paper 1 June 2022

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-51.png)

### Question 13

### Edexcel A-Level Maths Paper 1 June 2025

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-52.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-53.png)

### Question 14

### Edexcel A-Level Maths Paper 2 June 2025
### Edexcel A-Level Maths | Trigonometry
URL: https://www.a-level-maths-tutor.com/edexcel-a-level-maths-trigonometry/
Last updated: 2026-04-23T13:00:19.000Z
## Trig Modelling

### Question 1

### Edexcel A-Level Maths Paper 1 June 2018

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-28.png)

### Question 2

### Edexcel A-Level Maths Paper 2 June 2021

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-29.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-30.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-31.png)

### Question 3

### Edexcel A-Level Maths Paper 2 June 2022

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-32.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-34.png)

### Question 4

### Edexcel A-Level Maths Paper 2 June 2023

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-36.png)

### Question 5

### Edexcel A-Level Maths Paper 1 June 2024

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-37.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-38.png)
### Edexcel A-Level Maths | Differential Equations
URL: https://www.a-level-maths-tutor.com/edexcel-a-level-maths-differential-equations/
Last updated: 2026-05-22T14:41:52.000Z
### Question 1

### Edexcel A-Level Maths Paper 1 June 2018

[![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/02/image-3.png)](https://www.youtube.com/watch?v=1KOy5fvShiQ&pp=ygUrRWRleGNlbCBBLUxldmVsIE1hdGhzIEp1bmUgMjAxOCBQYXBlciAxIFExMA%3D%3D&ref=a-level-maths-tutor.com)

### Question 2

### Edexcel A-Level Maths Paper 2 June 2018

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/02/image-4.png)

### Question 3

### Edexcel A-Level Maths Paper 2 June 2019

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-9.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-10.png)

### Question 4

### Edexcel A-Level Maths Paper 1 June 2020

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-11.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-12.png)

### Question 5

### Edexcel A-Level Maths Paper 2 June 2021

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-13.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-14.png)

### Question 6

### Edexcel A-Level Maths Paper 2 June 2022

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-15.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-16.png)

[Video Solution](https://www.youtube.com/watch?v=8iF7yG216zg&ref=a-level-maths-tutor.com)

### Question 7

### Edexcel A-Level Maths Paper 2 June 2023

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-19.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-18.png)

[Video Solution](https://www.youtube.com/watch?v=kSc9wEIliTw&t=5721s&ref=a-level-maths-tutor.com)

### Question 8

### Edexcel A-Level Maths Paper 1 June 2024

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-20.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-21.png)

### Question 9

### Edexcel A-Level Maths Paper 1 June 2024

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-22.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-23.png)

### Question 10

### Edexcel A-Level Maths Paper 2 June 2024

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-25.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-26.png)

[Video Solution](https://www.youtube.com/watch?v=L-NxJ1oAWw0&t=6s&pp=ygUrcTEyIEVkZXhjZWwgQS1MZXZlbCBNYXRocyBQYXBlciAyIEp1bmUgMjAyNA%3D%3D&ref=a-level-maths-tutor.com)

### Question 11

### Edexcel A-Level Maths Paper 2 June 2025

### 

###
### A-Level Maths | Exponentials & Logs
URL: https://www.a-level-maths-tutor.com/a-level-maths-logs/
Last updated: 2026-09-09T21:10:05.000Z
Rules of Logarithms

$$1.\\ \\log(a)+\\log(b)=\\log(ab)$$ $$2.\\ \\log(a)-\\log(b)=\\log\\left(\\frac{a}{b}\\right)$$ $$3.\\ \\log(a^n) = n\\log(a)$$ $$4.\\ \\log\_a(a) = 1$$ $$5.\\ \\text{If } \\log\_a(x) = 5 \\text{ then } x = a^5$$ 

