Author
Mhairi Sim
Published:
July 2026
Key takeaways
GCSE maths questions are across six topics: Number, Algebra, Ratio and Proportion, Geometry and Measures, Probability, and Statistics
The GCSE maths exam is split into two tiers: Foundation (grades 1-5) and Higher (grades 4-9)
Always show your working – examiners marking GCSE maths questions award marks for method, not just the final answer.
Table of contents
The GCSE maths qualification is widely considered a gateway qualification, meaning it is a requirement for entry to many sixth form colleges and further education establishments, as well as for many future careers.
GCSE maths is a compulsory subject for students in England, Wales, and Northern Ireland (students in Scotland sit an equivalent qualification), and most students will typically begin their studies at age 15 or 16.
The exam will present students with GCSE maths questions across six main topic areas: Number, Algebra, Ratio and Proportion, Geometry and Measures, Probability, and Statistics. The exam exists at two different difficulty levels, referred to as tiers, where students can achieve different GCSE grades:
Visit our guide on GCSE Grade Boundaries to learn more about the GCSE grading system.
Whatever tier you’re sitting, completing GCSE practice questions is one of the most effective revision tools! Working through problems, checking your answers, and understanding where you went wrong is proven to boost performance far more than simply reading a textbook or looking over your notes.
With that in mind, we’ve put together 25 curriculum-aligned practice GCSE maths questions split by topic and tier. Each question has a fully worked answer, so you can check your work at every step. Before you get started, here are some tips to help you get the best out of these practice questions.
Working through these GCSE maths questions is only useful if you’re learning from them. Here are a few tips to get the most out of your revision:
Grab some paper, a pen, and your calculator. You’ve got everything you need to get started now.
As a rough guide, GCSE exam questions follow a 1 mark per minute rule of thumb, so the following questions should take around 1 hour to complete.
You may only use a calculator for the questions indicated. A calculator symbol will appear next to the question number if it is allowed.
Q1.
A family buys 4 tickets at 3.30 pm. They also buy one portion of popcorn.
How much do the family spend on their cinema trip?
(3 marks)
4 x £6.50 = £26.00
10% of £26.00 = £2.60 (1 mark)
£26.00 – £2.60 = £23.40 (1 mark)
£23.40 + £5.25 = £28.65 (1 mark)
Q2.
Write the numbers in order of size from smallest to largest.
¼, 45%, 0.55 (1 mark)
Q3.
Write the fraction 
in its simplest form.
(1 mark)
⅖ (1 mark)
Q4.
Solve 7x – 27 < 8
(2 marks)
7x < 8 +27
7x < 35 (1 mark)
(divide by 7)
x < 5 (1 mark)
Q5. 
A shop reduces all prices by 15%. Sophie buys a jumper which originally cost £40 and one other item. After the discount, her total comes to £57.80. What was the original cost of the other item she bought?
(3 marks)
£57.80 ÷ 0.85 (1 mark)
= £68.00 (1 mark)
£68.00 – £40.00 = £28.00 (1 mark)
Q7.
Solve:
4 (x – 5) = 18
(2 marks)
4x – 20 = 18 (1 mark)
4x = 18 + 20
4x = 38
x = 9.5 (1 mark)
Q8.
Expand and simplify:
(x + 5)(x + 2)
(2 marks)
x
+ 2x + 5x + 10 (at least ¾ terms here correct: 1 mark)
x + 7x + 10 (1 mark)
Q9.
Simplify fully:
(2 marks)
= 
(top line correct: 1 mark)
= x + 4 (1 mark)
Q10.
Here is a sketch of a curve.
The equation of the curve is y = x² + ax + b, where a and b are integers.
The points (0, – 5) and (5, 0) lie on the curve.
Find the coordinates of the turning point of the curve.
(5 marks)
Step 1: Sub in (0, -5)
– 5 = 0 + 0 + b
b = – 5 (1 mark)
Step 2: Sub in (5, 0) and b = – 5 from step 1
0 = 5² + 5a – 5 (1 mark)
0 = 25 + 5a – 5
0 = 20 + 5a
5a = – 20
a = – 4 (1 mark)
Step 3: Complete the square
y = x² – 4x – 5 (1 mark)
Q11.
