2025 OCR
2025
A Level
OCR
2025
Further
A Level
OCR Mathematics
Further
A Level Mathematics
Further
B (MEI)
Mathematics
Y431-01
B (MEI) Y431-01
BMechanics
(MEI) Y431-01
Mechanics
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2025 OCR A Level Further Mathematics B (MEI)
Y431/01 Mechanics Minor
Verified Question paper with Marking Scheme Attached
Oxford Cambridge and RSA
Friday 6 June 2025 – Afternoon A
Level Further Mathematics B (MEI) Y431/01
Mechanics Minor
Time allowed: 1 hour 15 minutes
You must have:
• the Printed Answer Booklet
• the Formulae Booklet for Further Mathematics B
QP
(MEI)
• 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 page 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 your final answers to a degree of accuracy that is appropriate to the context.
• 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 it in the centre or recycle it.
INFORMATION
• The total mark for this paper is 60.
• 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 [K/508/5595] OCR is an exempt Charity
DC (CE/SG) 358261/3 Turn over
2025 OCR
2025
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2025
Further
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,2025 OCR
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A Level
OCR
2025
Further
A Level
OCR Mathematics
Further
A Level Mathematics
Further
B (MEI)
Mathematics
Y431-01
B (MEI) Y431-01
BMechanics
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Mechanics
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2
1 Particles A and B move towards each other on a smooth horizontal surface. Particle A has speed
3 m s-1 and particle B has speed 8 m s-1.
After they collide directly, A and B move away from each other, A with a speed of 5.2 m s-1 and B
with a speed of v m s-1 . The collision between A and B is perfectly elastic.
(a) Find the value of v. [1]
(b) State the kinetic energy lost in the collision between A and B. [1]
Two different particles, C and D, move on a smooth horizontal surface. Particle C has a speed of
6.4 m s-1 towards D and particle D has a speed of 1.9 m s-1 away from C.
After they collide directly, the particles move away from each other. The speed of C after the
collision is 0.2 m s-1 . The coefficient of restitution between C and D is 0.8.
You are given that the mass of C is 3.5 kg.
(c) Determine the mass of D. [4]
© OCR 2025 Y431/01 Jun25
2025 OCR
2025
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2025
Further
A Level
OCR Mathematics
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B (MEI)
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,2025 OCR
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OCR
2025
Further
A Level
OCR Mathematics
Further
A Level Mathematics
Further
B (MEI)
Mathematics
Y431-01
B (MEI) Y431-01
BMechanics
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Mechanics
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3
2 (a) (i) State the dimensions of force. [1]
(ii) State the dimensions of energy. [1]
The surface tension, S, of a liquid can be defined as force per unit length. It can also be defined as
energy per unit area.
(a) Show that these two definitions of surface tension are dimensionally consistent with one
another. [2]
When a droplet of liquid is placed on a non-absorbent horizontal surface, the maximum height h
m of the droplet is modelled by the formula
h = m Sagbtc ,
where
• m is a dimensionless constant,
• S is the surface tension of the liquid in Nm–1,
• g is the acceleration due to gravity in ms–2,
• t is the density of the liquid in kg m–3.
(b) Use dimensional analysis to determine the values of a , b and c . [4]
At room temperature, water has a density of 1 g cm-3 and a surface tension of 0.073 N m-1 .
When a small droplet of water is placed on a non-absorbent horizontal surface, it has maximum
height
0.53 cm.
(c) Find the value of m . [2]
© OCR 2025 Y431/01 Jun25 Turn over
2025 OCR
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OCR
2025
Further
A Level
OCR Mathematics
Further
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B (MEI)
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2025
Further
A Level
OCR Mathematics
Further
A Level Mathematics
Further
B (MEI)
Mathematics
Y431-01
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BMechanics
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4
3 The diagram shows a crate of mass 30 kg on a smooth inclined plane. One end of a light
inextensible rope is attached to the crate. The rope passes over a smooth pulley which is fixed
at the top of the plane. The other end of the rope is held by a worker.
