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GCSE Maths mock exam Free full practice test

Written by STEM-Tutor's tutors · Updated October 2026 · 30 questions and 4 exam-style questions · about 85 minutes

A full-length practice test built from our exam-style questions on every topic of GCSE Maths. Each answer is marked as you go, and every question has a worked solution to open afterwards.

On this page
  1. Before you start
  2. Section I
  3. Section II
  4. After the mock

Before you start

Section I: 30 exam-style questions

Q1Exam-style
A price rises from £80 to £92. Work out the percentage increase.
%

Hint

Divide the increase by the original price.

Worked solution
  1. Increase = 92 − 80 = 12.
  2. 12 ÷ 80 × 100 = 15%.
Q2Exam-style
Work out 23 × 25 ÷ 24.

Hint

Add the powers when multiplying, subtract when dividing.

Worked solution
  1. 23 + 5 − 4 = 24.
  2. = 16.
Q3Exam-style
After a 20% increase, a jacket costs £96. What was the price before the increase?
£

Hint

A 20% increase means multiplying by 1.2. Undo it.

Worked solution
  1. Original × 1.2 = 96.
  2. Original = 96 ÷ 1.2 = 80, so £80.
Q4Exam-styleHigher
Simplify √50 + √18, writing your answer as a√2. What is a?

Hint

Find square factors: 50 = 25 × 2 and 18 = 9 × 2.

Worked solution
  1. √50 = 5√2 and √18 = 3√2.
  2. 5√2 + 3√2 = 8√2, so a = 8.
Q5ChallengeHigher
A rectangle is 12 cm long and 5 cm wide, each measured to the nearest centimetre. Work out the upper bound of its area.
cm²

Hint

The upper bounds are half a unit above each measurement.

Worked solution
  1. Upper bounds: 12.5 cm and 5.5 cm.
  2. Upper bound of area = 12.5 × 5.5 = 68.75 cm².
Q6Exam-style
Solve 5(x − 2) = 2x + 11.

Hint

Expand the bracket first.

Worked solution
  1. 5x − 10 = 2x + 11.
  2. 3x = 21.
  3. x = 7.
Q7Exam-style
Solve the simultaneous equations 2x + y = 11 and x − y = 1. What is x?

Hint

Add the equations to eliminate y.

Worked solution
  1. Adding: 3x = 12, so x = 4.
  2. Then y = 3. So x = 4.
Q8Exam-style
Find the gradient of the straight line through (1, 3) and (4, 12).

Hint

Change in y divided by change in x.

Worked solution
  1. (12 − 3)/(4 − 1) = 9/3.
  2. Gradient = 3.
Q9Exam-styleHigher
Solve x2 − 4x − 7 = 0, giving the positive solution to 2 decimal places.

Hint

It does not factorise. Use the quadratic formula with a = 1, b = −4, c = −7.

Worked solution
  1. x = (4 ± √(16 + 28))/2 = (4 ± √44)/2.
  2. x = (4 + 6.633)/2 = 5.32 (the other solution is −1.32).
Q10ChallengeHigher
Solve (x + 3)/2 + (x − 1)/3 = 4.

Hint

Multiply every term by 6 to clear the fractions.

Worked solution
  1. 3(x + 3) + 2(x − 1) = 24.
  2. 3x + 9 + 2x − 2 = 24, so 5x = 17.
  3. x = 3.4.
Q11Exam-style
A recipe uses 250 g of flour for 10 biscuits. How much flour is needed for 24 biscuits?
g

Hint

Find the flour for one biscuit, then scale up.

Worked solution
  1. 250 ÷ 10 = 25 g per biscuit.
  2. 25 × 24 = 600 g.
Q12Exam-style
£2000 is invested at 3% compound interest a year. How much is it worth after 4 years, to the nearest penny?
£

Hint

Multiply by 1.03 once for each year.

Worked solution
  1. 2000 × 1.034 = 2000 × 1.12551.
  2. = 2251.02, so £2251.02.
Q13Exam-style
6 workers take 10 days to build a wall. How long would 4 workers take, working at the same rate?
days

Hint

Fewer workers take longer: this is inverse proportion.