Use algebra to solve the simultaneous equations
4x – 5y = 20
6x + 7y = – 57
You must show all your working.
(4 marks)
Step 1: Make the x coefficients match (1 mark if both are correct below)
(4x – 5y = 20) x 6 → 24x – 30y = 120
(6x + 7y = – 57) x 4 → 24x + 28y = – 228
Step 2: Subtract one equation from the other
(24x + 28y) – (24x – 30y) = – 228 – 120 (1 mark)
28y + 30y = – 348
= 
y = – 6 (1 mark)
Step 3: Substitute the y value into equation 1
4x – 5y = 20
4x – 5(-6) = 20
4x + 30 = 20
4x = 20 – 30
= 
x = – 2.5 (1 mark)
(To check your work, you can substitute both values back into the second equation to get an equal result.)
Q12.
A paint mixture uses red, blue and green paint in the ratio 2 : 3 : 4. If a decorator uses 12 litres of green paint, what is the total amount of paint in the mixture?
(2 marks)
= 
1 part = 3 litres (1 mark)
2 + 3 + 4 = 9
9 x 3 litres = 27 litres (1 mark)
Q14.
Given that
a:b = 2:5 and b:c = 3:4
Find a:b:c.
(2 marks)
Find the least common multiple of 5 & 3 (15) (1 mark if 15 is identified and at least 1 of a:b or b:c is scaled correctly as below)
a:b = 2:5 (x3) → 6:15
b:c = 3:4 (x5) → 15:20
a:b:c = 6:15:20 (1 mark)
Q15.
x is proportional to 
where y > 0
y is increased by 44%
Work out the percentage increase in x.
(3 marks)
x = k
Step 1: Work out the y value
y = 44% increase = 100% + 44% = 144% = 1.44
(1 mark if: x = k and y = 1.44y has been written)
Step 2: Substitute in the y value to calculate the x value (1 mark for below 2 lines)
x = k
x = k1.2
Step 3: Compare the new x value to the previous
k1.2 – k
0.2 = 20% increase (1 mark)
Q16.
A car travelled for 7.04 miles at an average speed of 30.2 miles per hour.
Work out an estimate for the time taken for the car to complete the journey. Give your answer in minutes.
(2 marks)
Round answers for estimates
7 miles ÷ 30 miles per hour (1 mark)
= 0.233 hours
0.2333 hours x 60 minutes = 14 minutes (1 mark – accept answers between 13-15 minutes)
Q17.
Here is a triangle and a rectangle. Area of triangle = 5 x 7 = 35 ÷ 2 = 17.5 cm² (1 mark) Area of rectangle = 17.5 x 6 = 105 cm² (1 mark)
Width = 105 ÷ 14 = 7.5 cm (1 mark)
Q19.
Determine whether this triangle is right-angled. Show your working.
(3 marks)
7² + 9² = 49 + 81 = 130 (1 mark)
12² = 144 (1 mark)
130 ≠ 144, therefore the triangle is not right-angled (1 mark – written statement conclusion required)
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Q20.
A bag contains 3 red and 2 blue counters. One counter is picked at random. What is the probability that it is red?
(1 mark)
P(red) = ⅗ (1 mark)
Q21.
A fair spinner numbered 1-5 is spun twice, and the numbers landed on are recorded. Find the probability that:
Q21a.
The total of the two numbers is even
(2 marks)
P(both odd) = 3/5 x 3/5 = 9/25
P(both even) = 2/5 x 2/5 = 4/25
(1 mark – both of the above written)
P(even total) = 9/25 + 4/25
= 13/25 (1 mark)
Q21b.
The spinner does not land on the same number twice
(2 marks)
There are 5 ways the same number can happen (1,1 or 2,2 or 3,3 or 4,4 or 5,5) out of a possible 25 outcomes in total.
P(same number both times) = 5/25 = 1/5 (1 mark)
P(not the same number) = 1 – 1/5
= 4/5 (1 mark)
Q22.
