AQA A‑Level Maths questions by topic

June 2025 Paper 1, question 1: The equation of a curve is given by y = 3ex Find an expression for dy dx Circle your answer. [1 mark] 3e–x 3e1 3ex 3xex–1

June 2025 Paper 1, question 2: A sequence is defined by xn+1 = – 1 4 xn with x1 = 32 The first four terms of the sequence are 32, –8, 2, –0.5 Which one of the following can be used to describ

June 2025 Paper 1, question 3: Express log3 2x – log3 x as a single logarithm. Circle your answer. [1 mark] log3 1 2 log3 2 log3 x log3 2 x2

June 2025 Paper 1, question 4: The first three terms, in ascending powers of x, of the binomial expansion of (1 – 8x) 1 2 are 1 + nx – 8x2 where n is a constant. 4 (a) State the range of valu

June 2025 Paper 1, question 5: Find ∫(4x – 3 + x – 1 2)dx [3 marks]

June 2025 Paper 1, question 6: An arithmetic series has first term 3 and common difference –0.5 Find the sum of the first 250 terms. [2 marks]

June 2025 Paper 1, question 7: It is given that 0 &lt; a &lt; 1 Sketch the graph with equation y = ax on the axes below. [2 marks] x O y

June 2025 Paper 1, question 8: Show that, for small values of x, the graph with equation y = 4 + sin 5x – 3 cos 2x 1 + 2 tan x can be approximated by the straight line with equation of the fo

June 2025 Paper 1, question 9: (a) A geometric series, S, has second term 60 The common ratio of S is 0.2 Find the exact value of the sum of the first five terms of S [4 marks] 9 (b) A differ

June 2025 Paper 1, question 10: A researcher working for a frozen-food manufacturer uses the formula θ = 21 – Ae–kt to model the temperature of a dessert once it is taken out of a freezer. In

June 2025 Paper 1, question 11: The equation of a curve is x2y + 4y3 = 8x The curve has two stationary points. 11 (a) Use implicit differentiation to show that at the stationary points y = 4 x

June 2025 Paper 1, question 12: Functions f and g are defined by f(x) = x2 + 5 x ∈ ℝ g(x) = √ x x ≥ 0 12 (a) Using set notation, state the range of f [2 marks] 12 (b) Determine whether f has a

June 2025 Paper 1, question 13: A curve C has parametric equations x = 4(4t + 1)2 y = e–4t for – 1 4 ≤ t ≤ 0 13 (a) Find dy dx in terms of t [3 marks] 13 (b) Find an equation of the tangent to

June 2025 Paper 1, question 14: The graph of y = 4x sin 2x for 0 ≤ x ≤ π is shown below. x y O Show that the shaded area enclosed by the x-axis and the curve is kπ, where k is an integer to be

June 2025 Paper 1, question 15: A curve has equation y = x2 The point Q has coordinates (3, 2.5) The point P on the curve which is closest to the point Q is shown on the diagram below. x Q (3,

June 2025 Paper 1, question 16: The triangle ABC is shown in the diagram below. The angle ABC is π 3 radians. The angle BCA is x radians. A B C x 3 16 (a) Explain why angle BAC = 2π 3 – x [1 m

June 2025 Paper 1, question 17: (a) Use the substitution u = ex + 1 to show that ∫ e2x ex + 1 dx = ex – ln(ex + 1) + k [5 marks] 17 (b) Solve the differential equation ( ex + 1 e2x ) dy dx = c