Power rule

### Question 1

Express in the form $p\\log\_a x$

a) $\\log\_a x^5$

c) $\\log\_a x^7$

d) $\\log\_a x^{-4}$

e) $\\log\_a x^{1/2}$

b) $\\frac{1}{2}\\log\_a x^{15}$

f) $3\\log\_a x^4$

Show Answers 

a) $5\\log\_a x$

c) $7\\log\_a x$

d) $-4\\log\_a x$

e) $\\frac{1}{2}\\log\_a x$

b) $\\frac{15}{2}\\log\_a x$

f) $12\\log\_a x$

Adding and subtracting logs

### Question 2

Simplify each of the following, giving the final answer as a single logarithm.

a) $\\log\_2 7+\\log\_2 2$

b) $\\log\_3 5+\\log\_3 2$

c) $\\log\_2 20-\\log\_2 4$

d) $\\log\_2 24-\\log\_2 8$

e) $\\log\_{10} 8+\\log\_{10} 5-\\log\_{10} 0.5$

f) $\\log\_6 2-(3\\log\_6 3+\\log\_6 0.25)$

Show Answers 

a) $\\log\_2 14$

b) $\\log\_3 10$

c) $\\log\_2 5$

d) $\\log\_2 3$

e) $\\log\_{10} 80$

f) $\\log\_6\\left(\\frac{8}{27}\\right)$

### Question 3

Simplify each of the following, giving the final answer as a single logarithm.

a) $3\\log\_5 2+\\log\_5 8$

b) $3\\log\_4 8-3\\log\_4 6$

c) $2\\log\_6 8-5\\log\_6 2$

Show Answers 

a) $\\log\_5 64$

b) $\\log\_4\\left(\\frac{64}{27}\\right)$

c) $\\log\_6 2$

Solving exponential equations

$$3^x = 11$$ $$x\\log 3 = \\log 11$$ $$x = \\frac{\\log 11}{\\log 3}$$ $$x \\approx 2.18$$ 

### Question 4

Solve each of the following exponential equations.

a) $3^x=11$

b) $4^x=200$

c) $2^x=50$

d) $5^x=30$

e) $4^{y-1}=18$

f) $2^{2z+1}=80$

g) $5^{3w}=30$

h) $12^{3t+4}=75$

Show Answers 

a) $x \\approx 2.18$

b) $x \\approx 3.82$

c) $x \\approx 5.64$

d) $x \\approx 2.11$

e) $y \\approx 3.08$

f) $z \\approx 2.66$

g) $w \\approx 0.704$

h) $t \\approx -0.754$

Solving log equations

### Question 5

Solve each equation, giving your answers correct to 3 significant figures.

a) $\\log\_3 x=1.8$

b) $\\log\_5 x=-0.3$

c) $\\log\_2 x=3.5$

d) $\\log\_7 x=-1.2$

e) $\\log\_4 x=2.6$

f) $\\log\_6 x=0.9$

g) $\\ln x=2.1$

h) $\\ln x=-0.4$

i) $\\ln x=0.7$

j) $\\ln x=3.2$

k) $\\ln x=-1.5$

Show Answers 

a) $x \\approx 7.22$

b) $x \\approx 0.617$

c) $x \\approx 11.3$

d) $x \\approx 0.0968$

e) $x \\approx 36.8$

f) $x \\approx 5.02$

g) $x \\approx 8.17$

h) $x \\approx 0.670$

i) $x \\approx 2.01$

j) $x \\approx 24.5$

k) $x \\approx 0.223$

### Question 6

a) $\\log\_2(x+1)-\\log\_2 x=\\log\_2 3$

b) $\\log\_a x=\\log\_a 3+\\log\_a(2x-1)$

c) $\\log\_a(2x+7)=\\log\_a x+2\\log\_a 3$

d) $\\log\_a(3x+10)-\\log\_a x=2\\log\_a 3$

Show Answers 

a) $x=0.5$

b) $x=0.6$

c) $x=1$

d) $x=\\frac{5}{3}$

### Question 7

a) $\\log\_3(3x+4)-\\log\_3 x=2$

b) $\\log\_5(4x+3)-\\log\_5(x-1)=2$

c) $\\log\_5(4x+7)-\\log\_5 x=2$

d) $\\log\_2(2x+1)=2+\\log\_2 x$

e) $\\log\_3(4x+1)-\\log\_3(x-1)=2$

f) $\\log\_2(3x+4)-\\log\_2 x=3$

Show Answers 

a) $x=\\frac{2}{3}$

b) $x=\\frac{4}{3}$

c) $x=\\frac{1}{3}$

d) $x=\\frac{1}{2}$

e) $x=2$

f) $x=\\frac{4}{5}$

Modelling with logs

### Question 8

The value of a rare painting, $V$ pounds, is modelled by $V = pq^t$, where $p$ and $q$ are constants and $t$ is the number of years since the value was first recorded on 1st January 1980.

