A-Level A-Level Mathematics

Question 1

What is the derivative of f(x) = x⁴ − 3x² + 5x − 2?

Accepted Answer

4x³ − 6x + 5

Answer

4x³ + 6x − 5

Answer

4x³ − 3x + 5

Answer

x⁵ − x³ + 5x²

Question 2

What does ∫(3x² + 2x) dx equal?

Accepted Answer

x³ + x² + C

Answer

6x + 2 + C

Answer

3x³ + x² + C

Answer

x³ + 2x + C

Question 3

What is the binomial expansion of (1 + x)ⁿ for small x?

Accepted Answer

1 + nx + n(n−1)/2! · x² + n(n−1)(n−2)/3! · x³ + ...

Answer

1 + nx only

Answer

nxⁿ

Answer

1 + x + x² + x³

Question 4

Solve: 2sin²θ − sinθ − 1 = 0 for 0° ≤ θ ≤ 360°

Accepted Answer

θ = 90°, 210°, 330°

Answer

θ = 30°, 150°

Answer

θ = 30°, 150°, 270°

Answer

θ = 60°, 120°, 270°

Question 5

What is the chain rule for differentiation?

Accepted Answer

dy/dx = dy/du × du/dx

Answer

dy/dx = dy/du + du/dx

Answer

dy/dx = du/dy × dx/du

Answer

dy/dx = (dy/du) ÷ (du/dx)

Question 6

What is the sum of an infinite geometric series with first term a and common ratio r (|r| < 1)?

Accepted Answer

a/(1 − r)

Answer

a(1 − r)

Answer

ar/(1 − r)

Answer

a/(1 + r)