30 kg
At first, the crate is at rest at a point A on the plane. The worker pulls continuously on the rope so
that the crate moves up the plane.
Subsequently, the crate comes to rest, in equilibrium with the rope taut, at a point B on the plane.
The vertical distance between A and B is 3.5 m.
(a) Calculate the work done by the tension in the rope as the crate moves from A to B. [1]
At a point C, which is between A and B on the plane, the rope makes an angle of 12° with AB.
The crate passes through C with a speed of 0.8 m s-1 . The tension in the rope when the crate is
at C is 206 N.
(b) Calculate the power of the tension in the rope when the crate is at C. [2]
The worker now lets the crate slide back down to A, starting from rest at B. While moving from B
to A, 894 J of work is done against the tension in the rope.
(c) Calculate the speed of the crate when it reaches A. [2]
(d) State one limitation of the model that could affect the answer to part (c). [1]
4 A block of mass m kg rests on a rough plane inclined at an angle a to the horizontal. The
coefficient of friction between the block and the plane is n. At first the block is in equilibrium,
and then a is gradually increased.
(a) Assuming that the block does not topple first, show that at the point of n = tan a . [2]
sliding
© OCR 2025 Y431/01 Jun25
2025 OCR
2025
A Level
OCR
2025
Further
A Level
OCR Mathematics
Further
A Level Mathematics
Further
B (MEI)
Mathematics
Y431-01
B (MEI) Y431-01
BMechanics
(MEI) Y431-01
Mechanics
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2025
A Level
OCR
2025
Further
A Level
OCR Mathematics
Further
A Level Mathematics
Further
B (MEI)
Mathematics
Y431-01
B (MEI) Y431-01
BMechanics
(MEI) Y431-01
Mechanics
MinorMechanics
Verified
Minor Question
Verified
Minor Question
Verified
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Question
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Marking
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Marking
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Attache.pdf
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Attache.pdf
2025 OCR A Level Further Mathematics B (MEI)
Y431/01 Mechanics Minor
Verified Question paper with Marking Scheme Attached
Oxford Cambridge and RSA
Friday 6 June 2025 – Afternoon A
Level Further Mathematics B (MEI) Y431/01
Mechanics Minor
Time allowed: 1 hour 15 minutes
You must have:
• the Printed Answer Booklet
• the Formulae Booklet for Further Mathematics B
QP
(MEI)
• 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 page 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 your final answers to a degree of accuracy that is appropriate to the context.
• 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 it in the centre or recycle it.
INFORMATION
• The total mark for this paper is 60.
• 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 [K/508/5595] OCR is an exempt Charity
DC (CE/SG) 358261/3 Turn over
2025 OCR
2025
A Level
OCR
2025
Further
A Level
OCR Mathematics
Further
A Level Mathematics
Further
B (MEI)
Mathematics
Y431-01
B (MEI) Y431-01
BMechanics
(MEI) Y431-01
Mechanics
MinorMechanics
Verified
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Marking
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,2025 OCR
2025
A Level
OCR
2025
Further
A Level
OCR Mathematics
Further
A Level Mathematics
Further
B (MEI)
Mathematics
Y431-01
B (MEI) Y431-01
BMechanics
(MEI) Y431-01
Mechanics
MinorMechanics
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2
1 Particles A and B move towards each other on a smooth horizontal surface. Particle A has speed
3 m s-1 and particle B has speed 8 m s-1.
After they collide directly, A and B move away from each other, A with a speed of 5.2 m s-1 and B
with a speed of v m s-1 . The collision between A and B is perfectly elastic.
(a) Find the value of v. [1]
(b) State the kinetic energy lost in the collision between A and B. [1]
Two different particles, C and D, move on a smooth horizontal surface. Particle C has a speed of
6.4 m s-1 towards D and particle D has a speed of 1.9 m s-1 away from C.