Worked solution
  1. Total work = 6 × 10 = 60 worker-days.
  2. 60 ÷ 4 = 15 days.
Q14Exam-style
A metal block has a mass of 540 g and a volume of 200 cm³. Work out its density.
g/cm³

Hint

Density = mass ÷ volume.

Worked solution
  1. 540 ÷ 200 = 2.7 g/cm³.
Q15ChallengeHigher
a : b = 3 : 4 and b : c = 2 : 5. If a = 12, find c.

Hint

Make the b parts match: write b : c as 4 : 10.

Worked solution
  1. b : c = 2 : 5 = 4 : 10, so a : b : c = 3 : 4 : 10.
  2. a = 12 means 1 part = 4, so c = 10 × 4 = 40.
Q16Exam-style
A right-angled triangle has shorter sides of 9 cm and 12 cm. Find the hypotenuse.
cm

Hint

Use Pythagoras' theorem.

Worked solution
  1. c2 = 92 + 122 = 225.
  2. c = 15 cm.
Q17Exam-style
In a right-angled triangle the hypotenuse is 10 cm and one angle is 35°. Find the side opposite the 35° angle, to 3 significant figures.
cm

Hint

Opposite and hypotenuse: use sine.

Worked solution
  1. sin 35° = opp/10.
  2. opp = 10 × sin 35° = 5.74 cm.
Q18Exam-style
Find the volume of a cylinder with radius 3 cm and height 10 cm, to 1 decimal place.
cm³

Hint

V = πr2h.

Worked solution
  1. V = π × 9 × 10 = 90π.
  2. V = 282.7 cm³.
Q19Exam-style
Find the size of each interior angle of a regular hexagon.
°

Hint

Each exterior angle is 360° ÷ 6.

Worked solution
  1. Exterior angle = 60°.
  2. Interior angle = 180 − 60 = 120°.
Q20ChallengeHigher
Two sides of a triangle are 7 cm and 9 cm, with an angle of 60° between them. Find the third side, to 3 significant figures.
cm

Hint

Two sides and the angle between them: use the cosine rule.

Worked solution
  1. a2 = 72 + 92 − 2 × 7 × 9 × cos 60° = 49 + 81 − 63 = 67.
  2. a = √67 = 8.19 cm.
Q21Exam-style
A and B are independent, with P(A) = 0.3 and P(B) = 0.6. Find P(A and B).

Hint

Multiply for independent events.

Worked solution
  1. 0.3 × 0.6 = 0.18.
Q22Exam-style
A bag has 3 red and 5 blue counters. Two are taken without replacement. What is the probability that both are red?

Hint

After the first red is taken, there are 2 red left out of 7.

Worked solution
  1. P = 3/8 × 2/7 = 6/56.
  2. = 3/28 (about 0.107).
Q23Exam-style
In a class of 30, 18 play football, 12 play tennis and 5 play both. A student is picked at random. What is the probability they play neither?

Hint

Draw a Venn diagram, starting with the 5 in the overlap.

Worked solution
  1. Football only 13, tennis only 7, both 5: total 25.
  2. Neither = 30 − 25 = 5, so P = 5/30 = 1/6.
Q24Exam-style
A spinner lands on 3 in 46 of 200 spins. Estimate the probability of landing on 3.

Hint

Relative frequency = frequency ÷ trials.

Worked solution
  1. 46 ÷ 200 = 0.23.
Q25ChallengeHigher
Using the class of 30 above, a student who plays football is chosen at random. What is the probability they also play tennis?

Hint

Given they play football, only the 18 football players count.

Worked solution
  1. 5 of the 18 football players also play tennis.
  2. P = 5/18 (about 0.278).
Q26Exam-style
The table shows scores 1, 2, 3 and 4 with frequencies 3, 5, 8 and 4. Work out the mean score.

Hint

Multiply each score by its frequency, add, then divide by the total frequency.

Worked solution
  1. Σfx = 3 + 10 + 24 + 16 = 53, and Σf = 20.
  2. Mean = 53 ÷ 20 = 2.65.
Q27Exam-style
The mean of five numbers is 12. Four of them are 10, 11, 13 and 15. Find the fifth number.

