2025 OCR
2025
A OCR
Level
2025AFurther
OCR
Level AFurther
Mathematics
Level Further
Mathematics
B Mathematics
(MEI)BY421-01
(MEI)BY421-01
Mechanics
(MEI) Y421-01
Mechanics
Major
Mechanics
Verified
Major Verified
Question
Major Verified
Question
paperQuestion
with
paper
Marking
with
paper
Marking
Scheme
with Marking
Scheme
Attached.pdf
Scheme
Attached.pdf
Attached.pdf
2025 OCR A Level Further Mathematics B (MEI)
Y421/01 Mechanics Major
Verified Question paper with Marking Scheme Attached
Oxford Cambridge and RSA
Friday 6 June 2025 – Afternoon A
Level Further Mathematics B (MEI) Y421/01
Mechanics Major
Time allowed: 2 hours 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 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 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 120.
• The marks for each question are shown in brackets [ ].
• This document has 12 pages.
ADVICE
• Read each question carefully before you start your answer.
© OCR 2025 [D/508/5593] OCR is an exempt Charity
DC (ST/TC) 356295/6 Turn over
2025 OCR
2025
A OCR
Level
2025AFurther
OCR
Level AFurther
Mathematics
Level Further
Mathematics
B Mathematics
(MEI)BY421-01
(MEI)BY421-01
Mechanics
(MEI) Y421-01
Mechanics
Major
Mechanics
Verified
Major Verified
Question
Major Verified
Question
paperQuestion
with
paper
Marking
with
paper
Marking
Scheme
with Marking
Scheme
Attached.pdf
Scheme
Attached.pdf
Attached.pdf
,2025 OCR
2025
A OCR
Level
2025AFurther
OCR
Level AFurther
Mathematics
Level Further
Mathematics
B Mathematics
(MEI)BY421-01
(MEI)BY421-01
Mechanics
(MEI) Y421-01
Mechanics
Major
Mechanics
Verified
Major Verified
Question
Major Verified
Question
paperQuestion
with
paper
Marking
with
paper
Marking
Scheme
with Marking
Scheme
Attached.pdf
Scheme
Attached.pdf
Attached.pdf
2
Section A (33 marks)
1 A small box of mass 3 kg is pulled along a horizontal floor by a constant force of magnitude 35 N.
The force acts at an angle of i above the horizontal.
The total resistance to the motion of the box has magnitude 25 N.
The box starts from rest at a point O, and passes through a point 4 m from O with
speed 1.5 m s-1 .
Use an energy method to determine the value of i. [3]
2
y
4
A 7m
2 B 2m
–4 –2 0 2 4 x
–2
C km
The diagram shows a system of three particles of masses 7m, 2m and km situated in the x-y
plane at the points A(-2, 3), B(4, 2) and C(1, -2) respectively.
The centre of mass of the three particles is at the point with coordinates (0, d ).
(a) Find the value of k. [2]
(b) Find the value of d. [2]
© OCR 2025 Y421/01 Jun25
2025 OCR
2025
A OCR
Level
2025AFurther
OCR
Level AFurther
Mathematics
Level Further
Mathematics
B Mathematics
(MEI)BY421-01
(MEI)BY421-01
Mechanics
(MEI) Y421-01
Mechanics
Major
Mechanics
Verified
Major Verified
Question
Major Verified
Question
paperQuestion
with
paper
Marking
with
paper
Marking
Scheme
with Marking
Scheme
Attached.pdf
Scheme
Attached.pdf
Attached.pdf
,2025 OCR
2025
A OCR
Level
2025AFurther
OCR
Level AFurther
Mathematics
Level Further
Mathematics
B Mathematics
(MEI)BY421-01
(MEI)BY421-01
Mechanics
(MEI) Y421-01
Mechanics
Major
Mechanics
Verified
Major Verified
Question
Major Verified
Question
paperQuestion
with
paper
Marking
with
paper
Marking
Scheme
with Marking
Scheme
Attached.pdf
Scheme
Attached.pdf
Attached.pdf
3
JK32 cos 2tNO
3 At time t seconds, the total force acting on a particle P of mass 4 kg is K - 8 sin t O N.
KK OO
L 0 P
KJK0 NO -1
When t = 0 the velocity of P is .
KK 5 OO ms
6
L P
(a) Find, in column vector form, the acceleration of P at time t seconds. [1]
(b) Determine the speed of P when t =31 r. [5]
4
C
B
4m
50°
A
A uniform rod AB of mass 3 kg and length 4 m rests with one end A on rough horizontal ground.
A light inextensible string has one end attached to the rod at B and the other end attached to a
fixed point C.
The string is perpendicular to the rod and lies in the same vertical plane as the rod. The rod is in
equilibrium, inclined at 50° to the ground, as shown in the diagram.
