AS LEVEL FURTHER MATHEMATICS A: Actual May 2025 PAST PAPER 1:
Mechanics. All Assessment Questions & Mark Scheme [OCR Y533/01]
Exam Resource Summary
The AS Level Further Mathematics A May 2025 Paper Y533/01: Mechanics (OCR) – All
Assessment Questions & Mark Scheme document combines the full official examination paper
with its complete mark scheme to provide a detailed and effective revision resource. This paper
assesses students’ understanding of advanced mechanics topics, including kinematics, forces
and equilibrium, work, energy and power, momentum, and centres of mass. It requires the
application of mathematical modelling and problem-solving techniques to analyse motion,
predict outcomes, and interpret real-world physical systems. The merged format presents each
question alongside its corresponding marking criteria, offering clarity on examiner expectations,
mark distribution, and structured solution methods. This resource is essential for focused
revision, self-assessment, and strengthening analytical and problem-solving skills, making it a key
tool for preparation for the May 2026 OCR AS Level Further Mathematics A Paper Y533/01:
Mechanics examination.
Turn over
, 2
1 A cricket ball of mass 0.16 kg is at rest on rough horizontal ground when it is struck by a bat.
Immediately after the ball is struck its speed is 15 ms -1 in a horizontal direction.
(a) Find the magnitude of the impulse exerted by the bat on the ball. [1]
The ball remains in contact with the ground and the resistance to the motion of the ball is
modelled as constant.
The ball comes to rest again after it has travelled 30 m along the ground.
(b) Use the work-energy principle to find the magnitude of the resistance to the motion of the
ball. [3]
2 Two particles, A of mass m kg and B of mass 2m kg, are connected by a light inextensible string.
The particles are initially placed together at rest on a smooth horizontal surface with the string
slack.
At a certain instant, A and B are projected along the surface, directly away from each other, with
speeds of 3 ms -1 and u ms -1 respectively. You are given that u11.5.
(a) Find, in terms of u, the speed of A immediately after the string becomes taut. [2]
(b) (i) State the direction of motion of B immediately after the string becomes taut. [1]
(ii) Find, in terms of m and u, the magnitude of the impulse exerted on B as a result of the
string becoming taut. [2]
(iii) Write down an expression for the impulse exerted on A as a result of the string becoming
taut. [1]
m (3 + u) 2
(c) Show that the loss of kinetic energy as a result of the string becoming taut is J. [3]
3
© OCR 2025 Y533/01 Jun25
, 3
3 A car of mass 900 kg has an engine that is capable of working at a maximum power of 12 kW.
When the car is travelling along a straight horizontal road, the maximum constant speed that it can
maintain is 40 ms -1 .
In an initial model of the motion of the car it is assumed that the total resistance to motion is
constant.
(a) (i) Show that when the car is travelling at 15 ms -1 along the horizontal road with the engine
working at a constant rate of 10 kW, the acceleration of the car is 0.407 ms -2 correct to
3 significant figures. [3]
(ii) Find the speed of the car when it is accelerating at 0.2 ms -2 along the horizontal road
with the engine working at a constant rate of 9.6 kW. [2]
(iii) The car now starts to descend a straight road which is inclined at 1° to the horizontal.
Find the power produced by the engine of the car when it is travelling along this road at
a constant speed of 40 ms -1 . [2]
In a refined model of the motion of the car it is assumed that the total resistance to motion is
proportional to the speed of the car.
(b) (i) Show that the total resistance to the motion of the car is now given by 7.5v N where
v ms -1 is the speed of the car. [1]
(ii) State one way in which the refined model is an improvement over the initial model. [1]
(iii) Find, according to the refined model, the speed of the car when it is accelerating at
0.2 ms -2 along the horizontal road with the engine working at a constant rate of 9.6 kW.
[3]
4 Two particles, A of mass 4 kg and B of mass 2 kg, are free to move along the same straight line
on a smooth horizontal surface. They are projected directly towards each other with speeds of
6 ms -1 and 5 ms -1 respectively.
After A and B collide the speed of A is 1 ms -1.