a) Write $V = pq^t$ in the form $y = mx + c$.

b) The gradient of the line is $0.05$ and the $y$-intercept is $4.8$. Find the value of $p$ and the value of $q$, each to 4 significant figures.

Show Answers 

a) $\\log\_{10}V = t\\log\_{10}q + \\log\_{10}p$

b) $\\log\_{10}p = 4.8 \\implies p = 63100$ (4 s.f.). $\\log\_{10}q = 0.05 \\implies q = 1.122$ (4 s.f.).

### Question 9

The total number of views, $V$, of an online advert in the first $t$ days is modelled by $V = ab^t$, where $a$ and $b$ are constants.

a) Write $V = ab^t$ in the form $y = mx + c$.

b) The gradient of the line is $0.072$ and the $y$-intercept is $2.379$. Find $a$ to the nearest whole number and $b$ to 3 significant figures.

Show Answers 

a) $\\log\_{10}V = t\\log\_{10}b + \\log\_{10}a$

b) $\\log\_{10}a = 2.379 \\implies a = 239$ (nearest whole number). $\\log\_{10}b = 0.072 \\implies b = 1.18$ (3 s.f.).

### Question 10

The resting heart rate, $h$ beats per minute, of a mammal is modelled by $h = pm^q$, where $p$ and $q$ are constants and $m$ is the mass of the mammal in kg.

a) Write $h = pm^q$ in the form $y = mx + c$.

b) The gradient of the line is $-0.235$ and the $y$-intercept is $2.25$. Find the value of $p$ and the value of $q$, each to 3 significant figures.

Show Answers 

a) $\\log\_{10}h = q\\log\_{10}m + \\log\_{10}p$

b) $q = -0.235$ (3 s.f.). $\\log\_{10}p = 2.25 \\implies p = 178$ (3 s.f.).

---

### A-Level Maths Tutoring

I offer one-to-one and small group A-Level Maths tutoring for students across the UK and internationally. With 94+ five-star Google reviews and tutoring experience since 2017, I specialise in helping students understand difficult concepts and improve their exam technique.

[A-Level Maths Tutoring](https://www.a-level-maths-tutor.com/a-level-maths-tutor/)

[94+ 5-star Google Reviews](https://www.a-level-maths-tutor.com/reviews/)

[Contact Me](https://www.a-level-maths-tutor.com/contact/)

[Back to A-Level Maths Revision](https://www.a-level-maths-tutor.com/a-level-maths-revision/)
### A-Level Maths | Binomial Distribution
URL: https://www.a-level-maths-tutor.com/a-level-maths-binomial-distribution/
Last updated: 2026-07-22T11:51:23.000Z
A binomial distribution models the number of successes in a fixed number of independent trials, where each trial has only two possible outcomes: success or failure.

$X \\sim B(n, p)$ means we are modelling the distribution $X$ binomially, where:

$n$: the number of trials

$p$: the probability of success on each trial

If $X \\sim B(n,p)$, then $P(X=r) = \\dbinom{n}{r}p^r(1-p)^{n-r}$

**Worked Example**

$X \\sim B(10, 0.3)$. Find $P(X=4)$.

