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A-level · Last updated November 2026

A-level Mathematics Exam: free practice test

A-level Mathematics is a two-year linear qualification covering pure maths, statistics and mechanics, taken by sixth form and college students in England. It is assessed by three 2-hour written papers of 100 marks each, all sat at the end of the course. Exams run in May and June only.

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About the A-level Maths exam

A-level Mathematics is a two-year linear qualification covering pure maths, statistics and mechanics, taken by sixth form and college students in England. It is assessed by three 2-hour written papers of 100 marks each, all sat at the end of the course. Exams run in May and June only.

What's on the exam

A-level Maths
Proof, Algebra and Functions
7 key facts
Coordinate Geometry, Sequences, Series and Vectors
7 key facts
Trigonometry
8 key facts
Exponentials and Logarithms
7 key facts
Differentiation
7 key facts
Integration and Numerical Methods
7 key facts
Statistics
8 key facts
Mechanics
8 key facts

Each branch is a topic in the official outline. Members see every key fact on the full mind map. Read the free study guide →

How to pass the A-level Maths exam

  • 100 marks in 120 minutes is 1.2 minutes per mark. A 10-mark question deserves about 12 minutes; if you are stuck, write down what you know, move on and come back.
  • Show every step. 'Show that' and proof questions give no credit for a correct final line without the working, and method marks are available even when the answer is wrong.
  • Learn what is NOT in the formula booklet: differentiation and integration of standard functions, the quadratic formula, sin² x + cos² x = 1, the laws of logarithms and the suvat equations.
  • Know your board's large data set well. Questions assume you know its variables, units and quirks, and these are easy marks if you have explored it in lessons.
  • In statistics and mechanics, finish with a sentence in context: state the conclusion of a hypothesis test in words, and give units and a sensible accuracy (usually 3 significant figures) for every answer.

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Create a free account after the test: your score by topic, a mistakes bank, the complete study notes for the first topic, flashcards and the GCSE Maths Formula Sheet.

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What's in the premium A-level Maths prep

Premium A-level Maths prep is studied one topic at a time. Each step starts with that topic's key notes and flashcard deck, then its own question sets of 25, so you master one topic before you move to the next. When every topic is strong, the 6 full mock exams show you're ready.

3,000practice questions, every answer explained
6full-length mock exams, 50 questions each, timed
800flashcards with spaced repetition, sorted by topic
60comprehensive key notes across 8 topics

Your step-by-step study path

  1. 1
    Proof, Algebra and Functions8 key notes, 100 flashcards, then 375 practice questions in 15 sets of 25
    Notes free with an account
  2. 2
    Coordinate Geometry, Sequences, Series and Vectors8 key notes, 100 flashcards, then 375 practice questions in 15 sets of 25
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  3. 3
    Trigonometry8 key notes, 100 flashcards, then 375 practice questions in 15 sets of 25
    Premium
  4. 4
    Exponentials and Logarithms8 key notes, 100 flashcards, then 375 practice questions in 15 sets of 25
    Premium
  5. 5
    Differentiation7 key notes, 100 flashcards, then 375 practice questions in 15 sets of 25
    Premium
  6. 6
    Integration and Numerical Methods7 key notes, 100 flashcards, then 375 practice questions in 15 sets of 25
    Premium
  7. 7
    Statistics7 key notes, 100 flashcards, then 375 practice questions in 15 sets of 25
    Premium
  8. 8
    Mechanics7 key notes, 100 flashcards, then 375 practice questions in 15 sets of 25
    Premium
  9. Final step: 6 full mock exams50 questions each, timed like exam day. Hit your target on them before your first paper.
    Premium
Free with an account

Read the complete A-level Maths study notes for “Proof, Algebra and Functions”

Our first full set of comprehensive notes, about 20 minutes of reading: The four kinds of proof · Setting out a proof · Indices, surds and quadratics · Simultaneous equations and inequalities · Polynomials, the factor theorem and partial fractions · Functions: domain, range, composites and inverses · Graphs and transformations, a worked exam example, the traps examiners use and a one-minute recap. Create a free account to read it and see how premium notes work before you decide.

