AQA A-Level Mathematics Paper 3, June 2025
Every question from AQA A-Level Mathematics Paper 3, June 2025 (7357): 20 questions, 100 marks, each with its mark scheme and topic.
- Question 1 1 mark
Identify the counterexample to the claim that the product of two irrational numbers is always irrational.
Pure Mathematics · A: Proof
- Question 2 1 mark
Identify the value of the horizontal asymptote parameter $a$ for the graph of $y = \arctan x$.
Pure Mathematics · E: Trigonometry
- Question 3 1 mark
Identify whether the function f(x) = e^x is increasing or decreasing, and concave or convex.
Pure Mathematics · F: Exponentials and logarithms · G: Differentiation
- Question 4 3 marks
Evaluate logarithmic expressions involving powers of a, including log_a(a^2) and log_a(sqrt(a)) - log_a(1/a^2).
Pure Mathematics · F: Exponentials and logarithms · B: Algebra and functions
- Question 5 2 marks
Shade the region R defined by the inequalities (x - 3)(x + 4) ≤ y ≤ 2x and x ≤ 0 on the given diagram.
Pure Mathematics · B: Algebra and functions
- Question 6 4 marks
Find the coefficients in a binomial expansion of (2 - 3x)^5 and use it to calculate an approximation for 1.94^5.
Pure Mathematics · D: Sequences and series
- Question 7 3 marks
Solve the equation involving sigma notation $\sum_{r=1}^{3} (ar + 5) = 57$ to find the value of the constant $a$.
Pure Mathematics · D: Sequences and series
- Question 8 7 marks
Express a rational algebraic fraction in partial fractions and use the result to evaluate a definite integral in the form $\ln q$.
Pure Mathematics · B: Algebra and functions · F: Exponentials and logarithms · H: Integration
- Question 9 5 marks
Describe transformations mapping reciprocal graphs, find the vertical asymptote, and critique a change of sign argument across a discontinuity.
Pure Mathematics · B: Algebra and functions · I: Numerical methods
- Question 10 10 marks
Express $2\sin x + 5\cos x$ in the form $R\sin(x + \alpha)$ and use this model to find the minimum/maximum water temperature and the number of weeks the temperature exceeds 15 °C.
Pure Mathematics · E: Trigonometry
- Question 11 10 marks
Form a differential equation for the melting of a cuboid block of ice, use the chain rule to find dx/dt, and interpret the result in context.
Pure Mathematics · G: Differentiation · H: Integration
- Question 12 3 marks
Use proof by contradiction to show that if the product of two real numbers is irrational, then at least one of the numbers must be irrational.
Pure Mathematics · A: Proof
- Question 13 1 mark
Identify which of the four scatter diagrams corresponds to a product moment correlation coefficient of 0.47.
Statistics · L: Data presentation and interpretation
- Question 14 1 mark
Identify the values of $a$ and $b$ such that approximately 95% of a normal distribution with mean 9 and standard deviation 1.5 lies between $a$ and $b$.
Statistics · N: Statistical distributions
- Question 15 5 marks
Calculate binomial probabilities for the number of vegan diners in a random sample of 25 and state an assumption required for the binomial distribution model.
Statistics · N: Statistical distributions
- Question 16 7 marks
Use a histogram showing travel distances for 340 individuals to estimate the frequency within a given interval, justify why it is an estimate, identify the skewness, and explain the use of frequency density.
Statistics · L: Data presentation and interpretation
- Question 17 7 marks
Calculate the mean and variance of attendance data, evaluate a proposed binomial distribution model, and identify and evaluate an opportunity sampling method.
Statistics · K: Statistical sampling · L: Data presentation and interpretation · N: Statistical distributions
- Question 18 10 marks
Find the interquartile range of a normal distribution, then carry out a one-tailed hypothesis test for the population mean at the 5% significance level using a sample of 160 adults.
Statistics · N: Statistical distributions · O: Statistical hypothesis testing
- Question 19 10 marks
Given probabilities relating to three events X, Y, and Z, where X and Z are mutually exclusive, find P(Z), complete a Venn diagram, calculate compound and conditional probabilities, and show whether two events are independent.
Statistics · M: Probability
- Question 20 9 marks
Use a normal distribution to calculate probabilities for car emissions, explain properties of continuous models, compare distributions using mean and standard deviation, and answer questions based on the Large Data Set.
Statistics · K: Statistical sampling · L: Data presentation and interpretation · N: Statistical distributions