Sample GCSE Maths Questions 2026: 18 Qs + Mark Schemes
GCSE maths sample questions are one of the most effective ways to identify strengths, uncover weaknesses, and improve exam performance before the 2026 GCSEs. By working through realistic Foundation and Higher-tier questions, students can develop the problem-solving skills, mathematical reasoning, and exam technique needed to achieve their target grade.
The key benefit of using sample questions is that they highlight exactly where marks are being lost. Whether the issue is algebra, percentages, geometry, ratio, or exam timing, targeted practice allows students to focus on the areas that will have the biggest impact on their final result. Combined with regular review and worked solutions, sample questions help students build confidence while reinforcing the methods examiners expect to see.
Students often combine GCSE maths sample questions with GCSE Maths Study Help to create a structured revision plan and identify the topics that require the most attention. Reviewing mistakes, tracking progress, and revisiting weaker areas is often far more effective than simply completing additional questions.
In this guide, you’ll find GCSE maths sample questions with worked answers and mark scheme guidance covering a range of commonly tested topics. Whether you’re aiming to secure a pass or target the highest grades, these questions can help build the confidence and exam technique needed for GCSE success.
Looking for grammar school maths papers? Download our Free 11 Plus Maths Papers With Answers PDF for printable papers, answer sheets, and exam-style practice questions.
Page Contents
How to use these GCSE maths sample questions (without wasting time)
Use GCSE maths sample questions in short, timed bursts: 12–15 minutes, then 10 minutes correcting and rewriting the method. Marks are usually lost on setup (wrong equation), accuracy (sign errors), and exam technique (not showing steps), not because a child “can’t do maths”.
Rule we use in high-performing sets: after every question, write one line: “What was the decision step?” (for example, “Form simultaneous equations” or “Use Pythagoras”). That trains method selection, which is what examiners reward.
Paper-style practice set: GCSE maths sample questions (Foundation + Higher)
These GCSE maths sample questions are written to match UK exam expectations: clear method marks, realistic numbers, and common traps. Do them in order, mark strictly, and circle any question where the first line wasn’t obvious within 20 seconds.
Foundation (aim Grades 1–5) GCSE maths sample questions
Do Questions F1–F9 in 35–40 minutes. If your child is running out of time, they should still write an equation or a diagram: method marks often survive even when the final answer doesn’t.
Foundation Question Set
| Q | Topic | Question | Answer (Worked) | Marks Focus |
|---|---|---|---|---|
| F1 | Fractions | Work out 3/5 of 40. | 40 ÷ 5 = 8. 8 × 3 = 24. | One clean method line |
| F2 | Percentages | A coat costs £80. It is reduced by 15%. New price? | 15% of 80 = 0.15 × 80 = 12. New price: 80 – 12 = £68. | Don’t add by mistake |
| F3 | Ratio | Split £42 in the ratio 2:5. | Total parts = 7. One part: 42 ÷ 7 = 6. Shares: 2 × 6 = 12, 5 × 6 = 30. | Identify total parts |
| F4 | Algebra | Simplify 3x + 2x – 7. | 5x – 7. | Like terms only |
| F5 | Linear equation | Solve 5y – 3 = 17. | 5y = 20. y = 4. | Two-step layout |
| F6 | Area | A rectangle is 9 cm by 4 cm. Area? | 9 × 4 = 36 cm². | Units must be squared |
| F7 | Angles | A straight line is split into angles x and 73°. Find x. | x + 73 = 180. x = 107°. | Use 180° fact |
| F8 | Coordinates | Point A is (2, 5). Move 3 right and 4 down. New coordinate? | Right: x = 2 + 3 = 5. Down: y = 5 – 4 = 1. New point: (5, 1). | Sign on “down” |
| F9 | Probability | A bag has 3 red, 5 blue balls. Pick one. Probability of red? | Total balls = 8. P(red) = 3/8. | Simplify fraction if possible |
Higher Question Set (Grades 6–9)
- Target Time: 45–55 minutes.
