surname names
Number Number
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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
• If pencil is used for diagrams/sketches/graphs it must be dark (HB or B).
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 numerical 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.
• There are 7 questions in this question paper. The total mark for this paper is 75.
– 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.
• 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.
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)
2
■■■■
,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
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,
(b) find d in terms of a.
(4)
4
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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
• If pencil is used for diagrams/sketches/graphs it must be dark (HB or B).
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 numerical 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.
• There are 7 questions in this question paper. The total mark for this paper is 75.
– 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.
• 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.
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)
2
■■■■
,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
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,
(b) find d in terms of a.
(4)
4
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