Callum goes to the cinema and will watch either a sci-fi, horror or a romantic comedy movie. The probability he chooses a romantic comedy is 0.56. There is an equal chance that he picks a sci-fi or horror.
Find:
Q22A.
The probability that he picks a horror movie.
(2 marks)
1 – 0.56 = 0.44 (1 mark)
0.44 ÷ 2 = 0.22 (1 mark)
Q22B.
The probability that he picks a horror or romantic comedy.
(1 mark)
0.22 + 0.56 = 0.78 (1 mark)
Q23.
The mean of 6, 8, 19, 8, and x is 8.4. Find x.
(2 marks)
8.4 x 5 = 42
6 + 8 + 19 + 8 = 41 (1 mark)
42 – 41 = 1
x = 1 (1 mark)
Q24.
The pie charts show information about the meals that children at two different schools ate for lunch.
The same number of students at each school had pizza for lunch. Is this statement correct? Show your working that helps you reach your answer.
(3 marks)
School A: 
x 480 = 80 students (1 mark)
School B: 
x 760 = 190 students (1 mark)
80 ≠ 190, so the statement is incorrect. (1 mark)
Q25.
A teacher records the number of hours students spent revising for a GCSE maths test and their percentage score in the test. The table below shows the results for 8 students:
| Hours revised | Test score (%) |
|---|---|
| 2 | 41 |
| 3 | 48 |
| 4 | 52 |
| 5 | 61 |
| 6 | 66 |
| 7 | 71 |
| 8 | 78 |
| 10 | 62 |
Q25a.
Describe the relationship between revision time and test score.
(1 mark)
There is a positive correlation between revision time and test score (1 mark)
Q25b.
Which result may be considered an outlier? Explain your answer.
(1 mark)
The student who studied for 10 hours but scored 62% is the outlier, as the pattern suggests they should have scored much higher. (1 mark)
Q25c.
You want to estimate the test score of a student who revised for 9 hours. Describe the method and steps you would use to do this.
(2 marks)
1. Plot the data on a scatter graph
2. Ignore the outlier (10 hours, 62%)
3. Draw a line of best fit through the remaining points
4. Find 9 hours on the horizontal axis and draw a line up to the line of best fit
5. Read across to the vertical axis to find the estimated score. (2 marks)
Congratulations! You’ve reached the end of our practice GCSE maths questions! Were you able to stick to the 1-minute-per-mark timing? Now it’s time to go back and mark your work using our answers.
Remember, don’t let incorrect answers get you down. These are all part of the learning! If you did get any wrong, use our worked answers to figure out what went wrong and try the question again in a couple of days.
Looking for more GCSE support? DoodleLearning has a range of articles to help you navigate exam season, from understanding your results and grade boundaries to what to expect on GCSE results day.
Congratulations! You’ve reached the end of our practice GCSE maths questions! Were you able to stick to the 1-minute-per-mark timing? Now it’s time to go back and mark your work using our answers.
Looking for more GCSE support? DoodleLearning has a range of articles to help you navigate exam season, from understanding your results and grade boundaries to what to expect on GCSE results day.
Looking for more SATs practice? DoodleLearning is an award-winning maths and English app that’s filled with thousands of questions and games aligned to the national curriculum!
Designed by teachers, it creates each child a unique work programme tailored to their needs, doubling their progression with just 10 minutes of use a day.* Try it for free!
*Based on children earning 24 stars a day. Read the full study here.
Lesson credits
Mhairi Sim
Mhairi is an experienced teacher, freelance writer and parent. After completing her bachelor's degree in Psychology, she graduated as a teacher from the University of Strathclyde. She then built experience teaching across KS1 and KS2 throughout the UK. In addition to working in mainstream education, Mhairi specialised in the additional support needs sector, including social, emotional, and behavioural support.
Mhairi
Mhairi is an experienced teacher, freelance writer and parent. After completing her bachelor's degree in Psychology, she graduated as a teacher from the University of Strathclyde. She then built experience teaching across KS1 and KS2 throughout the UK. In addition to working in mainstream education, Mhairi specialised in the additional support needs sector, including social, emotional, and behavioural support.
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