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GCSE maths questions are most useful when you practise them actively, mark them honestly, and act on your mistakes. This page gives you 12 questions across six topic areas, split by Foundation and Higher tier, with mark scheme style answers and the common mistake for each one. Use them as a targeted practice set, not a passive read-through.
How to Use These GCSE Maths Questions to Improve Fast
Pick a topic block, attempt both questions under timed conditions without looking at the answers, then mark them strictly against the answers provided. The four-step routine that produces real improvement is simple: timed attempt, honest marking, error log, reattempt from a different question on the same topic within seven days. Students who skip the error log and reattempt steps improve more slowly than those who do not.
Foundation vs Higher: Which Questions Should You Practise?
If you are entered for Foundation tier, focus on Foundation questions first until they feel reliable, then attempt Higher questions for stretch. If you are entered for Higher tier, you need to be comfortable with both tiers of question, as Higher papers include accessible questions at the lower end alongside the harder material. If you are unsure which tier you are entered for, check with your teacher.
Number and Percentages GCSE Maths Questions
Foundation: A jacket costs £85. It is reduced by 20% in a sale. What is the sale price?
Answer: 20% of 85 = 17. Sale price = 85 – 17 = £68. Method mark for finding 20% correctly even if subtraction goes wrong.
Common mistake: Calculating 20% correctly but giving £17 as the answer instead of subtracting it from the original price.
Higher: Without a calculator, work out 3.6 × 10⁴ ÷ 1.2 × 10². Give your answer in standard form.
Answer: 3.6 ÷ 1.2 = 3. 10⁴ ÷ 10² = 10². Answer = 3 × 10². Method mark for dividing coefficients and indices separately.
Common mistake: Subtracting the indices incorrectly or writing the answer as 300 rather than converting back to standard form.
Algebra GCSE Maths Questions
Foundation: Solve 4x + 3 = 19.
Answer: 4x = 16, x = 4. Method mark for subtracting 3 from both sides correctly.
Common mistake: Dividing 19 by 4 before subtracting 3, giving a wrong first step that loses the method mark.
Higher: Expand and simplify (2x + 3)(x – 5).
Answer: 2x² – 10x + 3x – 15 = 2x² – 7x – 15. Method mark for four correct terms before simplification.
Common mistake: Only multiplying the first terms in each bracket (2x × x) and the last terms (3 × -5), missing the two cross-multiplication terms entirely.
Ratio and Proportion GCSE Maths Questions
Foundation (word problem): Tom and Aisha share £120 in the ratio 3:5. How much does Aisha receive?
Answer: Total parts = 8. One part = 120 ÷ 8 = 15. Aisha’s share = 5 × 15 = £75. Method mark for finding the value of one part correctly.
Common mistake: Dividing £120 by 5 directly without finding the total number of parts first.
Higher: A recipe for 4 people requires 320 g of flour. How much flour is needed for 7 people? Give your answer in grams.
Answer: 320 ÷ 4 = 80 g per person. 80 × 7 = 560 g. Method mark for finding the per-person quantity correctly.
Common mistake: Using the ratio 4:7 and multiplying 320 by 7 without dividing first, giving 2240 g.
Geometry and Measures GCSE Maths Questions
Foundation: A rectangle has a length of 9 cm and a width of 4 cm. What is its perimeter?
Answer: Perimeter = 2(9 + 4) = 2 × 13 = 26 cm. Method mark for correct formula or correct addition before doubling.
Common mistake: Calculating area (36 cm²) instead of perimeter, or adding all four sides incorrectly as 9 + 4 = 13 only.
Higher: A right-angled triangle has legs of 5 cm and 12 cm. Find the length of the hypotenuse.
Answer: 5² + 12² = 25 + 144 = 169. √169 = 13 cm. Method mark for correct application of Pythagoras’ theorem.
Common mistake: Adding 5 + 12 = 17 before squaring, or forgetting to take the square root of the final sum.
Graphs and Coordinates GCSE Maths Questions
Foundation: A straight line has equation y = 2x + 1. What is the gradient and y-intercept?
Answer: Gradient = 2, y-intercept = (0, 1). One mark for each correct value.
Common mistake: Giving the y-intercept as 1 rather than (0, 1), or swapping gradient and intercept values.