$P(X=4) = \\dbinom{10}{4}(0.3)^4(0.7)^6 = 0.2001$

## Question 1

$X \\sim B(20, 0.4)$

**a)** Find $P(X=3)$

**b)** Find $P(X=6)$

**c)** Find $P(X=9)$

**d)** Find $P(X=12)$

**e)** Find $P(X=15)$

Show Answers 

**a)** $0.0123$

**b)** $0.1244$

**c)** $0.1597$

**d)** $0.0355$

**e)** $0.0013$

## Question 2

$X \\sim B(25, 0.35)$

**a)** Find $P(X \\leq 4)$

**b)** Find $P(X \\leq 7)$

**c)** Find $P(X \\leq 9)$

**d)** Find $P(X \\leq 12)$

**e)** Find $P(X \\leq 15)$

Show Answers 

**a)** $0.0320$

**b)** $0.3061$

**c)** $0.6303$

**d)** $0.9396$

**e)** $0.9971$

**Worked Example**

$X \\sim B(18, 0.25)$. Find $P(X < 7)$.

$P(X < 7) = P(X \\leq 6) = 0.8610$

## Question 3

$X \\sim B(30, 0.3)$

**a)** Find $P(X < 5)$

**b)** Find $P(X < 8)$

**c)** Find $P(X < 10)$

**d)** Find $P(X < 13)$

**e)** Find $P(X < 16)$

Show Answers 

**a)** $0.0302$

**b)** $0.2814$

**c)** $0.5888$

**d)** $0.9155$

**e)** $0.9936$

**Worked Example**

$X \\sim B(18, 0.25)$. Find $P(X \\geq 7)$.

$P(X \\geq 7) = 1 - P(X \\leq 6) = 1 - 0.8610 = 0.1390$

## Question 4

$X \\sim B(20, 0.4)$

**a)** Find $P(X \\geq 5)$

**b)** Find $P(X \\geq 8)$

**c)** Find $P(X \\geq 10)$

**d)** Find $P(X \\geq 13)$

**e)** Find $P(X \\geq 16)$

Show Answers 

**a)** $0.9490$

**b)** $0.5841$

**c)** $0.2447$

**d)** $0.0210$

**e)** $0.0003$

## Left tail hypothesis testing

### Question 5

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/CleanShot-2026-04-14-at-12.11.51@2x.png)

### Question 6

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/CleanShot-2026-04-14-at-12.12.21@2x-1.png)

### Question 7

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/CleanShot-2026-04-14-at-12.12.28@2x.png)

### Question 8

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/CleanShot-2026-04-14-at-12.12.40@2x.png)

## Right tail hypothesis testing

### Question 9

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/CleanShot-2026-04-14-at-12.13.50@2x.png)

### Question 10

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/CleanShot-2026-04-14-at-12.13.56@2x.png)

### Question 11

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/CleanShot-2026-04-14-at-12.14.01@2x.png)

### Question 12

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/CleanShot-2026-04-14-at-12.14.06@2x.png)

## Two-tail hypothesis testing

### Question 13

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/CleanShot-2026-04-14-at-12.14.42@2x.png)

### Question 14

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/CleanShot-2026-04-14-at-12.14.49@2x.png)

## Left tail hypothesis test critical values

### Left tail

### Question 15

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/CleanShot-2026-04-14-at-13.08.39@2x.png)

## Right tail hypothesis test critical values

### Question 16

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/CleanShot-2026-04-14-at-13.09.43@2x.png)

## Two-tail hypothesis test critical values

### Question 17

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/CleanShot-2026-04-14-at-13.09.55@2x.png)

### Question 18

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/CleanShot-2026-04-14-at-13.10.07@2x.png)

### Question 19

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/04/CleanShot-2026-04-14-at-13.10.12@2x.png)

---

### A-Level Maths Tutoring

I offer one-to-one and small group **A-Level Maths tutoring** for students across the UK and internationally. With 94+ five-star Google reviews and tutoring experience since 2017, I specialise in helping students understand difficult concepts and improve their exam technique.

