surname names
Number Number
Paper
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 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
andatcandidate
the top ofnumber.
this page with your name,
•
centre number
Answer all questions and ensure that your answers to parts of questions are clearly labelled.
• Answer
–You
there the questions
may
should be more
show
in thethan
space
sufficient
spaces
youprovided
working need.
to make your methods clear.
••
•
Answers without working may not gain full credit.
–2
Unless otherwise indicated, whenever a value of g is required, take g = 9.8 m s 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 8 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.
2025 Pearson Edexcel A Level Further Mathematics Question Paper
Option 3C June+ Mark scheme
,1. A particle A has mass 4m and a particle B has mass 3m. The particles are moving along
the same straight line on a smooth horizontal table. The particles are moving in opposite
directions towards each other when they collide directly.
DO NOT WRITE IN THIS AREA
As a result of the collision, the direction of motion of each particle is reversed.
Immediately before the collision, the speed of A is u and the speed of B is ku, where k
is a constant.
Immediately after the collision, the speed of A is 2v and the speed of B is 3v.
The magnitude of the impulse received by A in the collision is 20mv.
(a) Find u in terms of v only.
(3)
(b) Find the exact value of k.
(3)
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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
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Question 1 continued
(Total for Question 1 is 6 marks)
3
Turn over
, 2. A van of mass 900 kg is moving along a straight horizontal road.
When the speed of the van is v ms−1, the resistance to the motion of the van is
DO NOT WRITE IN THIS AREA
modelled as a force of magnitude 50v N.
The engine of the van is working at a constant rate of 12 kW.
At the instant when the speed of the van is V ms−1, the acceleration of the van
is 0.2 ms−2
Using the model,
(a) find the value of V.
(4)
Later on, the van is moving up a straight road that is inclined at an angle α to the
1
horizontal, where sin α = . When the speed of the van is v ms−1, the resistance
12
to the motion of the van from non-gravitational forces is modelled as a force of
magnitude 50v N.
When the van has constant speed U ms−1, the engine of the van is working at a constant
DO NOT WRITE IN THIS AREA
rate of 15 kW.
Using the model,
(b) find the value of U.
(4)
DO NOT WRITE IN THIS AREA
4
■■■■
Number Number
Paper
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 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
andatcandidate
the top ofnumber.
this page with your name,
•
centre number
Answer all questions and ensure that your answers to parts of questions are clearly labelled.
• Answer
–You
there the questions
may
should be more
show
in thethan
space
sufficient
spaces
youprovided
working need.
to make your methods clear.
••
•
Answers without working may not gain full credit.
–2
Unless otherwise indicated, whenever a value of g is required, take g = 9.8 m s 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 8 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.
2025 Pearson Edexcel A Level Further Mathematics Question Paper
Option 3C June+ Mark scheme
,1. A particle A has mass 4m and a particle B has mass 3m. The particles are moving along
the same straight line on a smooth horizontal table. The particles are moving in opposite
directions towards each other when they collide directly.
DO NOT WRITE IN THIS AREA
As a result of the collision, the direction of motion of each particle is reversed.
Immediately before the collision, the speed of A is u and the speed of B is ku, where k
is a constant.
Immediately after the collision, the speed of A is 2v and the speed of B is 3v.
The magnitude of the impulse received by A in the collision is 20mv.
(a) Find u in terms of v only.
(3)
(b) Find the exact value of k.
(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 6 marks)
3
Turn over
, 2. A van of mass 900 kg is moving along a straight horizontal road.
When the speed of the van is v ms−1, the resistance to the motion of the van is
DO NOT WRITE IN THIS AREA
modelled as a force of magnitude 50v N.
The engine of the van is working at a constant rate of 12 kW.
At the instant when the speed of the van is V ms−1, the acceleration of the van
is 0.2 ms−2
Using the model,
(a) find the value of V.
(4)
Later on, the van is moving up a straight road that is inclined at an angle α to the
1
horizontal, where sin α = . When the speed of the van is v ms−1, the resistance
12
to the motion of the van from non-gravitational forces is modelled as a force of
magnitude 50v N.
When the van has constant speed U ms−1, the engine of the van is working at a constant
DO NOT WRITE IN THIS AREA
rate of 15 kW.
Using the model,
(b) find the value of U.
(4)
DO NOT WRITE IN THIS AREA
4
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