AQA A-Level Mathematics Paper 2, June 2025
Every question from AQA A-Level Mathematics Paper 2, June 2025 (7357): 19 questions, 100 marks, each with its mark scheme and topic.
- Question 1 1 mark
Identify the single transformation that maps the curve y = ln x onto the curve y = 2 ln x.
Pure Mathematics · B: Algebra and functions · F: Exponentials and logarithms
- Question 2 1 mark
Identify the correct sketch of the graph of y = cosec x° for 0 ≤ x ≤ 360 from four given options.
Pure Mathematics · E: Trigonometry
- Question 3 1 mark
Identify the set notation representing the solution to the quadratic inequality $(x + 2)(x - 7) > 0$ using the provided graph.
Pure Mathematics · B: Algebra and functions
- Question 4 2 marks
Solve the exponential equation 5^(x - 1) = 20, giving the answer in an exact form.
Pure Mathematics · F: Exponentials and logarithms
- Question 5 2 marks
Find the area of a circular sector with radius 8 cm and an angle of 1.4 radians.
Pure Mathematics · E: Trigonometry
- Question 6 6 marks
Use the trapezium rule to approximate the area under the curve y = e^(x/2)/(x - 3) between x = 4 and x = 8, and evaluate a claim about whether the approximation is an under- or overestimate.
Pure Mathematics · I: Numerical methods
- Question 7 9 marks
Find unknown coefficients of a cubic curve given a stationary point and determine the coordinates of the second stationary point.
Pure Mathematics · B: Algebra and functions · G: Differentiation
- Question 8 6 marks
Use trigonometric identities to evaluate sec²(x) - tan²(x), simplify an expression involving sec(x) and tan(x) to an integer constant, and state values of x where the expression is undefined.
Pure Mathematics · E: Trigonometry
- Question 9 9 marks
Analyze a circle and a modulus function intersecting at points A, B, and D, determining coordinates, finding an unknown coordinate, calculating angle ADB in radians, and finding the minor arc length AB.
Pure Mathematics · B: Algebra and functions · C: Coordinate geometry in the (x, y) plane · E: Trigonometry
- Question 10 13 marks
Differentiate a curve given by $y = x^k \ln x$, find the $y$-coordinate of its stationary point in terms of $k$, determine $k$ from a given point, and prove the curve has no point of inflection.
Pure Mathematics · G: Differentiation · F: Exponentials and logarithms · A: Proof
- Question 11 1 mark
Find the coefficient of friction given a normal reaction force of 125 N and a frictional force of 40 N.
Mechanics · R: Forces and Newton’s laws
- Question 12 1 mark
Find the displacement of a particle after 8 seconds from its velocity-time graph.
Mechanics · Q: Kinematics
- Question 13 3 marks
Use constant acceleration equations to show a car starts from rest, and explain why the constant acceleration model would eventually become invalid.
Mechanics · Q: Kinematics
- Question 14 4 marks
Calculate the speed of an arrow when it hits the ground after being projected from a height of 2.5 m with an initial velocity vector of (40, 25) m/s.
Mechanics · Q: Kinematics
- Question 15 8 marks
Find the resultant of two forces given by magnitudes and bearings, calculate the angle it makes with one force, and determine the magnitude and bearing of an equilibrant force.
Mechanics · R: Forces and Newton’s laws
- Question 16 12 marks
Calculate the tension and acceleration of a sledge pulled up an inclined plane at an angle to the slope, and state an assumption used in both models.
Mechanics · R: Forces and Newton’s laws
- Question 17 7 marks
Find the displacement vector AB, calculate its magnitude, and show that triangle ABC is scalene using 3D position vectors.
Pure Mathematics · J: Vectors
- Question 18 6 marks
Find the normal reaction force at a support by taking moments for a horizontal platform in equilibrium, and explain qualitatively how the forces change as a person moves across the platform.
Mechanics · S: Moments
- Question 19 8 marks
Find the velocity expression by differentiating displacement, and integrate acceleration to find the value of a constant when two particles move parallel at a given time.
Mechanics · Pure Mathematics · Q: Kinematics · J: Vectors