2025 OCR AS Level Further Mathematics B (MEI) Y411/01 Mechanics a Combined
Question Paper & Final Marking Scheme
Oxford Cambridge and RSA
Friday 16 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 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 12 pages.
ADVICE
• Read each question carefully before you start your answer.
, © OCR 2025 [T/508/5552] OCR is an exempt Charity
DC (DE/CB) 357562/4 Turn over
*1865455949*
, 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 = mm 2 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 kg s–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 is 57 .
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
Question Paper & Final Marking Scheme
Oxford Cambridge and RSA
Friday 16 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 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 12 pages.
ADVICE
• Read each question carefully before you start your answer.
, © OCR 2025 [T/508/5552] OCR is an exempt Charity
DC (DE/CB) 357562/4 Turn over
*1865455949*
, 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 = mm 2 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 kg s–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 is 57 .
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
