2025 OCR A Level Further Mathematics A Y543/01 Mechanics
Combined Question Paper & Final Marking Scheme
Oxford Cambridge and RSA
Friday 13 June 2025 – Afternoon
A Level Further Mathematics A
Y543/01 Mechanics
Time allowed: 1 hour 30 minutes
You must have:
• the Printed Answer Booklet
• the Formulae Booklet for A Level Further
QP
Mathematics A
• a scientific or graphical calculator
INSTRUCTIONS
• Use black ink. You can use an HB pencil, but only for graphs and diagrams.
• Write your answer to each question in the space provided in the Printed Answer
Booklet. If you need extra space use the lined pages at the end of the Printed Answer
Booklet. The question numbers must be clearly shown.
• Fill in the boxes on the front of the Printed Answer Booklet.
• Answer all the questions.
• Where appropriate, your answer should be supported with working. Marks might be
given for using a correct method, even if your answer is wrong.
• Give non-exact numerical answers correct to 3 significant figures unless a different
degree of accuracy is specified in the question.
• The acceleration due to gravity is denoted by g m s–2. When a numerical value is
needed use g = 9.8 unless a different value is specified in the question.
• Do not send this Question Paper for marking. Keep in the centre or recycle it.
INFORMATION
• The total mark for this paper is 75.
• The marks for each question are shown in brackets [ ].
• This document has 8 pages.
ADVICE
• Read each question carefully before you start your answer.
, © OCR 2025 [603/1325/0] OCR is an exempt Charity
DC (DE/CB) 357860/3 Turn over
*1920696858*
, 2
1 A particle P of mass 4 kg is moving in a straight line with a speed of 7 m s-1 on a smooth
horizontal surface.
A constant force of magnitude 12 N acts on P for 5 seconds in the same direction as P’s motion.
(a) Find the magnitude of the impulse exerted by the force on P. You must include the units. [2]
(b) Hence determine the speed of P at the instant when the force stops acting. [2]
(c) By considering the change in the kinetic energy of P, determine the work done by the force
over the 5 seconds that it acts. [2]
(d) Hence find the distance travelled by P while the force is acting on it. [2]
2 Dynamic viscosity is a physical property of liquids and is denoted by h.
The units of h are Ns /m 2 .
(a) Determine the dimensions of h. [3]
Kinematic viscosity is another physical property of liquids and is denoted by o.
h
Kinematic viscosity and dynamic viscosity are related by the formula o = where t is the
t
density (mass per unit volume) of the liquid.
(b) By finding the dimensions of o, state a possible unit for o. [3]
© OCR 2025 Y543/01 Jun25
, 3
3 In this question you must show detailed reasoning.
A particle P of mass 3.25 kg is moving on a smooth horizontal plane with velocity v m s-1
where v = 4i - 6j.
(a) Find the kinetic energy of P. [2]
A system of horizontal forces starts to act on P. One of the forces is F N where F = i - (3 + t) j
and t is the time, in seconds, after the system of forces starts to act.
(b) Find the power developed by F at time t = 0. [2]
(c) Given that the velocity of P does not change at any time, find the total power developed by
the forces other than F at time t = 6. [2]
4 Two particles, P of mass 2 kg and Q of mass 0.5 kg, are moving on a smooth horizontal surface.
Particle P is moving with speed 1.5 m s-1 directly towards a vertical wall. Particle Q is between P
and the wall and is moving directly towards P with speed 3.5 m s-1 (see diagram).
1.5 m s–1 3.5 m s–1
2 kg 0.5 kg
P Q
The particles collide directly. After the collision, P moves away from the wall with speed
0.3 m s-1 . The coefficient of restitution between P and Q is denoted by e.
(a) Determine the value of e. [4]
After this collision, Q goes on to collide directly with the wall. The coefficient of restitution
1
between Q and the wall is 10e.
