Please check the examination details below before entering your candidate information
Candidate surname Other names
Centre Number Candidate Number
Pearson Edexcel Level 3 GCE
Monday 22 June 2026
Afternoon (Time: 1 hour 30 minutes) Paper
reference 9FM0/4C
Further Mathematics
Advanced
PAPER 4C: Further Mechanics 2
You must have: Total Marks
Mathematical Formulae and Statistical Tables (Green), calculator
Candidates may use any calculator permitted by Pearson regulations. Calculators
must not have the facility for symbolic algebra manipulation, differentiation and
integration, or have retrievable mathematical formulae stored in them.
Instructions
•• Use black ink or ball-point pen.
•
If pencil is used for diagrams/sketches/graphs it must be dark (HB or B).
Fill in the boxes at the top of this page with your name,
••
centre number and candidate number.
Answer all questions and ensure that your answers to parts of questions are clearly labelled.
Answer the questions in the spaces provided
•
– there may be more space than you need.
You should show sufficient working to make your methods clear.
•
Answers without working may not gain full credit.
Unless otherwise indicated, whenever a value of g is required, take
g = 9.8 m s–2 and give your answer to either 2 significant figures or 3 significant figures.
Information
•• A booklet ‘Mathematical Formulae and Statistical Tables’ is provided.
•
There are 7 questions in this question paper. The total mark for this paper is 75.
The marks for each question are shown in brackets
– use this as a guide as to how much time to spend on each question.
Advice
•• Read each question carefully before you start to answer it.
•
Try to answer every question.
Check your answers if you have time at the end.
Turn over
P79404A
©2026 Pearson Education Ltd.
P:1/1/1/1/
*P79404A0128*
,1.
A
DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA
l
0.4 l
P
O
Figure 1
A particle P of mass m is attached to one end of a light inextensible string of length l.
The other end of the string is attached to a fixed point A that is vertically above a
point O.
The point O lies on a smooth horizontal plane, where OA = 0.4l , as shown in Figure 1.
The particle P moves on the plane in a horizontal circle with centre O and with the
string taut.
Given that the magnitude of the normal reaction between P and the plane is 0.2mg
(a) find, in terms of m and g, the tension in the string.
(3)
Given also that P moves with constant angular speed ω
2g
(b) show that
l (3)
(c) Hence state the exact time taken for P to make 5 complete revolutions, giving your
answer in terms of l and g.
(2)
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2
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, Question 1 continued
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(Total for Question 1 is 8 marks)
3
*P79404A0328* Turn over
, 2.
O r
DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA
h
2r
2r
Figure 2
Figure 2 shows a solid cylindrical paperweight S.
The paperweight S is formed by removing a solid cone from the top of a solid wooden
cylinder and replacing it with a solid glass cone.
• the wooden cylinder is uniform and has radius 2r and height 2r
• the removed wooden cone is a right circular cone with radius r and height h
• the glass cone replacement is uniform and is also a right circular cone with radius r
and height h
The plane face of the glass cone is part of the upper plane face of S.
The centres of the two plane faces coincide at the point O, as shown in Figure 2.
The density of the glass is four times the density of the wood.
The centre of mass of S is a distance d from O.
(a) Show that
32r 2
h 2
d
4(8r
h)
(5)
The paperweight S is placed on an inclined plane
• the wooden circular base of S is in contact with the plane
• the plane is inclined at an angle
to the horizontal
• the plane is sufficiently rough to prevent S from slipping
• h = 1.6r
Given that S is on the point of toppling,
(b) find the value of α
(3)
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4
*P79404A0428*
Candidate surname Other names
Centre Number Candidate Number
Pearson Edexcel Level 3 GCE
Monday 22 June 2026
Afternoon (Time: 1 hour 30 minutes) Paper
reference 9FM0/4C
Further Mathematics
Advanced
PAPER 4C: Further Mechanics 2
You must have: Total Marks
Mathematical Formulae and Statistical Tables (Green), calculator
Candidates may use any calculator permitted by Pearson regulations. Calculators
must not have the facility for symbolic algebra manipulation, differentiation and
integration, or have retrievable mathematical formulae stored in them.
Instructions
•• Use black ink or ball-point pen.
•
If pencil is used for diagrams/sketches/graphs it must be dark (HB or B).
Fill in the boxes at the top of this page with your name,
••
centre number and candidate number.
Answer all questions and ensure that your answers to parts of questions are clearly labelled.
Answer the questions in the spaces provided
•
– there may be more space than you need.
You should show sufficient working to make your methods clear.
•
Answers without working may not gain full credit.
Unless otherwise indicated, whenever a value of g is required, take
g = 9.8 m s–2 and give your answer to either 2 significant figures or 3 significant figures.
Information
•• A booklet ‘Mathematical Formulae and Statistical Tables’ is provided.
•
There are 7 questions in this question paper. The total mark for this paper is 75.
The marks for each question are shown in brackets
– use this as a guide as to how much time to spend on each question.
Advice
•• Read each question carefully before you start to answer it.
•
Try to answer every question.
Check your answers if you have time at the end.
Turn over
P79404A
©2026 Pearson Education Ltd.
P:1/1/1/1/
*P79404A0128*
,1.
A
DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA
l
0.4 l
P
O
Figure 1
A particle P of mass m is attached to one end of a light inextensible string of length l.
The other end of the string is attached to a fixed point A that is vertically above a
point O.
The point O lies on a smooth horizontal plane, where OA = 0.4l , as shown in Figure 1.
The particle P moves on the plane in a horizontal circle with centre O and with the
string taut.
Given that the magnitude of the normal reaction between P and the plane is 0.2mg
(a) find, in terms of m and g, the tension in the string.
(3)
Given also that P moves with constant angular speed ω
2g
(b) show that
l (3)
(c) Hence state the exact time taken for P to make 5 complete revolutions, giving your
answer in terms of l and g.
(2)
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_____________________________________________________________________________________
_____________________________________________________________________________________
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_____________________________________________________________________________________
2
*P79404A0228*
, Question 1 continued
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(Total for Question 1 is 8 marks)
3
*P79404A0328* Turn over
, 2.
O r
DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA
h
2r
2r
Figure 2
Figure 2 shows a solid cylindrical paperweight S.
The paperweight S is formed by removing a solid cone from the top of a solid wooden
cylinder and replacing it with a solid glass cone.
• the wooden cylinder is uniform and has radius 2r and height 2r
• the removed wooden cone is a right circular cone with radius r and height h
• the glass cone replacement is uniform and is also a right circular cone with radius r
and height h
The plane face of the glass cone is part of the upper plane face of S.
The centres of the two plane faces coincide at the point O, as shown in Figure 2.
The density of the glass is four times the density of the wood.
The centre of mass of S is a distance d from O.
(a) Show that
32r 2
h 2
d
4(8r
h)
(5)
The paperweight S is placed on an inclined plane
• the wooden circular base of S is in contact with the plane
• the plane is inclined at an angle
to the horizontal
• the plane is sufficiently rough to prevent S from slipping
• h = 1.6r
Given that S is on the point of toppling,
(b) find the value of α
(3)
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4
*P79404A0428*
