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GCSE Maths Practice Questions

Practice exam-style questions covering all GCSE Maths topics. Each question includes detailed step-by-step solutions.

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Question 1
Algebra Easy

Solve the equation: 3x + 7 = 22

Solution:
  1. Subtract 7 from both sides:
    3x + 7 - 7 = 22 - 7
    3x = 15
  2. Divide both sides by 3:
    x = 15 ÷ 3
    x = 5
Answer: x = 5
Question 2
Geometry Medium

A circle has a radius of 8 cm. Calculate the area of the circle.

Give your answer in terms of π.

Solution:
  1. Formula for area of a circle: A = πr²
  2. Where r = radius = 8 cm
  3. Substitute the values:
    A = π × 8²
    A = π × 64
    A = 64π cm²
Answer: 64π cm²
Question 3
Number Easy

Calculate 15% of 240

Solution:
  1. Convert percentage to decimal: 15% = 0.15
  2. Multiply by the number:
    0.15 × 240 = 36
Answer: 36
Question 4
Algebra Medium

Expand and simplify: (x + 3)(x + 5)

Solution:
  1. Use FOIL method (First, Outer, Inner, Last):
  2. First: x × x = x²
  3. Outer: x × 5 = 5x
  4. Inner: 3 × x = 3x
  5. Last: 3 × 5 = 15
  6. Combine: x² + 5x + 3x + 15
  7. Simplify: x² + 8x + 15
Answer: x² + 8x + 15
Question 5
Geometry Hard

A right-angled triangle has sides of 5 cm and 12 cm.

Calculate the length of the hypotenuse.

Solution:
  1. Use Pythagoras' theorem: a² + b² = c²
  2. Where a = 5 cm, b = 12 cm, c = hypotenuse
  3. Substitute:
    5² + 12² = c²
    25 + 144 = c²
    169 = c²
  4. Take square root of both sides:
    c = √169
    c = 13 cm
Answer: 13 cm
Question 6
Statistics Medium

Find the mean of the following numbers:

12, 15, 18, 20, 25

Solution:
  1. Add all the numbers together:
    12 + 15 + 18 + 20 + 25 = 90
  2. Count how many numbers there are: 5 numbers
  3. Divide the total by the count:
    Mean = 90 ÷ 5 = 18
Answer: 18
Question 7
Number Medium

Simplify the fraction: 36/48

Solution:
  1. Find the highest common factor (HCF) of 36 and 48:
  2. Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
  3. Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
  4. HCF = 12
  5. Divide both numerator and denominator by 12:
    36 ÷ 12 = 3
    48 ÷ 12 = 4
Answer: 3/4
Question 8
Algebra Hard

Solve the simultaneous equations:

2x + y = 10

x - y = 2

Solution:
  1. Add the two equations together to eliminate y:
    (2x + y) + (x - y) = 10 + 2
    3x = 12
  2. Solve for x:
    x = 12 ÷ 3
    x = 4
  3. Substitute x = 4 into the second equation:
    4 - y = 2
    -y = 2 - 4
    -y = -2
    y = 2
Answer: x = 4, y = 2
Question 9
Geometry Medium

Calculate the volume of a cylinder with radius 5 cm and height 10 cm.

Give your answer in terms of π.

Solution:
  1. Formula for volume of a cylinder: V = πr²h
  2. Where r = 5 cm, h = 10 cm
  3. Substitute the values:
    V = π × 5² × 10
    V = π × 25 × 10
    V = 250π cm³
Answer: 250π cm³
Question 10
Number Hard

A shirt costs £45 after a 25% discount.

What was the original price?

Solution:
  1. If there's a 25% discount, the sale price is 75% of the original price
  2. Let original price = x
  3. Set up equation: 0.75x = 45
  4. Divide both sides by 0.75:
    x = 45 ÷ 0.75
    x = 60
  5. Check: 75% of £60 = 0.75 × 60 = £45 ✓
Answer: £60