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Study tools included

3,000 practice questions

3,000 exam-style questions per exam, organised topic by topic in sets of 25. Every answer explained, with the rule it comes from.

6 full mock exams

6 full-length timed mock exams per exam, with real question counts and time limits, so test day feels like practice day.

Exam Readiness Score

One 0 to 100 number that tells you when you're ready for exam day. Reach 80 and you're covered by our Pass Guarantee.

800 flashcards + spaced repetition

800 flashcards per exam, in a deck for each topic, that come back right before you'd forget them. Five minutes a day keeps every number fresh.

60 comprehensive key notes

60 key notes per exam, split across its topics and each explained in full: the concepts, worked exam examples, the traps examiners use and a quick recap. Your first set is free with an account.

Mind maps

See the whole exam on one screen: every topic and the facts under it.

Sample questions with answers

These are the questions in the free test above, with answers. Try the test first. You'll learn more by getting some wrong.

1. Find the remainder when f(x) = x³ - 2x² + 4x - 5 is divided by (x - 2).
Answer: 3. By the remainder theorem the remainder is f(2) = 8 - 8 + 8 - 5 = 3. Using f(-2) = -29 is the common sign error: divide by (x - a) means substitute x = a.
2. f(x) = 2x + 3 and g(x) = x². Find fg(x).
Answer: 2x² + 3. fg(x) means apply g first, then f: f(g(x)) = f(x²) = 2x² + 3. (2x + 3)² is gf(x), the other order.
3. Find the centre and radius of the circle x² + y² - 6x + 4y - 12 = 0.
Answer: Centre (3, -2), radius 5. Complete the square: (x - 3)² - 9 + (y + 2)² - 4 - 12 = 0, so (x - 3)² + (y + 2)² = 25. The centre is (3, -2) and the radius is √25 = 5.
4. Find the sum to infinity of the geometric series 8 + 4 + 2 + 1 + ...
Answer: 16. a = 8 and r = 1/2. Since |r| < 1 the series converges, and S∞ = a / (1 - r) = 8 / (1/2) = 16.
5. Find the coefficient of x² in the binomial expansion of (1 + 2x)⁵.
Answer: 40. The x² term is 5C2 × (2x)² = 10 × 4x² = 40x². Forgetting to square the 2 gives 20.
6. Solve sin θ = 0.5 for 0° ≤ θ < 360°.
Answer: θ = 30° and 150°. The principal value is 30°. Sine is positive in the first and second quadrants, so the other solution is 180° - 30° = 150°. 330° would solve cos θ = √3/2, not sin θ = 0.5.
7. 3 sin x + 4 cos x is written in the form R sin(x + α), where R > 0. What is the value of R?
Answer: 5. Expanding R sin(x + α) gives R cos α = 3 and R sin α = 4. Squaring and adding: R² = 3² + 4² = 25, so R = 5 (and tan α = 4/3).
8. Solve 2^x = 20, giving your answer to 3 significant figures.
Answer: 4.32. Take logs of both sides: x ln 2 = ln 20, so x = ln 20 / ln 2 = 2.9957 / 0.6931 = 4.32. 1.30 is log₁₀ 20, which forgets to divide by log 2.
9. Simplify log₃ 81 - log₃ 9.
Answer: 2. log a - log b = log(a/b), so log₃ 81 - log₃ 9 = log₃ 9 = 2, because 3² = 9. Subtracting the 81 and 9 inside the log is not a valid law.
10. Find the x-coordinates of the stationary points of y = x³ - 6x² + 9x.
Answer: x = 1 and x = 3. dy/dx = 3x² - 12x + 9 = 3(x² - 4x + 3) = 3(x - 1)(x - 3). Setting this to 0 gives x = 1 and x = 3. (x = 2 is where d²y/dx² = 0, the point of inflection.)
11. Differentiate y = x² e^(3x).
Answer: x e^(3x)(2 + 3x). Product rule with u = x², v = e^(3x): dy/dx = 2x e^(3x) + x² × 3e^(3x) = x e^(3x)(2 + 3x). The chain rule gives the factor 3 when differentiating e^(3x).
12. Evaluate the integral of (6x² - 2) with respect to x, from x = 1 to x = 2.
Answer: 12. Integrate: 2x³ - 2x. At x = 2: 16 - 4 = 12. At x = 1: 2 - 2 = 0. The definite integral is 12 - 0 = 12.
13. X ~ B(10, 0.3). What is the variance of X?
Answer: 2.1. For a binomial distribution Var(X) = np(1 - p) = 10 × 0.3 × 0.7 = 2.1. The mean is np = 3 and the standard deviation is √2.1 ≈ 1.45.
14. X ~ N(50, 16). Find P(X > 58), to 4 decimal places.
Answer: 0.0228. In N(μ, σ²) the 16 is the variance, so σ = 4. z = (58 - 50) / 4 = 2, and P(Z > 2) = 1 - 0.9772 = 0.0228. Using 16 as the standard deviation gives z = 0.5 and the wrong answer 0.3085.
15. A car accelerates uniformly from 4 m/s to 20 m/s in 8 seconds. How far does it travel in this time?
Answer: 96 m. Use s = ½(u + v)t = ½ × (4 + 20) × 8 = 12 × 8 = 96 m. Using only the final speed (20 × 8 = 160 m) ignores the fact that the car started slower.

