GCSE Maths

GCSE Maths | Circle Theorems

1. The angle between a tangent and radius is always 90o 2. The angle at the centre is always double the angle at the circumference 3. The angle formed by a semi circle is always 900. 4. Opposite angles in a cyclic quadrilateral add up to 180o. 5. Two angles

GCSE Maths

GCSE Maths | Functions

Functions Question 1 Given $f(x) = 3x + 5$, work out the values of a) $f(2)$ b) $f(8)$ c) $f(0)$ d) $f(-2)$ Show Answers a) $11$ b) $29$ c) $5$ d) $-1$ Question 2 Given $h(x) = x^2 - 5$, work out the values of a) $h(

GCSE Maths

GCSE Maths | Algebraic Fractions

Simplifying algebraic fractions Question 1 Simplify each of the following. a) $\dfrac{42xyz}{56}$ b) $\dfrac{45ab}{60abc}$ c) $\dfrac{16mn}{18n}$ d) $\dfrac{40x^2y}{32xy}$ e) $\dfrac{17cf}{34c^3}$ f) $\dfrac{8x^4}{2x^2}$ g) $\dfrac{33a^2b^2}{44a^3b}$ h) $\dfrac{12x^3}{20x^

GCSE Maths

GCSE Maths | Algebra

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)

GCSE Maths

GCSE Maths | Trigonometry

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 Show Answers a) $x = 6.39$ cm b) $x = 6.65$ cm c) $x = 60.5$ mm Question 2 - finding an angle using the

GCSE Maths

GCSE Maths | Surds

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}

GCSE Maths

GCSE Maths | Ratios

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)

GCSE Maths

GCSE Maths | Compound Interest

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.

GCSE Maths

GCSE Maths | Percentages

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:

GCSE Maths

Probability Tree Diagrams | GCSE Maths

Question 1 Question 2 Question 3 Question 4 Question 5 Question 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

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GCSE Maths | Quadratic Simultaneous Equations

Question 1 Question 2

GCSE Maths