[A-Level Maths Tutoring](https://www.a-level-maths-tutor.com/a-level-maths-tutor/)

[94+ 5-star Google Reviews](https://www.a-level-maths-tutor.com/reviews/)

[Contact Me](https://www.a-level-maths-tutor.com/contact/)

[Back to A-Level Maths Revision](https://www.a-level-maths-tutor.com/a-level-maths-revision/)
### A-Level Maths | Normal Distribution
URL: https://www.a-level-maths-tutor.com/a-level-maths-normal-distribution/
Last updated: 2026-04-23T10:59:53.000Z
## Normal Distribution

### Question 1

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/02/CleanShot-2026-02-16-at-15.47.04@2x.png)

### Question 2

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/02/CleanShot-2026-02-16-at-15.49.00@2x.png)

### Question 3

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/02/CleanShot-2026-02-16-at-15.51.04@2x.png)

## Inverse normal

### Question 4

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/02/CleanShot-2026-02-16-at-15.53.32@2x.png)

### Question 5

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/02/CleanShot-2026-02-16-at-15.53.42@2x.png)

### Question 6

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/02/CleanShot-2026-02-16-at-15.54.47@2x.png)

## Standard normal

### Question 7

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/02/CleanShot-2026-02-16-at-15.57.20@2x.png)

### Question 8

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/02/CleanShot-2026-02-16-at-16.04.03@2x.png)

### Question 9

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/CleanShot-2026-03-20-at-14.04.18@2x.png)

### Question 10

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/CleanShot-2026-03-20-at-14.04.53@2x.png)

### Question 11

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/CleanShot-2026-03-20-at-14.05.40@2x-1.png)

## Hypothesis Testing

### Question 12

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/CleanShot-2026-03-23-at-13.46.05@2x.png)

### Question 13

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/CleanShot-2026-03-23-at-13.54.09@2x.png)

### Question 14

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/CleanShot-2026-03-23-at-14.08.01@2x.png)

### Question 15

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/CleanShot-2026-03-23-at-14.08.43@2x.png)

## Binomial approximations

### Question 16

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/CleanShot-2026-03-20-at-14.07.07@2x.png)

### Question 17

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/CleanShot-2026-03-20-at-14.07.12@2x.png)

### Question 18

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/CleanShot-2026-03-20-at-14.07.19@2x.png)

### Question 19

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/CleanShot-2026-03-20-at-14.07.56@2x.png)
### A-Level Maths | Differential Equations
URL: https://www.a-level-maths-tutor.com/a-level-maths-differential-equations/
Last updated: 2026-04-23T10:59:42.000Z
### Question 1

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/02/CleanShot-2026-02-27-at-14.51.16@2x.png)

### Question 2

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/02/CleanShot-2026-02-27-at-14.58.04@2x.png)

### Question 3

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/02/CleanShot-2026-02-27-at-15.01.42@2x.png)
### A-Level Maths | Friction
URL: https://www.a-level-maths-tutor.com/a-level-maths-friction/
Last updated: 2026-04-23T10:58:50.000Z
### Question 1

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-3.png)

### Question 2

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-4.png)

### Question 3

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-5.png)
### A-Level Maths
URL: https://www.a-level-maths-tutor.com/a-level-maths-revision/
Last updated: 2026-09-12T10:57:52.000Z
### Year 12 Pure