(a) Complete the diagram in the Printed Answer Booklet to show all the forces acting on the
rod. [1]
(b) By taking moments about A, find the tension in the string. [2]
(c) Determine the magnitude of the total contact force between the rod and the ground. [4]
© OCR 2025 Y421/01 Jun25 Turn over
2025 OCR
2025
A OCR
Level
2025AFurther
OCR
Level AFurther
Mathematics
Level Further
Mathematics
B Mathematics
(MEI)BY421-01
(MEI)BY421-01
Mechanics
(MEI) Y421-01
Mechanics
Major
Mechanics
Verified
Major Verified
Question
Major Verified
Question
paperQuestion
with
paper
Marking
with
paper
Marking
Scheme
with Marking
Scheme
Attached.pdf
Scheme
Attached.pdf
Attached.pdf
, 2025 OCR
2025
A OCR
Level
2025AFurther
OCR
Level AFurther
Mathematics
Level Further
Mathematics
B Mathematics
(MEI)BY421-01
(MEI)BY421-01
Mechanics
(MEI) Y421-01
Mechanics
Major
Mechanics
Verified
Major Verified
Question
Major Verified
Question
paperQuestion
with
paper
Marking
with
paper
Marking
Scheme
with Marking
Scheme
Attached.pdf
Scheme
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Attached.pdf
4
dr r
5 In this question you may assume that if r and s are any physical quantities then ; E = ; E.
ds s
You may also assume that all given numerical constants are dimensionless.
(a) Find the dimensions of power. [1]
A car of mass m moves horizontally in a straight line. When the car is a distance x from a point O,
it is moving away from O with speed v.
The power developed by the car is P. The maximum possible speed of the car during its motion
is U.
The differential equation for the motion of the car is given by
J
a b dv c K vd NO
m v .
d x = P K1 - U3O
L P
(b) Explain why d = 3. [1]
dv
(c) Show that the dimensions ofd x are T-1. [1]
(d) Use dimensional analysis to determine the values of a, b and c. [3]
Once the car attains a speed of 21 U , the power developed by the car is immediately reduced to
zero.
A student
1 calculates that the time taken, t, for the speed of the car to reduce from to 1 U is
U
2 4
2mU2
given by t =
P .
(e) Determine whether this expression for t is dimensionally consistent. [2]
© OCR 2025 Y421/01 Jun25
2025 OCR
2025
A OCR
Level
2025AFurther
OCR
Level AFurther
Mathematics
Level Further
Mathematics
B Mathematics
(MEI)BY421-01
(MEI)BY421-01
Mechanics
(MEI) Y421-01
Mechanics
Major
Mechanics
Verified
Major Verified
Question
Major Verified
Question
paperQuestion
with
paper
Marking
with
paper
Marking
Scheme
with Marking
Scheme
Attached.pdf
Scheme
Attached.pdf
Attached.pdf
2025
A OCR
Level
2025AFurther
OCR
Level AFurther
Mathematics
Level Further
Mathematics
B Mathematics
(MEI)BY421-01
(MEI)BY421-01
Mechanics
(MEI) Y421-01
Mechanics
Major
Mechanics
Verified
Major Verified
Question
Major Verified
Question
paperQuestion
with
paper
Marking
with
paper
Marking
Scheme
with Marking
Scheme
Attached.pdf
Scheme
Attached.pdf
Attached.pdf
2025 OCR A Level Further Mathematics B (MEI)
Y421/01 Mechanics Major
Verified Question paper with Marking Scheme Attached
Oxford Cambridge and RSA
Friday 6 June 2025 – Afternoon A
Level Further Mathematics B (MEI) Y421/01
Mechanics Major
Time allowed: 2 hours 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 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 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 120.
• The marks for each question are shown in brackets [ ].
• This document has 12 pages.
ADVICE
• Read each question carefully before you start your answer.
© OCR 2025 [D/508/5593] OCR is an exempt Charity
DC (ST/TC) 356295/6 Turn over
2025 OCR
2025
A OCR
Level
2025AFurther
OCR
Level AFurther
Mathematics
Level Further
Mathematics
B Mathematics
(MEI)BY421-01
(MEI)BY421-01
Mechanics
(MEI) Y421-01
Mechanics
Major
Mechanics
Verified
Major Verified
Question
Major Verified
Question
paperQuestion
with
paper
Marking
with
paper
Marking
Scheme
with Marking
Scheme
Attached.pdf
Scheme
Attached.pdf
Attached.pdf
,2025 OCR
2025
A OCR
Level
2025AFurther
OCR
Level AFurther
Mathematics
Level Further
Mathematics
B Mathematics
(MEI)BY421-01
(MEI)BY421-01
Mechanics
(MEI) Y421-01
Mechanics
Major
Mechanics
Verified
Major Verified
Question
Major Verified
Question
paperQuestion
with
paper
Marking
with
paper
Marking
Scheme
with Marking
Scheme
Attached.pdf
Scheme
Attached.pdf
Attached.pdf
2
Section A (33 marks)
1 A small box of mass 3 kg is pulled along a horizontal floor by a constant force of magnitude 35 N.
The force acts at an angle of i above the horizontal.
The total resistance to the motion of the box has magnitude 25 N.
The box starts from rest at a point O, and passes through a point 4 m from O with
speed 1.5 m s-1 .