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Exam guide

A-level Maths exam guide (2027): A-level Mathematics is one of the most popular A-levels in England and a requirement for many university courses in science, engineering, economics and computing. Every board assesses it with three 2-hour written papers of 100 marks each, sat at the end of the two-year course. About two thirds of the marks are pure maths and one third is statistics and mechanics. This guide explains how the papers are split, how grading works and how to plan your revision for summer 2027.

A-level Maths exam FAQ

How many questions are on the A-level Maths exam?

3 written papers, 100 marks each (300 marks in total), with a time limit of 6 hours in total (3 × 2 hours). Format: written exam, calculator allowed on all three papers. a formula booklet is provided. about two thirds pure maths and one third statistics and mechanics.

What is the passing score for A-level Maths?

Graded A* to E; grade E is a pass. Boundaries are set after every exam series, so aim for 70% in practice.

How much does the A-level Maths exam cost?

No fee for school and college students (the school pays). Private candidates pay the exam centre; fees vary by centre. School and college students don't pay exam fees themselves. Private candidates pay the exam centre, and fees vary by centre and board.

Which languages is the A-level Maths exam offered in?

English.

Where do I take the A-level Maths exam?

At your school or sixth form college, or as a private candidate at an exam centre that accepts them.

Is this A-level Maths practice test free?

Yes. The 15-question practice test on this page is free, with an explanation for every answer and no signup. A free account also unlocks the complete study notes for the first topic. The full A-level Maths prep is Premium at £29 a month for this exam.

What's in the premium A-level Maths prep?

3,000 practice questions organised topic by topic (Proof, Algebra and Functions: 375; Coordinate Geometry, Sequences, Series and Vectors: 375; Trigonometry: 375; Exponentials and Logarithms: 375; Differentiation: 375; Integration and Numerical Methods: 375; Statistics: 375; Mechanics: 375), 6 full-length timed mock exams of 50 questions, 800 flashcards and 60 comprehensive key notes split across all 8 topics, plus a mistakes bank and the Readiness Score.

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Exam details are summarised from the exam boards' published specifications available in November 2026. the exam boards changes formats and fees, so confirm with AQA, Pearson Edexcel and OCR before you book. Kennington College is not affiliated with any exam board or with Ofqual.

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