1. Indices | [Revision](https://www.a-level-maths-tutor.com/a-level-maths-indices/)
2. Quadratics | [Revision](https://www.a-level-maths-tutor.com/a-level-maths-quadratics/) | [Edexcel AS](https://www.a-level-maths-tutor.com/edexcel-as-level-maths-quadratics/) | [Edexcel AS](https://www.a-level-maths-tutor.com/edexcel-a-level-maths-quadratics/)
3. Graphs & Transformations | [Revision](https://www.a-level-maths-tutor.com/a-level-maths-graphs-transformations/) | [Edexcel AS](https://www.a-level-maths-tutor.com/edexcel-as-level-maths-graphs-transformations/)
4. Co-ordinate Geometry | [Revision](https://www.a-level-maths-tutor.com/a-level-maths-coordinate-geometry/) | [Edexcel AS](https://www.a-level-maths-tutor.com/edexcel-as-level-maths-coordinate-geometry/)
5. Cubics | [Revision](https://www.a-level-maths-tutor.com/a-level-maths-cubics/)
6. Binomial Expansion | [Revision](https://www.a-level-maths-tutor.com/as-level-maths-binomial-expansion/)
7. Trigonometry of any Triangle | Revision | [Edexcel AS](https://www.a-level-maths-tutor.com/edexcel-as-level-maths-trigonometry-any-triangle/)
8. Trigonometry | [Revision](https://www.a-level-maths-tutor.com/as-level-maths-trigonometry/) | [Edexcel AS](https://www.a-level-maths-tutor.com/edexcel-as-level-maths-trigonometry/)
9. Differentiation | [Revision](https://www.a-level-maths-tutor.com/as-level-maths-differentiation/)
10. Integration | [Revision](https://www.a-level-maths-tutor.com/as-level-maths-integration/)
11. Exponentials | [Revision](https://www.a-level-maths-tutor.com/a-level-maths-logs/) | [Edexcel AS](https://www.a-level-maths-tutor.com/exponential-modelling-edexcel-as-level-maths/)
12. Logs | [Revision](https://www.a-level-maths-tutor.com/a-level-maths-logs/) | [Edexcel AS](https://www.a-level-maths-tutor.com/logs-edexcel-as-level-maths/)
13. Vectors

### Year 13 Pure

1. Functions | [Revision](https://www.a-level-maths-tutor.com/a-level-maths-functions/) | [Edexcel](https://www.a-level-maths-tutor.com/functions-edexcel-a-level-maths/)
2. Partial Fractions | [Revision](https://www.a-level-maths-tutor.com/a-level-maths-partial-fractions/)
3. Proof | Revision
4. Sequences and Series | [Revision](https://www.a-level-maths-tutor.com/a-level-maths-sequences-series/) | [Edexcel](https://www.a-level-maths-tutor.com/edexcel-a-level-maths-sequences-series/)
5. Binomial Expansion | [Revision](https://www.a-level-maths-tutor.com/a-level-maths-binomial-expansion/)
6. Radians | [Revision](https://www.a-level-maths-tutor.com/a-level-maths-radians/) | [Edexcel](https://www.a-level-maths-tutor.com/edexcel-a-level-maths-radians/)
7. Trigonometry | Revision | [Edexcel](https://www.a-level-maths-tutor.com/edexcel-a-level-maths-trigonometry/)
8. Differentiation | Revision | [Edexcel](https://www.a-level-maths-tutor.com/edexcel-a-level-maths-differentiation/)
9. Implicit differentiation | [Revision](https://www.a-level-maths-tutor.com/a-level-maths-implicit-differentiation/) | [Edexcel](https://www.a-level-maths-tutor.com/edexcel-a-level-maths-implicit-differentiation/)
10. Integration | [Revision](https://www.a-level-maths-tutor.com/a-level-maths-integration/) | [Edexcel](https://www.a-level-maths-tutor.com/integration-edexcel-a-level-maths/)
11. Differential equations | [Revision](https://www.a-level-maths-tutor.com/a-level-maths-differential-equations/) | [Edexcel](https://www.a-level-maths-tutor.com/edexcel-a-level-maths-differential-equations/)
12. Parametric equations | [Revision](https://www.a-level-maths-tutor.com/a-level-maths-parametric-equations/) | [Edexcel](https://www.a-level-maths-tutor.com/edexcel-a-level-maths-parametric-equations/)
13. Numerical methods | Revision
14. Vectors | Revision

## Year 12 Statistics

1. Probability | [Revision](https://www.a-level-maths-tutor.com/as-level-maths-probability/) | Edexcel
2. Probability distribution | [Revision](https://www.a-level-maths-tutor.com/a-level-maths-probability-distribution/) | Edexcel
3. Binomial distribution | [Revision](https://www.a-level-maths-tutor.com/a-level-maths-binomial-distribution/) | Edexcel

## Year 12 Mechanics

1. Constant acceleration | [Revision](https://www.a-level-maths-tutor.com/a-level-maths-constant-acceleration/) | Edexcel
2. Connected particles | [Revision](https://www.a-level-maths-tutor.com/as-level-maths-connected-particles/) | [Edexcel](https://www.a-level-maths-tutor.com/edexcel-as-level-maths-connected-particles/)
3. Variable acceleration | Revision | Edexcel
4. Vector applications | Revision | Edexcel