Use an energy method to determine the value of i. [3]
2
y
4
A 7m
2 B 2m
–4 –2 0 2 4 x
–2
C km
The diagram shows a system of three particles of masses 7m, 2m and km situated in the x-y
plane at the points A(-2, 3), B(4, 2) and C(1, -2) respectively.
The centre of mass of the three particles is at the point with coordinates (0, d ).
(a) Find the value of k. [2]
(b) Find the value of d. [2]
© OCR 2025 Y421/01 Jun25
2025 OCR
2025
A OCR
Level
2025AFurther
OCR
Level AFurther
Mathematics
Level Further
Mathematics
B Mathematics
(MEI)BY421-01
(MEI)BY421-01
Mechanics
(MEI) Y421-01
Mechanics
Major
Mechanics
Verified
Major Verified
Question
Major Verified
Question
paperQuestion
with
paper
Marking
with
paper
Marking
Scheme
with Marking
Scheme
Attached.pdf
Scheme
Attached.pdf
Attached.pdf
,2025 OCR
2025
A OCR
Level
2025AFurther
OCR
Level AFurther
Mathematics
Level Further
Mathematics
B Mathematics
(MEI)BY421-01
(MEI)BY421-01
Mechanics
(MEI) Y421-01
Mechanics
Major
Mechanics
Verified
Major Verified
Question
Major Verified
Question
paperQuestion
with
paper
Marking
with
paper
Marking
Scheme
with Marking
Scheme
Attached.pdf
Scheme
Attached.pdf
Attached.pdf
3
JK32 cos 2tNO
3 At time t seconds, the total force acting on a particle P of mass 4 kg is K - 8 sin t O N.
KK OO
L 0 P
KJK0 NO -1
When t = 0 the velocity of P is .
KK 5 OO ms
6
L P
(a) Find, in column vector form, the acceleration of P at time t seconds. [1]
(b) Determine the speed of P when t =31 r. [5]
4
C
B
4m
50°
A
A uniform rod AB of mass 3 kg and length 4 m rests with one end A on rough horizontal ground.
A light inextensible string has one end attached to the rod at B and the other end attached to a
fixed point C.
The string is perpendicular to the rod and lies in the same vertical plane as the rod. The rod is in
equilibrium, inclined at 50° to the ground, as shown in the diagram.
(a) Complete the diagram in the Printed Answer Booklet to show all the forces acting on the
rod. [1]
(b) By taking moments about A, find the tension in the string. [2]
(c) Determine the magnitude of the total contact force between the rod and the ground. [4]
© OCR 2025 Y421/01 Jun25 Turn over
2025 OCR
2025
A OCR
Level
2025AFurther
OCR
Level AFurther
Mathematics
Level Further
Mathematics
B Mathematics
(MEI)BY421-01
(MEI)BY421-01
Mechanics
(MEI) Y421-01
Mechanics
Major
Mechanics
Verified
Major Verified
Question
Major Verified
Question
paperQuestion
with
paper
Marking
with
paper
Marking
Scheme
with Marking
Scheme
Attached.pdf
Scheme
Attached.pdf
Attached.pdf
, 2025 OCR
2025
A OCR
Level
2025AFurther
OCR
Level AFurther
Mathematics
Level Further
Mathematics
B Mathematics
(MEI)BY421-01
(MEI)BY421-01
Mechanics
(MEI) Y421-01
Mechanics
Major
Mechanics
Verified
Major Verified
Question
Major Verified
Question
paperQuestion
with
paper
Marking
with
paper
Marking
Scheme
with Marking
Scheme
Attached.pdf
Scheme
Attached.pdf
Attached.pdf
4
dr r
5 In this question you may assume that if r and s are any physical quantities then ; E = ; E.
ds s
You may also assume that all given numerical constants are dimensionless.
(a) Find the dimensions of power. [1]
A car of mass m moves horizontally in a straight line. When the car is a distance x from a point O,
it is moving away from O with speed v.
The power developed by the car is P. The maximum possible speed of the car during its motion
is U.
The differential equation for the motion of the car is given by
J
a b dv c K vd NO
m v .
d x = P K1 - U3O
L P
(b) Explain why d = 3. [1]
dv
(c) Show that the dimensions ofd x are T-1. [1]
(d) Use dimensional analysis to determine the values of a, b and c. [3]
Once the car attains a speed of 21 U , the power developed by the car is immediately reduced to
zero.
A student
1 calculates that the time taken, t, for the speed of the car to reduce from to 1 U is
U
2 4
2mU2
given by t =
P .
(e) Determine whether this expression for t is dimensionally consistent. [2]
© OCR 2025 Y421/01 Jun25
2025 OCR
2025
A OCR
Level
2025AFurther
OCR
Level AFurther
Mathematics
Level Further
Mathematics
B Mathematics
(MEI)BY421-01
(MEI)BY421-01
Mechanics
(MEI) Y421-01
Mechanics
Major
Mechanics
Verified
Major Verified
Question
Major Verified
Question
paperQuestion
with
paper
Marking
with
paper
Marking
Scheme
with Marking
Scheme
Attached.pdf
Scheme
Attached.pdf
Attached.pdf