- Strategy: If execution is inconsistent, write down the formula first, substitute values, then calculate.
| Q | Topic | Question | Answer (Worked) | Marks Focus |
|---|---|---|---|---|
| H1 | Simultaneous equations | Solve x + y = 11 and 2x – y = 7. | Add equations: 3x = 18 → x = 6. Then substitute: y = 11 – 6 = 5. | Choose add/subtract |
| H2 | Quadratic | Solve x² – 9 = 0. | x² = 9 → x = ±3. | Include both roots |
| H3 | Pythagoras | Right triangle legs 6 cm and 8 cm. Hypotenuse? | c² = 6² + 8² = 36 + 64 = 100. c = 10 cm. | Square root step |
| H4 | Standard form | Write 0.00052 in standard form. | 5.2 × 10⁻⁴. | One non-zero digit before decimal |
| H5 | Indices | Simplify a³ × a⁵. | a³⁺⁵ = a⁸. | Add powers rule |
| H6 | Circle area | Radius 7 cm. Area? | A = πr² = π × 49 = 49π ≈ 153.94 cm². | Exact vs decimal |
| H7 | Compound interest | £500 at 3% for 2 years. | 500 × 1.03² = 500 × 1.0609 = £530.45. | Use multiplier twice |
| H8 | Similarity | Scale factor 1.5. Original length 8 cm. New length? | 8 × 1.5 = 12 cm. | Multiply, not add |
| H9 | Graphs | Line: y = 2x – 3. Find y when x = 4. | y = 2(4) – 3 = 8 – 3 = 5. | Substitution accuracy |
Strategic Revision Roadmap (Years 10–11)
- This structure targets the elimination of repeated errors under time pressure to secure competitive Grade 7+ marks.
| Week | Focus Area | Time Commitment | Output Parents Should Expect |
|---|---|---|---|
| 1 | Baseline Assessment | 2–3 hours | Top 5 weakest topics ranked by marks lost |
| 2 | Target Topic Rebuild | 2–3 hours | Fewer method errors, clearer written layout |
| 3 | Secondary Weakness & Calculator Skills | 2–3 hours | Reduction in arithmetic slips and rounding mistakes |
| 4 | Timed Section Sprints | 3 hours | Clear time management plan per question type |
| 5 | Mixed Practice & Examiner Vocabulary | 3 hours | Method marks secured even on challenging questions |
| 6 | Full Exam Mock Review | 3–4 hours | Clear predicted grade band with final priority list |
- Design a printable mock exam tracking sheet based on these sets.
- Extract specific practice drills for any weak topic identified above.
- Explain the CPA framework (Concrete-Pictorial-Abstract) to help explain these methods to a student.
A realistic UK GCSE exam hall with spaced desks, students writing under timed conditions, an invigilator walking the aisle, and a large wall clock emphasising exam timing.
People Also Ask: GCSE maths sample questions
Q1: How many GCSE maths sample questions should my child do per week?
For most Year 10–11 students, 25–40 GCSE maths sample questions per week is enough if they’re corrected properly. The non-negotiable is review time: aim for at least 1 minute of correction for every 1 minute spent answering, otherwise mistakes repeat.
Q2: Are GCSE maths sample questions the same across exam boards?
Core content overlaps heavily, but question style and mark schemes vary. If your school hasn’t confirmed, check the exam board on your child’s latest assessment or school communication. For board specifications, use AQA, Pearson, or OCR.
Q3: What’s the quickest way to improve from Grade 5 to Grade 6?
Stop “topic hopping” and target the highest-frequency skills: algebra manipulation (collecting terms, solving equations), ratio/percentages, and geometry basics (area, angles), then practise them timed. Most Grade 5 students lose 10–20 marks per paper from avoidable slips: wrong rounding, missing units, or not showing steps.
Q4: Should my child do timed practice or untimed first?
Untimed for the first attempt at a topic (to build method), timed once accuracy is above 70% on that topic set. A practical trigger: if they need more than 90 seconds to decide the method, they’re not ready for full timing yet.Conclusion & Next StepsIf you use GCSE maths sample questions in timed sets, mark strictly, and force a written “decision step” for every error, your child’s marks usually rise within 4–6 weeks because method selection and exam structure improve. The parent’s role is to police the review process, not to re-teach every topic: the error log is the plan.To turn today’s practice into a grade target plan, start with GCSE maths sample questions and a diagnostic lesson. Think Academy UK provides elite online maths tuition for ages 5-13. From 11+ mastery to National Curriculum support, we help children excel. packs.
