A-Level Mathematics Practice Test 2026

About the A-Level Mathematics exam

The GCE Advanced Level - Mathematics (A-Level Mathematics) is a a-levels examination administered in UK. It is designed to assess candidates' knowledge and proficiency across 4 key subject areas including Pure Mathematics, Statistics, Mechanics, Decision Mathematics. This exam is widely recognized as an essential benchmark for students and professionals.

Use short A-Level Mathematics practice sets to identify topics to revisit. Choose a subject and difficulty, answer questions, then review the explanations. New accounts get 30 question credits; further new questions use paid credits. Retaking previously seen questions is free.

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A-Level Mathematics — quick answers

A-Level Mathematics at a glance

8 free A-Level Mathematics practice questions (2026)

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1. What is the range of the function f(x) = 3 + 2cos(x) for all real values of x?

   • [1, 5]
   • [2, 4]
   • (-∞, ∞)
   • [3, 5]
   Show answer & explanation

   Answer: A. [1, 5]

   The cosine function has a range of [-1, 1]. Therefore, 2cos(x) has a range of [-2, 2]. Adding 3 shifts the range to [1, 5].

   Topic: Pure Mathematics · medium

2. If log₂ (x + 3) = 4, what is the value of x?

   • 5
   • 13
   • 11
   • 19
   Show answer & explanation

   Answer: B. 13

   log₂ (x + 3) = 4 implies 2⁴ = x + 3. Thus, 16 = x + 3, so x = 13.

   Topic: Pure Mathematics · medium

3. What is the gradient of the line given by the parametric equations x = 2t + 1 and y = t - 3?

   • 2
   • 1/2
   • -2
   • -1/2
   Show answer & explanation

   Answer: B. 1/2

   dy/dt = 1 and dx/dt = 2. Therefore, dy/dx = (dy/dt) / (dx/dt) = 1/2.

   Topic: Pure Mathematics · medium

4. Which of the following is the correct partial fraction decomposition of (4x + 1) / (x(x + 1))?

   • 1/x + 3/(x+1)
   • 1/x + 4/(x+1)
   • 4/x + 1/(x+1)
   • 1/x + 5/(x+1)
   Show answer & explanation

   Answer: A. 1/x + 3/(x+1)

   Let (4x+1)/(x(x+1)) = A/x + B/(x+1). Then 4x+1 = A(x+1) + Bx. Setting x = 0, A = 1. Setting x = -1, -4+1 = -B, so B = 3. Thus, the decomposition is 1/x + 3/(x+1).

   Topic: Pure Mathematics · medium

5. What is the solution to the differential equation dy/dx = 2y, given that y = 1 when x = 0?

   • y = e^(2x)
   • y = 2e^x
   • y = e^(x/2)
   • y = 2e^(2x)
   Show answer & explanation

   Answer: A. y = e^(2x)

   Separating variables: ∫(1/y) dy = ∫2 dx => ln|y| = 2x + C. Since y = 1 when x = 0, ln(1) = 0 + C, so C = 0. Thus ln|y| = 2x, and y = e^(2x).

   Topic: Pure Mathematics · medium

6. The first three terms of an arithmetic sequence are 5, 9, 13. What is the sum of the first 20 terms?

   • 860
   • 870
   • 850
   • 840
   Show answer & explanation

   Answer: A. 860

   The common difference is 4. The nth term is 5 + (n-1)4 = 4n + 1. The sum of the first n terms is n/2 * (first term + last term). The 20th term is 4(20)+1 = 81. So the sum of the first 20 terms is 20/2 * (5 + 81) = 10 * 86 = 860.

   Topic: Pure Mathematics · medium

7. What is the derivative of y = ln(x²) with respect to x?

   • 2/x
   • 1/x²
   • 2ln(x)
   • 1/(2x)
   Show answer & explanation

   Answer: A. 2/x

   Using the chain rule, dy/dx = (1/x²) * (2x) = 2/x. Alternatively, y = ln(x²) = 2ln(x), so dy/dx = 2/x.

   Topic: Pure Mathematics · medium

8. Evaluate the integral ∫(2x + 1)e^(x²) dx

   • e^(x²) + C
   • (x² + x)e^(x²) + C
   • 2e^(x²) + C
   • e^(x² + x) + C
   Show answer & explanation

   Answer: A. e^(x²) + C

   Let u = x². Then du/dx = 2x, so du = 2x dx. Thus the integral becomes ∫e^u du = e^u + C = e^(x²) + C.

   Topic: Pure Mathematics · medium

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A-Level Mathematics Exam Subjects

Available practice subjects: Pure Mathematics, Statistics, Mechanics, Decision Mathematics. Select a subject for focused preparation. Coverage is not a guarantee of the complete official syllabus.

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