## Year 13 Statistics

1. Measures of location and spread | Revision | [Edexcel](https://www.a-level-maths-tutor.com/edexcel-a-level-maths-measures-of-location-spread/)
2. Correlation | Revision | [Edexcel](https://www.a-level-maths-tutor.com/edexcel-a-level-maths-correlation/)
3. Binomial Distribution | [Revision](https://www.a-level-maths-tutor.com/a-level-maths-binomial-distribution/) | [Edexcel](https://www.a-level-maths-tutor.com/edexcel-a-level-maths-binomial-distribution/)
4. Probability Distribution | [Revision](https://www.a-level-maths-tutor.com/a-level-maths-probability-distribution/) | [Edexcel](https://www.a-level-maths-tutor.com/edexcel-a-level-maths-probability-distribution/)
5. Normal Distribution | [Revision](https://www.a-level-maths-tutor.com/a-level-maths-normal-distribution/) | [Edexcel](https://www.a-level-maths-tutor.com/edexcel-a-level-maths-normal-distribution/)
6. Probability | [Revision](https://www.a-level-maths-tutor.com/a-level-maths-probability/) | [Edexcel](https://www.a-level-maths-tutor.com/edexcel-a-level-maths-probability/)

## Year 13 Mechanics

1. Forces | [Edexcel](https://www.a-level-maths-tutor.com/edexcel-a-level-maths-forces/)
2. Vector Applications | [Edexcel](https://www.a-level-maths-tutor.com/edexcel-a-level-maths-vector-applications/)
3. Projectiles | [Edexcel](https://www.a-level-maths-tutor.com/edexcel-a-level-maths-projectiles/)
4. Moments | [Edexcel](https://www.a-level-maths-tutor.com/edexcel-a-level-maths-moments/)
5. Other | [Edexcel](https://www.a-level-maths-tutor.com/edexcel-a-level-maths-mechanics-other/)

---

### A-Level Maths Tutoring

I offer one-to-one and small group A-Level Maths tutoring for students across the UK and internationally. With 94+ five-star Google reviews and tutoring experience since 2017, I specialise in helping students understand difficult concepts and improve their exam technique.

[A-Level Maths Tutoring](https://www.a-level-maths-tutor.com/a-level-maths-tutor/)

[94+ 5-star Google Reviews](https://www.a-level-maths-tutor.com/reviews/)

[Contact Me](https://www.a-level-maths-tutor.com/contact/)

[Back to A-Level Maths Revision](https://www.a-level-maths-tutor.com/a-level-maths-revision/)
### A-Level Maths | Probability
URL: https://www.a-level-maths-tutor.com/a-level-maths-probability/
Last updated: 2026-04-23T10:58:27.000Z
### What does P(A) mean?

P(A) is the probability of A happening

### What does P(A') mean?

P(A') is the probability of A not happening

### What does P(A∩B) mean?

P(A∩B) is the probability of A and B happening

### What does P(AUB) mean?

P(AUB) is the probability of only A happening, or only B happening, or both A and B happening

### What does P(A|B) mean?

 P(A|B) is the probability of A happening given that we know B is also happening.

### What does independent mean?

A and B are independent if **P(A∩B) = P(A) x P(B)**

### What does mutually exclusive mean?

A and B are mutually exclusive if **P(A∩B) = 0**

## Venn Diagrams

### Question 1

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/02/CleanShot-2026-02-13-at-13.40.36@2x.png)

### Question 2

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/02/CleanShot-2026-02-13-at-13.41.17@2x.png)

### Question 3

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/02/CleanShot-2026-02-13-at-13.41.45@2x.png)

## Conditional Probability in Venn Diagrams

### Question 4

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/02/CleanShot-2026-02-13-at-13.46.16@2x.png)

### Question 5

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/02/image-1.png)

### Question 6

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/02/CleanShot-2026-02-13-at-13.47.11@2x.png)

