AQA AS Level Mathematics Paper 1, June 2025
Every question from AQA AS Level Mathematics Paper 1, June 2025 (7356): 21 questions, 80 marks, each with its mark scheme and topic.
- Question 1 1 mark
Identify the trigonometric expression equivalent to tan x from a multiple-choice list.
Pure Mathematics · E: Trigonometry
- Question 2 1 mark
Find the value of $\log_b \frac{1}{b^2}$ from multiple choice options.
Pure Mathematics · B: Algebra and functions · F: Exponentials and logarithms
- Question 3 3 marks
Use the factor theorem to find the value of the constant a for the polynomial p(x) = 2x^3 - ax^2 + 6x + 2a given that (x - 2) is a factor.
Pure Mathematics · B: Algebra and functions
- Question 4 3 marks
Solve the trigonometric equation 2 tan(3θ) - 3 = 0 for 0° ≤ θ ≤ 180°, giving solutions to the nearest degree.
Pure Mathematics · E: Trigonometry
- Question 5 2 marks
Disprove by counterexample the claim that for two real numbers a and b, if a > b then a/b > 1.
Pure Mathematics · A: Proof
- Question 6 5 marks
Express logarithmic expressions containing powers, products, and quotients of x and y in terms of p and q, where p = log₂ x and q = log₂ y.
Pure Mathematics · B: Algebra and functions · F: Exponentials and logarithms
- Question 7 3 marks
Find the radius of a circle given in standard form and find the range of possible values for the y-coordinate of its centre given that it intersects the x-axis at two distinct points.
Pure Mathematics · B: Algebra and functions · C: Coordinate geometry in the (x, y) plane
- Question 8 4 marks
Sketch the graph of y = (x - k)^2(x + 2k) for a positive constant k, labelling all axis intercepts.
Pure Mathematics · B: Algebra and functions
- Question 9 6 marks
Find the first three terms in the binomial expansion of (1 - 5x)^7 and determine the constant k given the coefficient of x^2 in the expansion of (3 + kx)(1 - 5x)^7 is 1477.
Pure Mathematics · D: Sequences and series
- Question 10 5 marks
Find the x-coordinate of point P on the curve y = e^(3x) where the tangent is parallel to the line x - 9y = 23.
Pure Mathematics · C: Coordinate geometry in the (x, y) plane · F: Exponentials and logarithms · G: Differentiation
- Question 11 8 marks
Expand a cubic expression, evaluate a definite integral between -4 and 2, explain why this definite integral does not equal the total shaded area bounded by the curve and the x-axis, and calculate the actual total area.
Pure Mathematics · B: Algebra and functions · H: Integration
- Question 12 3 marks
Use the factorial definition of combinations to find an unknown value in a factorial expression and evaluate the ratio of two consecutive combinations.
Pure Mathematics · D: Sequences and series
- Question 13 9 marks
Use an exponential decay model for points scored in a computer game to interpret parameters, linearise using logarithms, determine constants from a line of best fit, and solve for time given a specific score.
Pure Mathematics · F: Exponentials and logarithms
- Question 14 1 mark
Calculate the acceleration of a 2 kg particle subjected to a single horizontal force of 5 N.
Mechanics · R: Forces and Newton’s laws
- Question 15 1 mark
Identify which pair of given force vectors, if any, are parallel.
Mechanics · Pure Mathematics · J: Vectors · R: Forces and Newton’s laws
- Question 16 2 marks
Calculate the speed from a linear displacement-time graph and sketch a more realistic displacement-time graph for a car starting from rest.
Mechanics · Q: Kinematics
- Question 17 2 marks
Find the normal reaction force exerted by the floor of a lift on a person of mass 60 kg when the lift is accelerating upwards at 1.2 m s⁻².
Mechanics · R: Forces and Newton’s laws
- Question 18 3 marks
Find the maximum height reached above the ground by a ball projected vertically upwards from a height of 1.8 metres with an initial speed of 12 m s⁻¹.
Mechanics · Q: Kinematics
- Question 19 3 marks
Find the possible values of a constant component of a force vector given its magnitude.
Mechanics · Pure Mathematics · J: Vectors · R: Forces and Newton’s laws
- Question 20 8 marks
Use a quadratic velocity-time model to find the initial speed, acceleration, maximum speed of an athlete, and evaluate the model's accuracy.
Mechanics · Pure Mathematics · Q: Kinematics · G: Differentiation
- Question 21 7 marks
Find the acceleration and tension in terms of g for two connected buckets over a pulley after a mass is added to one, and state a limitation of modelling the buckets as particles.
Mechanics · R: Forces and Newton’s laws