(a) Determine the possible values of the coefficient of restitution between A and B. [6]
(b) State whether the collision between A and B is perfectly elastic. Justify your answer. [1]
© OCR 2025 Y533/01 Jun25 Turn over
Mechanics. All Assessment Questions & Mark Scheme [OCR Y533/01]
Exam Resource Summary
The AS Level Further Mathematics A May 2025 Paper Y533/01: Mechanics (OCR) – All
Assessment Questions & Mark Scheme document combines the full official examination paper
with its complete mark scheme to provide a detailed and effective revision resource. This paper
assesses students’ understanding of advanced mechanics topics, including kinematics, forces
and equilibrium, work, energy and power, momentum, and centres of mass. It requires the
application of mathematical modelling and problem-solving techniques to analyse motion,
predict outcomes, and interpret real-world physical systems. The merged format presents each
question alongside its corresponding marking criteria, offering clarity on examiner expectations,
mark distribution, and structured solution methods. This resource is essential for focused
revision, self-assessment, and strengthening analytical and problem-solving skills, making it a key
tool for preparation for the May 2026 OCR AS Level Further Mathematics A Paper Y533/01:
Mechanics examination.
Turn over
, 2
1 A cricket ball of mass 0.16 kg is at rest on rough horizontal ground when it is struck by a bat.
Immediately after the ball is struck its speed is 15 ms -1 in a horizontal direction.
(a) Find the magnitude of the impulse exerted by the bat on the ball. [1]
The ball remains in contact with the ground and the resistance to the motion of the ball is
modelled as constant.
The ball comes to rest again after it has travelled 30 m along the ground.
(b) Use the work-energy principle to find the magnitude of the resistance to the motion of the
ball. [3]
2 Two particles, A of mass m kg and B of mass 2m kg, are connected by a light inextensible string.
The particles are initially placed together at rest on a smooth horizontal surface with the string
slack.
At a certain instant, A and B are projected along the surface, directly away from each other, with
speeds of 3 ms -1 and u ms -1 respectively. You are given that u11.5.
(a) Find, in terms of u, the speed of A immediately after the string becomes taut. [2]
(b) (i) State the direction of motion of B immediately after the string becomes taut. [1]
(ii) Find, in terms of m and u, the magnitude of the impulse exerted on B as a result of the
string becoming taut. [2]
(iii) Write down an expression for the impulse exerted on A as a result of the string becoming
taut. [1]
m (3 + u) 2
(c) Show that the loss of kinetic energy as a result of the string becoming taut is J. [3]
3
© OCR 2025 Y533/01 Jun25
, 3
3 A car of mass 900 kg has an engine that is capable of working at a maximum power of 12 kW.
When the car is travelling along a straight horizontal road, the maximum constant speed that it can
maintain is 40 ms -1 .
In an initial model of the motion of the car it is assumed that the total resistance to motion is
constant.
(a) (i) Show that when the car is travelling at 15 ms -1 along the horizontal road with the engine
working at a constant rate of 10 kW, the acceleration of the car is 0.407 ms -2 correct to
3 significant figures. [3]
(ii) Find the speed of the car when it is accelerating at 0.2 ms -2 along the horizontal road
with the engine working at a constant rate of 9.6 kW. [2]
(iii) The car now starts to descend a straight road which is inclined at 1° to the horizontal.
Find the power produced by the engine of the car when it is travelling along this road at
a constant speed of 40 ms -1 . [2]
In a refined model of the motion of the car it is assumed that the total resistance to motion is
proportional to the speed of the car.
(b) (i) Show that the total resistance to the motion of the car is now given by 7.5v N where
v ms -1 is the speed of the car. [1]
(ii) State one way in which the refined model is an improvement over the initial model. [1]
(iii) Find, according to the refined model, the speed of the car when it is accelerating at
0.2 ms -2 along the horizontal road with the engine working at a constant rate of 9.6 kW.
[3]
4 Two particles, A of mass 4 kg and B of mass 2 kg, are free to move along the same straight line
on a smooth horizontal surface. They are projected directly towards each other with speeds of
6 ms -1 and 5 ms -1 respectively.
After A and B collide the speed of A is 1 ms -1.
(a) Determine the possible values of the coefficient of restitution between A and B. [6]
(b) State whether the collision between A and B is perfectly elastic. Justify your answer. [1]
© OCR 2025 Y533/01 Jun25 Turn over
