AQA AS Level Mathematics Paper 2, June 2025
Every question from AQA AS Level Mathematics Paper 2, June 2025 (7356): 21 questions, 80 marks, each with its mark scheme and topic.
- Question 1 1 mark
Identify which of the four given sketches represents the curve with equation y = (x + a)^2, where a is a positive constant.
Pure Mathematics · B: Algebra and functions
- Question 2 1 mark
Find the second derivative of a function given its first derivative f'(x) = 3x^2.
Pure Mathematics · G: Differentiation
- Question 3 4 marks
Find the size of the obtuse angle CAB of a triangular prism's cross-section given side lengths 6 cm and 10 cm, prism length 20 cm, and volume 500 cm³.
Pure Mathematics · E: Trigonometry
- Question 4 5 marks
Find the gradient of a line, determine an unknown coordinate using the properties of a perpendicular bisector, and calculate the point of intersection.
Pure Mathematics · C: Coordinate geometry in the (x, y) plane
- Question 5 4 marks
Use the substitution u = 4^x to solve the quadratic-form exponential equation 16(4^(2x)) - 33(4^x) + 2 = 0.
Pure Mathematics · B: Algebra and functions · F: Exponentials and logarithms
- Question 6 4 marks
Solve the simultaneous equations x = 2y - 11 and y = 2x² - 4x + 1, fully justifying your answer.
Pure Mathematics · B: Algebra and functions
- Question 7 6 marks
Express a quadratic in completed square form, then use it to find the minimum value of a trigonometric expression and the smallest positive angle at which it occurs.
Pure Mathematics · B: Algebra and functions · E: Trigonometry
- Question 8 8 marks
Find the coordinates of the minimum point of the cubic curve y = x^3 - 5x^2 - 8x + 2 and fully justify your answer.
Pure Mathematics · B: Algebra and functions · G: Differentiation
- Question 9 3 marks
Find the values of definite integrals of transformed versions of a function f(x) given that the definite integral of f(x) from 1 to 3 is 8.
Pure Mathematics · H: Integration · B: Algebra and functions
- Question 10 4 marks
Show that 1/(sqrt(k) + sqrt(k + 1)) is equivalent to sqrt(k + 1) - sqrt(k) and use the result to evaluate a sum of surd fractions.
Pure Mathematics · B: Algebra and functions · A: Proof
- Question 11 4 marks
Find the range of possible values of k given that the quadratic equation x^2 + (2k - 1)x + 4 - 2k = 0 has two distinct real roots.
Pure Mathematics · B: Algebra and functions
- Question 12 9 marks
Use right-angled trigonometry to find expressions for side lengths in terms of $\cos\theta$ and solve a trigonometric quadratic equation to find $\theta$.
Pure Mathematics · B: Algebra and functions · E: Trigonometry
- Question 13 1 mark
Find the probability from a two-way table that a randomly chosen student is a Year 12 student whose favourite sport is netball.
Statistics · M: Probability
- Question 14 1 mark
Given independent events A and B with P(A) = 0.25 and P(B) = 0.6, find the value of P(A ∩ B).
Statistics · M: Probability
- Question 15 2 marks
Find the unknown frequency density $k$ in a histogram given that the frequency of one class interval is double that of another.
Statistics · L: Data presentation and interpretation
- Question 16 2 marks
Find the value of the constant p in a given discrete probability distribution table.
Statistics · N: Statistical distributions
- Question 17 4 marks
Interpret a scatter diagram relating wind speed and raincoat sales to identify an outlier, assess the effect of removing it on the correlation coefficient, describe the correlation in context, and comment on causality.
Statistics · L: Data presentation and interpretation
- Question 18 4 marks
State an assumption for modelling faulty batteries with a binomial distribution, calculate the probability of one faulty battery in a pack of 12, and determine the probability that at least two of 10 packs contain exactly one faulty battery.
Statistics · N: Statistical distributions
- Question 19 4 marks
Calculate summary statistics for carbon dioxide emissions from the Large Data Set and evaluate data validity across years.
Statistics · K: Statistical sampling · L: Data presentation and interpretation
- Question 20 4 marks
Calculate the probabilities of stopping at all four traffic lights and at exactly one of four independent traffic lights given their individual probabilities of being red.
Statistics · M: Probability
- Question 21 5 marks
Conduct a 5% significance level binomial hypothesis test to determine if the proportion of concert attendees having an excellent experience is less than 80%, given a sample of 42 out of 60.
Statistics · N: Statistical distributions · O: Statistical hypothesis testing