After they collide directly, the particles move away from each other. The speed of C after the
collision is 0.2 m s-1 . The coefficient of restitution between C and D is 0.8.
You are given that the mass of C is 3.5 kg.
(c) Determine the mass of D. [4]
© OCR 2025 Y431/01 Jun25
2025 OCR
2025
A Level
OCR
2025
Further
A Level
OCR Mathematics
Further
A Level Mathematics
Further
B (MEI)
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Y431-01
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BMechanics
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Mechanics
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,2025 OCR
2025
A Level
OCR
2025
Further
A Level
OCR Mathematics
Further
A Level Mathematics
Further
B (MEI)
Mathematics
Y431-01
B (MEI) Y431-01
BMechanics
(MEI) Y431-01
Mechanics
MinorMechanics
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3
2 (a) (i) State the dimensions of force. [1]
(ii) State the dimensions of energy. [1]
The surface tension, S, of a liquid can be defined as force per unit length. It can also be defined as
energy per unit area.
(a) Show that these two definitions of surface tension are dimensionally consistent with one
another. [2]
When a droplet of liquid is placed on a non-absorbent horizontal surface, the maximum height h
m of the droplet is modelled by the formula
h = m Sagbtc ,
where
• m is a dimensionless constant,
• S is the surface tension of the liquid in Nm–1,
• g is the acceleration due to gravity in ms–2,
• t is the density of the liquid in kg m–3.
(b) Use dimensional analysis to determine the values of a , b and c . [4]
At room temperature, water has a density of 1 g cm-3 and a surface tension of 0.073 N m-1 .
When a small droplet of water is placed on a non-absorbent horizontal surface, it has maximum
height
0.53 cm.
(c) Find the value of m . [2]
© OCR 2025 Y431/01 Jun25 Turn over
2025 OCR
2025
A Level
OCR
2025
Further
A Level
OCR Mathematics
Further
A Level Mathematics
Further
B (MEI)
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Y431-01
B (MEI) Y431-01
BMechanics
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, 2025 OCR
2025
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OCR
2025
Further
A Level
OCR Mathematics
Further
A Level Mathematics
Further
B (MEI)
Mathematics
Y431-01
B (MEI) Y431-01
BMechanics
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Mechanics
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4
3 The diagram shows a crate of mass 30 kg on a smooth inclined plane. One end of a light
inextensible rope is attached to the crate. The rope passes over a smooth pulley which is fixed
at the top of the plane. The other end of the rope is held by a worker.
30 kg
At first, the crate is at rest at a point A on the plane. The worker pulls continuously on the rope so
that the crate moves up the plane.
Subsequently, the crate comes to rest, in equilibrium with the rope taut, at a point B on the plane.
The vertical distance between A and B is 3.5 m.
(a) Calculate the work done by the tension in the rope as the crate moves from A to B. [1]
At a point C, which is between A and B on the plane, the rope makes an angle of 12° with AB.
The crate passes through C with a speed of 0.8 m s-1 . The tension in the rope when the crate is
at C is 206 N.
(b) Calculate the power of the tension in the rope when the crate is at C. [2]
The worker now lets the crate slide back down to A, starting from rest at B. While moving from B
to A, 894 J of work is done against the tension in the rope.
(c) Calculate the speed of the crate when it reaches A. [2]
(d) State one limitation of the model that could affect the answer to part (c). [1]
4 A block of mass m kg rests on a rough plane inclined at an angle a to the horizontal. The
coefficient of friction between the block and the plane is n. At first the block is in equilibrium,
and then a is gradually increased.
(a) Assuming that the block does not topple first, show that at the point of n = tan a . [2]
sliding
© OCR 2025 Y431/01 Jun25
2025 OCR
2025
A Level
OCR
2025
Further
A Level
OCR Mathematics
Further
A Level Mathematics
Further
B (MEI)
Mathematics
Y431-01
B (MEI) Y431-01
BMechanics
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Mechanics
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