(b) Determine whether there will be a subsequent collision between P and Q. [2]
© OCR 2025 Y543/01 Jun25 Turn over
Combined Question Paper & Final Marking Scheme
Oxford Cambridge and RSA
Friday 13 June 2025 – Afternoon
A Level Further Mathematics A
Y543/01 Mechanics
Time allowed: 1 hour 30 minutes
You must have:
• the Printed Answer Booklet
• the Formulae Booklet for A Level Further
QP
Mathematics A
• a scientific or graphical calculator
INSTRUCTIONS
• Use black ink. You can use an HB pencil, but only for graphs and diagrams.
• Write your answer to each question in the space provided in the Printed Answer
Booklet. If you need extra space use the lined pages at the end of the Printed Answer
Booklet. The question numbers must be clearly shown.
• Fill in the boxes on the front of the Printed Answer Booklet.
• Answer all the questions.
• Where appropriate, your answer should be supported with working. Marks might be
given for using a correct method, even if your answer is wrong.
• Give non-exact numerical answers correct to 3 significant figures unless a different
degree of accuracy is specified in the question.
• The acceleration due to gravity is denoted by g m s–2. When a numerical value is
needed use g = 9.8 unless a different value is specified in the question.
• Do not send this Question Paper for marking. Keep in the centre or recycle it.
INFORMATION
• The total mark for this paper is 75.
• The marks for each question are shown in brackets [ ].
• This document has 8 pages.
ADVICE
• Read each question carefully before you start your answer.
, © OCR 2025 [603/1325/0] OCR is an exempt Charity
DC (DE/CB) 357860/3 Turn over
*1920696858*
, 2
1 A particle P of mass 4 kg is moving in a straight line with a speed of 7 m s-1 on a smooth
horizontal surface.
A constant force of magnitude 12 N acts on P for 5 seconds in the same direction as P’s motion.
(a) Find the magnitude of the impulse exerted by the force on P. You must include the units. [2]
(b) Hence determine the speed of P at the instant when the force stops acting. [2]
(c) By considering the change in the kinetic energy of P, determine the work done by the force
over the 5 seconds that it acts. [2]
(d) Hence find the distance travelled by P while the force is acting on it. [2]
2 Dynamic viscosity is a physical property of liquids and is denoted by h.
The units of h are Ns /m 2 .
(a) Determine the dimensions of h. [3]
Kinematic viscosity is another physical property of liquids and is denoted by o.
h
Kinematic viscosity and dynamic viscosity are related by the formula o = where t is the
t
density (mass per unit volume) of the liquid.
(b) By finding the dimensions of o, state a possible unit for o. [3]
© OCR 2025 Y543/01 Jun25
, 3
3 In this question you must show detailed reasoning.
A particle P of mass 3.25 kg is moving on a smooth horizontal plane with velocity v m s-1
where v = 4i - 6j.
(a) Find the kinetic energy of P. [2]
A system of horizontal forces starts to act on P. One of the forces is F N where F = i - (3 + t) j
and t is the time, in seconds, after the system of forces starts to act.
(b) Find the power developed by F at time t = 0. [2]
(c) Given that the velocity of P does not change at any time, find the total power developed by
the forces other than F at time t = 6. [2]
4 Two particles, P of mass 2 kg and Q of mass 0.5 kg, are moving on a smooth horizontal surface.
Particle P is moving with speed 1.5 m s-1 directly towards a vertical wall. Particle Q is between P
and the wall and is moving directly towards P with speed 3.5 m s-1 (see diagram).
1.5 m s–1 3.5 m s–1
2 kg 0.5 kg
P Q
The particles collide directly. After the collision, P moves away from the wall with speed
0.3 m s-1 . The coefficient of restitution between P and Q is denoted by e.
(a) Determine the value of e. [4]
After this collision, Q goes on to collide directly with the wall. The coefficient of restitution
1
between Q and the wall is 10e.
(b) Determine whether there will be a subsequent collision between P and Q. [2]
© OCR 2025 Y543/01 Jun25 Turn over
