Oxford Cambridge and RSA
May 2025 – Afternoon
AS Level Further Mathematics B (MEI) Y411/01
Mechanics a
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 gms–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 12 pages.
ADVICE
• Read each question carefully before you start your answer.
OCR AS Level Further Mathematics B (MEI) Mechanics a (Y411/01) Question
Paper And Mark Scheme
, 2
1 A system consists of an object performing oscillations whilst suspended at the end of a spring S.
The period, t, is defined as the time taken for the object to complete one oscillation. The period is
given by the formula
1 -1
t = mm2 k 2,
where
• m is a constant,
• m is the mass of the object,
• k is the stiffness of S.
One possible unit which k can be measured in is kgs–2 .
(a) Show that m is dimensionless. [3]
For a given object P and S, the period of one oscillation is measured to be 1.48 seconds, correct
to 3 significant figures. The object P is replaced with another object Q which has three times the
mass of P.
(b) Find an estimate for the period of one oscillation of Q and S. [1]
© OCR 2025 Y411/01 Jun25
, 3
2 A small block of mass 5 kg is placed on a rough horizontal surface. The coefficient of friction
between the block and the surface is7 5 .
Two horizontal pulling forces act on the block. One pulling force has a magnitude of 14 N, and
the other pulling force has a magnitude of 23 N. The plan-view diagram shows these two forces,
along with the frictional force of magnitude F N, exerted by the surface on the block. The angle
between the two horizontal forces acting on the block is i°. There are no other horizontal forces
acting on the block. The block is in limiting equilibrium.
14 N
θ°
23 N
FN
(a) Show that F = 35. [1]
(b) Draw a triangle of forces to represent the system shown in the diagram. [2]
(c) Determine the value of i. Give your answer correct to 3 significant figures. [2]
The value of i is now increased slightly.
(d) Explain what happens to the block. [1]
© OCR 2025 Y411/01 Jun25 Turn over
, 4
3 In parts (a) and (b) of this question you should assume that the car experiences no
resistances to motion.
A car of mass 1200 kg is moving on a straight road.
At first the car travels up a section of the road inclined at 3° to the horizontal.
(a) Determine the power developed by the car at the instant when it has a speed of 22ms -1
and is accelerating at 0.4 m s-2. [3]
The maximum power that can be developed by the car is 40 kW.
(b) Calculate the greatest speed that can be maintained by the car when travelling up the road.
[2]
The car now moves down a section of the road inclined at 5° to the horizontal.
The car passes a signpost as it is travelling at 28 m s-1. At that instant, the driver applies the
brakes, so that 600 m later, when it passes a second signpost, the car has slowed down to 15 ms-
1. You should assume that the car experiences no other resistances to motion.
(c) Determine the work done by the braking force of the car as it travels between the two
signposts. [4]
(d) State one way in which the modelling of the car’s motion in this question could be refined.[1]
© OCR 2025 Y411/01 Jun25
May 2025 – Afternoon
AS Level Further Mathematics B (MEI) Y411/01
Mechanics a
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 gms–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 12 pages.
ADVICE
• Read each question carefully before you start your answer.
OCR AS Level Further Mathematics B (MEI) Mechanics a (Y411/01) Question
Paper And Mark Scheme
, 2
1 A system consists of an object performing oscillations whilst suspended at the end of a spring S.
The period, t, is defined as the time taken for the object to complete one oscillation. The period is
given by the formula
1 -1
t = mm2 k 2,
where
• m is a constant,
• m is the mass of the object,
• k is the stiffness of S.
One possible unit which k can be measured in is kgs–2 .
(a) Show that m is dimensionless. [3]
For a given object P and S, the period of one oscillation is measured to be 1.48 seconds, correct
to 3 significant figures. The object P is replaced with another object Q which has three times the
mass of P.
(b) Find an estimate for the period of one oscillation of Q and S. [1]
© OCR 2025 Y411/01 Jun25
, 3
2 A small block of mass 5 kg is placed on a rough horizontal surface. The coefficient of friction
between the block and the surface is7 5 .
Two horizontal pulling forces act on the block. One pulling force has a magnitude of 14 N, and
the other pulling force has a magnitude of 23 N. The plan-view diagram shows these two forces,
along with the frictional force of magnitude F N, exerted by the surface on the block. The angle
between the two horizontal forces acting on the block is i°. There are no other horizontal forces
acting on the block. The block is in limiting equilibrium.
14 N
θ°
23 N
FN
(a) Show that F = 35. [1]
(b) Draw a triangle of forces to represent the system shown in the diagram. [2]
(c) Determine the value of i. Give your answer correct to 3 significant figures. [2]
The value of i is now increased slightly.
(d) Explain what happens to the block. [1]
© OCR 2025 Y411/01 Jun25 Turn over
, 4
3 In parts (a) and (b) of this question you should assume that the car experiences no
resistances to motion.
A car of mass 1200 kg is moving on a straight road.
At first the car travels up a section of the road inclined at 3° to the horizontal.
(a) Determine the power developed by the car at the instant when it has a speed of 22ms -1
and is accelerating at 0.4 m s-2. [3]
The maximum power that can be developed by the car is 40 kW.
(b) Calculate the greatest speed that can be maintained by the car when travelling up the road.
[2]
The car now moves down a section of the road inclined at 5° to the horizontal.
The car passes a signpost as it is travelling at 28 m s-1. At that instant, the driver applies the
brakes, so that 600 m later, when it passes a second signpost, the car has slowed down to 15 ms-
1. You should assume that the car experiences no other resistances to motion.
(c) Determine the work done by the braking force of the car as it travels between the two
signposts. [4]
(d) State one way in which the modelling of the car’s motion in this question could be refined.[1]
© OCR 2025 Y411/01 Jun25
