Please check the examination details below before entering your candidate information
Candidate surname Other names
Centre Number Candidate Number
Pearson Edexcel Level 3 GCE
Friday 7 June 2024
Afternoon (Time: 1 hour 30 minutes) Paper
reference 9FM0/3C
Further Mathematics
� �
Advanced
PAPER 3C: Further Mechanics 1
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 algebraic manipulation,
differentiation and integration, or have retrievable mathematical formulae
stored in them.
Instructions
•• Use black ink or ball-point pen.
• Fill
If pencil is used for diagrams/sketches/graphs it must be dark (HB or B).
in the boxes at the top of this page with your name,
• Answer
centre number and candidate number.
all questions and ensure that your answers to parts of questions
• Answer
are clearly labelled.
the questions in the spaces provided
• You
– there may be more space than you need.
should show sufficient working to make your methods clear.
• Unless
Answers without working may not gain full credit.
otherwise indicated, whenever a numerical value of g is required,
−2
take g = 9.8 m s and give your answer to either 2 significant figures or
3 significant figures.
Information
••• There
A booklet ‘Mathematical Formulae and Statistical Tables’ is provided.
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.
• Read each question carefully before you start to answer it.
Advice
•• Try to answer every question.
Check your answers if you have time at the end. Turn over
, 1. [In this question, i and j are horizontal perpendicular unit vectors.]
A particle A has mass 3 kg and a particle B has mass 2 kg.
DO NOT WRITE IN THIS AREA
The particles are moving on a smooth horizontal plane when they collide directly.
Immediately before the collision, the velocity of A is (3i – j) m s–1 and the velocity of
B is (–6i + 2j) m s–1
2
Immediately after the collision the velocity of A is 2i j m s–1
3
(a) Find the total kinetic energy of the two particles before the collision.
(3)
(b) Find, in terms of i and j, the impulse exerted on A by B in the collision.
(3)
(c) Find, in terms of i and j, the velocity of B immediately after the collision.
(3)
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
2
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, DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA
Question 1 continued
(Total for Question 1 is 9 marks)
, 3
2. A rough plane is inclined to the horizontal at an angle θ, where tan θ =
4
DO NOT WRITE IN THIS AREA
A particle P of mass m is at rest at a point on the plane.
The particle is projected up the plane with speed 2ag
The particle moves up a line of greatest slope of the plane and comes to instantaneous
rest after moving a distance d.
1
The coefficient of friction between P and the plane is
7
(a) Show that the magnitude of the frictional force acting on P as it moves up the plane
4mg
is
35
(3)
Air resistance is assumed to be negligible.
Using the work-energy principle,
DO NOT WRITE IN THIS AREA
(b) find d in terms of a.
(4)
DO NOT WRITE IN THIS AREA
4
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Candidate surname Other names
Centre Number Candidate Number
Pearson Edexcel Level 3 GCE
Friday 7 June 2024
Afternoon (Time: 1 hour 30 minutes) Paper
reference 9FM0/3C
Further Mathematics
� �
Advanced
PAPER 3C: Further Mechanics 1
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 algebraic manipulation,
differentiation and integration, or have retrievable mathematical formulae
stored in them.
Instructions
•• Use black ink or ball-point pen.
• Fill
If pencil is used for diagrams/sketches/graphs it must be dark (HB or B).
in the boxes at the top of this page with your name,
• Answer
centre number and candidate number.
all questions and ensure that your answers to parts of questions
• Answer
are clearly labelled.
the questions in the spaces provided
• You
– there may be more space than you need.
should show sufficient working to make your methods clear.
• Unless
Answers without working may not gain full credit.
otherwise indicated, whenever a numerical value of g is required,
−2
take g = 9.8 m s and give your answer to either 2 significant figures or
3 significant figures.
Information
••• There
A booklet ‘Mathematical Formulae and Statistical Tables’ is provided.
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.
• Read each question carefully before you start to answer it.
Advice
•• Try to answer every question.
Check your answers if you have time at the end. Turn over
, 1. [In this question, i and j are horizontal perpendicular unit vectors.]
A particle A has mass 3 kg and a particle B has mass 2 kg.
DO NOT WRITE IN THIS AREA
The particles are moving on a smooth horizontal plane when they collide directly.
Immediately before the collision, the velocity of A is (3i – j) m s–1 and the velocity of
B is (–6i + 2j) m s–1
2
Immediately after the collision the velocity of A is 2i j m s–1
3
(a) Find the total kinetic energy of the two particles before the collision.
(3)
(b) Find, in terms of i and j, the impulse exerted on A by B in the collision.
(3)
(c) Find, in terms of i and j, the velocity of B immediately after the collision.
(3)
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
2
�
��
�
, DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA
Question 1 continued
(Total for Question 1 is 9 marks)
, 3
2. A rough plane is inclined to the horizontal at an angle θ, where tan θ =
4
DO NOT WRITE IN THIS AREA
A particle P of mass m is at rest at a point on the plane.
The particle is projected up the plane with speed 2ag
The particle moves up a line of greatest slope of the plane and comes to instantaneous
rest after moving a distance d.
1
The coefficient of friction between P and the plane is
7
(a) Show that the magnitude of the frictional force acting on P as it moves up the plane
4mg
is
35
(3)
Air resistance is assumed to be negligible.
Using the work-energy principle,
DO NOT WRITE IN THIS AREA
(b) find d in terms of a.
(4)
DO NOT WRITE IN THIS AREA
4
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��
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