Hint

Find the total of all five first.

Worked solution
  1. Total = 5 × 12 = 60.
  2. Fifth = 60 − (10 + 11 + 13 + 15) = 11.
Q28Exam-style
A box plot has lower quartile 14 and upper quartile 26. Find the interquartile range.

Hint

IQR = UQ − LQ.

Worked solution
  1. 26 − 14 = 12.
Q29Exam-style
Grouped data: 0 to 10 has frequency 4, 10 to 20 has frequency 6, 20 to 30 has frequency 10. Estimate the mean.

Hint

Use the midpoint of each class.

Worked solution
  1. Midpoints 5, 15, 25: Σfx = 20 + 90 + 250 = 360.
  2. Estimated mean = 360 ÷ 20 = 18.
Q30ChallengeHigher
On a histogram, the class 10 < x ≤ 25 has a frequency density of 2.4. How many values are in this class?

Hint

Frequency = frequency density × class width.

Worked solution
  1. Class width = 25 − 10 = 15.
  2. Frequency = 2.4 × 15 = 36.

Section II: 4 exam-style questions

Exam-style question 1: Number

Exam-style question style · 5 points · about 6 minutes

Sam earns £1800 a month. He spends 1/3 of it on rent. He then spends 15% of what is left on travel.

  1. (a) How much does Sam spend on rent?
  2. (b) How much does Sam spend on travel?
  3. (c) What fraction of his earnings does Sam have left after rent and travel? Give it in its simplest form.

Write your full answer on paper first, then open the scoring guide and tick each point you earned.

Scoring guide and model answer

Part (a)

1800 ÷ 3 = £600.

Part (b)

What is left: 1800 − 600 = 1200. 15% of 1200 = £180.

Part (c)

1800 − 600 − 180 = 1020. 1020/1800 = 17/30.

Your mark: 0 of 5

Exam-style question 2: Ratio, proportion and rates of change

Exam-style question style · 6 points · about 6 minutes

A car costs £15 000. Its value falls by 12% each year.

  1. (a) Work out its value after 1 year.
  2. (b) Work out its value after 3 years.
  3. (c) Work out the total percentage decrease over the 3 years, to 1 decimal place.

Write your full answer on paper first, then open the scoring guide and tick each point you earned.

Scoring guide and model answer

Part (a)

15 000 × 0.88 = £13 200.

Part (b)

15 000 × 0.883 = £10 222.08.

Part (c)

0.883 = 0.681472, so the value has fallen by 31.9%.

Your mark: 0 of 6

Exam-style question 3: Geometry and measures

Exam-style question style · 6 points · about 6 minutes

A ladder 6.5 m long leans against a vertical wall. The top of the ladder is 6 m above the ground, which is horizontal.

  1. (a) How far is the foot of the ladder from the wall?
  2. (b) Work out the angle between the ladder and the ground, to 1 decimal place.

Write your full answer on paper first, then open the scoring guide and tick each point you earned.

Scoring guide and model answer

Part (a)

d2 = 6.52 − 62 = 42.25 − 36 = 6.25, so d = 2.5 m.

Part (b)

sin θ = 6/6.5, so θ = 67.4°.

Your mark: 0 of 6

Exam-style question 4: Statistics

Exam-style question style · 5 points · about 5 minutes

Two classes sat the same test. Class A had median 64 and interquartile range 12. Class B had median 58 and interquartile range 20.

  1. (a) Compare the scores of the two classes.
  2. (b) Why is the IQR a better measure of spread than the range here?

Write your full answer on paper first, then open the scoring guide and tick each point you earned.

Scoring guide and model answer

Part (a)

Class A scored higher on average, since its median (64) is greater than Class B's (58). Class A's scores were more consistent, since its IQR (12) is smaller than Class B's (20).

Part (b)

The IQR is not affected by extreme scores, because it uses only the middle 50% of the data.

Your mark: 0 of 5

After the mock

Note every question you missed and its topic, then go back to that topic's practice page: all GCSE Maths topics. Then try the real thing with official GCSE Maths past papers.