2024 PEARSON EDEXCEL GCE A LEVEL FURTHER MATHEMATICS PAPER 3C MERGED QUESTION PAPER AND
MARKING SCHEME
surname names
Number Number
Further Mathematics
■ ■
Advanced
PAPER 3C: Further Mechanics 1
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
•• AThere
booklet ‘Mathematical Formulae and Statistical Tables’ is provided.
• The
are 7 questions in this question paper. The total mark for this paper is 75.
– usemarks
this asfor eachasquestion
a guide are shown
to how much in spend
time to brackets
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
P75322A
©2024 Pearson Education Ltd.
F:1/1/
,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
Turn over
, 3
A rough plane is inclined to the horizontal at an angle θ, where tan θ =
2. 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
■■■■
MARKING SCHEME
surname names
Number Number
Further Mathematics
■ ■
Advanced
PAPER 3C: Further Mechanics 1
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
•• AThere
booklet ‘Mathematical Formulae and Statistical Tables’ is provided.
• The
are 7 questions in this question paper. The total mark for this paper is 75.
– usemarks
this asfor eachasquestion
a guide are shown
to how much in spend
time to brackets
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
P75322A
©2024 Pearson Education Ltd.
F:1/1/
,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
Turn over
, 3
A rough plane is inclined to the horizontal at an angle θ, where tan θ =
2. 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
■■■■
