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A Level Maths Practice Questions, Exercises of Mathematics

Mathematics

Practice questions designed to help with A-Level maths

Typology: Exercises

2025/2026

Uploaded on 06/10/2026

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A-Level Mathematics Practice Questions
1. Differentiate y = (3x^2 + 2x - 1)(x - 4).
2. Solve the equation 2sin(x) = 1 for 0° ≤ x < 360°.
3. Find the coordinates of the turning point of y = x^2 - 6x + 5.
4. Evaluate ∫(2x^3 - 5x + 1) dx.
5. A sequence is defined by u_n = 3n + 2. Find u_15.
6. Find the equation of the tangent to y = x^3 at x = 2.
7. Solve: log₂(x + 1) = 4.
8. A vector a = (2, -1) and b = (4, 3). Find a + b.
9. Find the exact value of cos(60°) + sin(30°).
10. The first term of an arithmetic sequence is 5 and the common difference
is 3. Find the 20th term.
pf2

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A-Level Mathematics Practice Questions

  1. Differentiate y = (3x^2 + 2x - 1)(x - 4).
  2. Solve the equation 2sin(x) = 1 for 0° ≤ x < 360°.
  3. Find the coordinates of the turning point of y = x^2 - 6x + 5.
  4. Evaluate ∫(2x^3 - 5x + 1) dx.
  5. A sequence is defined by u_n = 3n + 2. Find u_15.
  6. Find the equation of the tangent to y = x^3 at x = 2.
  7. Solve: log₂(x + 1) = 4.
  8. A vector a = (2, -1) and b = (4, 3). Find a + b.
  9. Find the exact value of cos(60°) + sin(30°).
  10. The first term of an arithmetic sequence is 5 and the common difference is 3. Find the 20th term.

Answers

  1. y = 3x³ − 10x² − 9x + 4, so dy/dx = 9x² − 20x − 9.
  2. x = 30°, 150°.
  3. (3, −4).
  4. (1/2)x⁴ − (5/2)x² + x + C.
  5. u₁₅ = 47.
  6. Gradient = 12, tangent: y = 12x − 16.
  7. x = 15.
  8. (6, 2).