AQA A-Level Mathematics Paper 1, June 2025
Every question from AQA A-Level Mathematics Paper 1, June 2025 (7357): 17 questions, 100 marks, each with its mark scheme and topic.
- Question 1 1 mark
Find the derivative of the exponential curve y = 3e^x.
Pure Mathematics · G: Differentiation · F: Exponentials and logarithms
- Question 2 1 mark
Identify the property describing a given alternating sequence defined by a recurrence relation.
Pure Mathematics · D: Sequences and series
- Question 3 1 mark
Express the difference of logarithms log base 3 of 2x minus log base 3 of x as a single logarithm.
Pure Mathematics · F: Exponentials and logarithms
- Question 4 2 marks
Determine the validity range and the coefficient of the linear term for the binomial expansion of (1 - 8x)^(1/2).
Pure Mathematics · D: Sequences and series
- Question 5 3 marks
Find the indefinite integral of 4x - 3 + x^(-1/2) with respect to x.
Pure Mathematics · H: Integration
- Question 6 2 marks
Calculate the sum of the first 250 terms of an arithmetic series with first term 3 and common difference -0.5.
Pure Mathematics · D: Sequences and series
- Question 7 2 marks
Sketch the graph of the exponential function y = a^x given that 0 < a < 1.
Pure Mathematics · F: Exponentials and logarithms
- Question 8 5 marks
Show that for small values of x, the trigonometric rational function can be approximated by a linear equation of the form y = ax + 1.
Pure Mathematics · E: Trigonometry · B: Algebra and functions
- Question 9 10 marks
Work with geometric series to find the sum of five terms, express the sum to infinity in terms of the common ratio, and determine its range of values.
Pure Mathematics · B: Algebra and functions · D: Sequences and series
- Question 10 12 marks
Rearrange an exponential cooling/warming model into linear logarithmic form, determine the parameters from a straight-line graph, and calculate initial temperature and time taken to reach a given temperature.
Pure Mathematics · C: Coordinate geometry in the (x, y) plane · F: Exponentials and logarithms
- Question 11 7 marks
Use implicit differentiation to find a relation between x and y at the stationary points of x²y + 4y³ = 8x, and find the x-coordinates in the form ±√n.
Pure Mathematics · G: Differentiation
- Question 12 8 marks
Given functions f(x) = x² + 5 and g(x) = √x, state the range of f, determine whether f has an inverse, sketch the graph of g⁻¹(x), and find the expression and range for the composite function h(x) = gf(x).
Pure Mathematics · B: Algebra and functions
- Question 13 9 marks
Differentiate parametric equations involving quadratic and exponential terms to find dy/dx, determine the equation of a tangent at t = 0, and find the justified Cartesian equation in the form y = f(x).
Pure Mathematics · C: Coordinate geometry in the (x, y) plane · G: Differentiation
- Question 14 8 marks
Show that the shaded area enclosed by the curve y = 4x sin 2x and the x-axis for 0 ≤ x ≤ π is equal to kπ, finding the integer k.
Pure Mathematics · H: Integration · E: Trigonometry
- Question 15 12 marks
Use differentiation or normal line properties to form a cubic equation for the point on a parabola closest to a given point, derive the Newton–Raphson iteration formula, and calculate the minimum distance.
Pure Mathematics · C: Coordinate geometry in the (x, y) plane · G: Differentiation · I: Numerical methods
- Question 16 7 marks
Use the sine rule and compound angle identities in triangle ABC with angles π/3 and x to express BC/AB in terms of cot x, and deduce the value of x for a given ratio.
Pure Mathematics · E: Trigonometry
- Question 17 10 marks
Use integration by substitution to evaluate an integral involving exponentials, and solve a separable first-order differential equation with initial conditions.
Pure Mathematics · H: Integration · F: Exponentials and logarithms