## Probability Tree Diagrams

### Question 8

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/02/CleanShot-2026-02-13-at-13.53.53@2x.png)

### Question 9

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/02/CleanShot-2026-02-13-at-13.55.38@2x.png)

### Question 10

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/02/CleanShot-2026-02-13-at-13.56.19@2x.png)

## Conditional Probability in Tree Diagrams

### What is the formula for P(A|B)?

**P(A|B) = P(A∩B)/P(B)**

### Question 13

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/02/CleanShot-2026-02-13-at-13.58.59@2x.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/02/CleanShot-2026-02-13-at-13.59.15@2x.png)

### Question 14

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/02/CleanShot-2026-02-13-at-13.59.34@2x.png)

### Question 15

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/02/CleanShot-2026-02-13-at-13.59.59@2x.png)

### Question 16

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/02/CleanShot-2026-02-13-at-14.00.12@2x.png)
### AS-Level Maths| Connected Particles
URL: https://www.a-level-maths-tutor.com/as-level-maths-connected-particles/
Last updated: 2026-09-11T17:19:35.000Z
## Vertical pulleys

### Question 1

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/02/image-5.png)

Show Answers — Question 1 

a) $T = 33.6$ N

b) $a = 1.4$ ms⁻²

### Question 2

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/09/CleanShot-2026-09-11-at-15.37.49@2x.png)

Show Answers — Question 2 

a) $T = \\dfrac{12g}{7} = 16.8$ N

b) $m = 1.2$

### Question 3

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/02/image-7.png)

Show Answers — Question 3 

a) Using $s = \\frac{1}{2}at^2$: $2.5 = \\frac{1}{2} \\times a \\times 1.25^2 \\implies a = 3.2$ ms⁻²

b) $T = 39.0$ N

c) For $A$: $mg - T = ma \\implies m(9.8-3.2) = 39 \\implies m = \\dfrac{65}{11}$

### Question 4

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/02/image-6.png)

Show Answers — Question 4 

a) $T = 2mg$

b) For $P$: $T - kmg = km \\cdot \\dfrac{g}{3} \\implies 2mg = \\dfrac{4kmg}{3} \\implies k = 1.5$

## Horizontal pulleys

### Question 5

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/02/image-8.png)

Show Answers — Question 5 

a) $a = 2.0$ ms⁻²

b) $T = 14.0$ N

### Question 6

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/02/image-9.png)

Show Answers — Question 6 

a) Net force $= 1200 - 200 - 100 = 900$ N, total mass $= 1200$ kg, $a = \\dfrac{900}{1200} = 0.75$ ms⁻²

b) $T = 325$ N

### Question 7

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/02/image-10.png)

Show Answers — Question 7 

a) $a = 0.7$ ms⁻²

b) $T = 770$ N

## Mixed pulleys

### Question 8

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/09/CleanShot-2026-09-11-at-15.31.22@2x-1.png)

Show Answers — Question 8 

a) i) $a \\approx 2.84$ ms⁻²

a) ii) $T = 1.5g - 1.5a = 1.5(9.8) - 1.5(2.84) \\approx 10.4$ N

a) iii) $k \\approx 3.32$ N

### Question 9

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/09/CleanShot-2026-09-11-at-15.46.05@2x.png)

## 

Show Answers — Question 9 

a) $a = 3.2$ ms⁻²

b) $T = 5.28$ N

c) $F = 3.68$ N

---

### A-Level Maths Tutoring

I offer one-tQuestion 7o-one and small group A-Level Maths tutoring for students across the UK and internationally. With 94+ five-star Google reviews and tutoring experience since 2017, I specialise in helping students understand difficult concepts and improve their exam technique.

[A-Level Maths Tutoring](https://www.a-level-maths-tutor.com/a-level-maths-tutor/)

[94+ 5-star Google Reviews](https://www.a-level-maths-tutor.com/reviews/)

[Contact Me](https://www.a-level-maths-tutor.com/contact/)

[Back to A-Level Maths Revision](https://www.a-level-maths-tutor.com/a-level-maths-revision/)