AQA A Level Maths Paper 2 June 2025 question paper 7357/2

Describe the single transformation which maps the curve with the equation

y = ln x

onto the curve with the equation

y = 2 ln x

Tick () one box.

Stretch, scale factor 2, parallel to the y-axis

Stretch, scale factor , parallel to the x-axis

One of the diagrams below shows the graph of y = cosec x° for 0 ≤ x ≤ 360

Identify the correct graph.

Tick () one box.

The diagram shows the graph with equation y = (x + 2)(x – 7)

Solve the inequality.

(x + 2)(x – 7) > 0

Tick () one box.

The diagram shows a sector AOB of a circle with centre O and radius 8 cm.

The angle AOB is 1.4 radians.

Find the area of the sector.

The curve with equation y = is shown in the diagram.

The region shaded is bounded by the curve, the x-axis, and the lines x = 4 and x = 8

The trapezium rule with six ordinates (5 strips) is to be used to find an approximate value for the area of the shaded region.

Some of the values required to obtain this approximation are shown in the table below.

Find the y-value that is missing from the table.

Use the trapezium rule with six ordinates (5 strips) to find an approximate value for the area of the shaded region.

Give your answer to five significant figures.

A student finds an improved approximation for the area of the shaded region by using the trapezium rule with 11 ordinates.

The student correctly obtains 29.759 as their improved approximation.

The student claims that the exact area must be greater than 29.759

Without further calculation, explain whether or not the student is correct.

The point A lies on the curve with equation

Given that A has coordinates (– 5, 37), show that

5 p – q = 30

Given that A is a stationary point, show that

10 p – q = 75

Hence find the value of p and the value of q

The curve with equation

has a second stationary point B

Find the coordinates of B

Fully justify your answer.

Show that

where N is an integer to be found.

State the two values of x between 0° and 360° for which the value of N in part (b) is not valid.

A circle with centre C has equation

The graph with equation

y = │ 3 x – 36 │ – 8

intersects the circle at the points A, B and D as shown in the diagram.

Point D is vertically below point C

State the coordinates of C

State the coordinates of D

The coordinates of A are (a,10)

Find the value of a

Fully justify your answer.

Find, in radians, the angle ADB

Give your answer to three significant figures.

Hence or otherwise find the length of the minor arc AB

Give your answer to three significant figures.

A curve C has equation

where k is a positive integer.

Show that

where A is a constant to be found.

Hence show that the y-coordinate of the stationary point of C can be written as Fully justify your answer.

Given that the stationary point of C has coordinates – state the value of k

An object is pulled along a horizontal surface. The normal reaction between the surface and the object is 125 newtons.

The object experiences a constant frictional force of 40 newtons.

Find the value of the coefficient of friction.

Circle your answer.

0.245 0.32 0.5 3.125

A particle moves in a straight line for 8 seconds.

The velocity v, in m s^–1, of the particle at time t seconds is shown in the diagram.

Find the displacement, in metres, of the particle after 8 seconds.

Circle your answer.

–12 0 6 12

A car moves, in a straight line on a horizontal road, from a point A to a point B

The distance AB is 225 metres.

At the point B, the velocity of the car is 30 m s^–1

The car is modelled as having a constant acceleration of 2 m s^–2

Show that the car starts from rest at point A

The car continues to move past the point B in the same straight line.

Explain why the model would eventually become invalid.

A particle moves under the actions of two forces, F₁ and F₂

F₁ has magnitude 17 newtons and acts due East. F₂ has magnitude 26 newtons and acts at a bearing of 310°

The resultant of F₁ and F₂ is R

Show that the magnitude of R is 17.0 newtons, correct to three significant figures.

Find the angle that R makes with F₁

Give your answer to the nearest degree.

A third force, F₃, acts upon the particle so that the particle is in equilibrium.

State the magnitude of F₃

State the bearing on which F₃ acts.

– 2 16 In this question use g = 9.8 m s

A sledge is pulled in a straight line up a rough path, as shown in the diagram.

The path is inclined at an angle of 20° to the horizontal.

The sledge is pulled by a light, inextensible rope inclined at an angle of 30° to the path.

The mass of the sledge is 10 kilograms.

In one model, the sledge moves at a constant speed and experiences a combined resistance force of 15 newtons.

Find the tension in the rope for this model.

In a different model, the sledge experiences no air resistance.

The tension in the rope for this model is 54 N

The coefficient of friction between the sledge and the path is 0.2

Find the acceleration of the sledge for this model.

State an assumption you have used to answer both parts (a) and (b).

A triangle has vertices A, B and C with position vectors given by

Hence show that triangle ABC is a scalene triangle.

– 2 18 In this question use g = 9.81 m s

A uniform platform AD has length 2.5 metres and weight 400 newtons.

The platform is attached to a chain at A. The other end of the chain is fixed to the floor.

The platform rests on a support at a point B which is 0.6 metres from A

The support exerts an upwards reaction force on the platform.

A child of mass 30 kilograms stands at a point C

The point C is 0.2 metres from D, as shown in the diagram.

The system is in equilibrium with the platform resting horizontally.

By taking moments about A, find the reaction force at B

The child moves from C to B

State what happens to the reaction force at B during this movement.

Having reached B, the child steps off the platform.

State what happens to the tension in the chain during this movement.

The displacement, s metres, of a particle P, at time t seconds, is given by

Find an expression for the velocity of particle P after t seconds.

The acceleration, a m s^–2, of a particle Q, at time t seconds, is given by

a = 6 t i + 7 j

Particle Q has an initial velocity of 4j m s^–1

Particles P and Q are moving parallel to each other when t = 2

Find the value of q