Higher: Find the equation of the line passing through (2, 7) and (5, 13).
Answer: Gradient = (13 – 7) ÷ (5 – 2) = 6 ÷ 3 = 2. Using y = mx + c: 7 = 2(2) + c, c = 3. Equation = y = 2x + 3. Method marks for gradient calculation and substitution.
Common mistake: Calculating gradient correctly but substituting the wrong point, or not substituting at all and guessing c = 0.
Probability and Statistics GCSE Maths Questions
Foundation: A bag contains 3 red, 5 blue, and 2 green counters. What is the probability of picking a blue counter at random?
Answer: P(blue) = 5 ÷ (3 + 5 + 2) = 5 ÷ 10 = 1/2. One mark for correct fraction or decimal.
Common mistake: Writing the probability as 5 rather than 5/10, or using the wrong total by omitting one colour.
Higher: The mean of five numbers is 14. Four of the numbers are 11, 16, 9, and 20. Find the fifth number.
Answer: Total = 14 × 5 = 70. Fifth number = 70 – (11 + 16 + 9 + 20) = 70 – 56 = 14. Method mark for calculating the total correctly.
Common mistake: Finding the mean of the four known numbers instead of working backwards from the total.
How to Mark Your Answers (Without Fooling Yourself)
Mark your answers against the key steps, not just the final number. In GCSE Maths, method marks are awarded for correct working even when the final answer is wrong. This means an incorrect final answer with clear, correct working can still earn two or three marks on a question.
When you mark, ask two questions: did I get the final answer right, and did I show the correct method at each step? If the method was right but arithmetic went wrong, note that specifically. If the method itself was wrong, that is the gap to close.
Write every error in a log with the topic and what went wrong. Reattempt a similar question on that topic within a week.
Ofqual, which regulates qualifications in England, publishes guidance on how GCSE assessments are structured and standardised at gov.uk/ofqual. Understanding how marking works at a systemic level helps students take the mark scheme more seriously in their own practice.
Frequently
Asked Questions
Past papers with mark schemes are available free on the AQA, Edexcel, and OCR websites. Search for your exam board and subject, then navigate to past papers or assessment resources. The mark schemes are as important as the papers themselves and should always be used alongside them.
Both. Each topic block on this page includes one Foundation-style and one Higher-style question. Foundation questions cover grades 1 to 5. Higher questions cover grades 4 to 9. If you are unsure which tier applies to you, check with your maths teacher.
A realistic and effective target is one to two topic blocks of questions per session, three to four sessions per week. Consistency over several weeks matters more than volume in any single session. Marking and logging errors after each session is as important as the practice itself.
Identify which topics are losing most marks using past paper results and an error log. Grade 4 to 6 typically requires improvement in algebra, ratio, and graphs. Practise those specific question types repeatedly until the method becomes reliable. Timed practice under exam conditions builds the speed and confidence the higher grade requires.
Most silly mistakes follow a pattern: units, sign errors, or arithmetic in the final step. Identify your personal pattern from your error log and check specifically for those errors when reviewing each answer. Writing out every step clearly also catches errors before they reach the final answer.
Both, in that order. Start untimed on unfamiliar question types so you can focus on the method. Once the method is reliable, switch to timed practice to build exam-pace confidence. Sitting every practice session untimed means you are not practising the actual exam condition.
It depends on the paper. GCSE Maths has one non-calculator paper and one or two calculator papers depending on the exam board. Practise both with and without a calculator. Non-calculator questions test mental arithmetic, standard form, and estimation, which are skills that need separate, deliberate practice.
Tutoring is most effective when a student is putting in effort but marks are not improving, or when specific topic gaps are clearly identified but not closing through self-study. A tutor can diagnose exactly where the method breaks down question by question, which is difficult to do accurately through self-marking alone.
Final Summary + Next Step
These 12 GCSE maths questions cover the six most commonly tested topic areas across both tiers. Use them with the four-step routine: timed attempt, honest marking, error log, and reattempt. The topics where you drop marks most consistently are your actual revision priorities, not the ones you find most comfortable to practise.
If you want a structured programme that covers every topic area with built-in progress tracking, the GCSE maths course is designed for exactly that. If you would prefer to talk through what your child specifically needs before committing to anything, contact us and we will give you a straightforward answer.
