Created by T.

Madas

IYGB GCE
Mathematics FM1
Advanced Level
Practice Paper M
Difficulty Rating: 3.3067/1.4851

Time: 1 hour 30 minutes

Candidates may use any calculator allowed by the

regulations of this examination.

Information for Candidates

This practice paper follows closely the Pearson Edexcel Syllabus, suitable for first
assessment Summer 2018.
The standard booklet “Mathematical Formulae and Statistical Tables” may be used.
Full marks may be obtained for answers to ALL questions.
The marks for the parts of questions are shown in round brackets, e.g. (2).
There are 8 questions in this question paper.
The total mark for this paper is 75.

Advice to Candidates
You must ensure that your answers to parts of questions are clearly labelled.
You must show sufficient working to make your methods clear to the Examiner.
Answers without working may not gain full credit.
Non exact answers should be given to an appropriate degree of accuracy.
The examiner may refuse to mark any parts of questions if deemed not to be legible.

Created by T. Madas
 Created by T. Madas

Question 1 (***)
A car of mass 1600 kg is travelling up a straight road inclined at an angle θ to the
horizontal, where sin θ = 1 .
40

The car is modelled as a particle travelling at constant speed of 25 ms −1 and the

resistance to its motion due to non-gravitational forces has a constant magnitude of
500 N .

The car travels between two points on the road, A and B in 20 s .

Determine the work done by the engine of the car, as the car moves from A to B . (7)

Question 2 (***)
A light elastic string AB has natural length 2L m and modulus of elasticity λ N .

A different light elastic string CD has natural length 3L m and modulus of elasticity
1λ N.
4

The two strings are joined together at their ends, with A joined to C and with B
joined to D . The “ A to C ” end is fixed to a horizontal ceiling. A particle of weight
65 N is attached to the “ B to D ” end, and hangs in equilibrium, without touching
the ground.

Given that when the particle hangs in equilibrium the length of the string AB is twice
is natural length, determine the value of λ . ( 6)

Created by T. Madas
 Created by T. Madas

Question 3 (***+)
Two smooth spheres of equal radius, A and B , of mass 3 kg and m kg respectively,
are moving in the same direction, along a straight line on a smooth horizontal plane.

The spheres collide and the magnitude of impulse exerted on B by A is 15 Ns .

Before the collision, the respective speeds of A and B are 8 ms −1 and 2 ms −1 .

After the collision B is moving with speed 2 ms −1 relative to A .

Determine the value of m and the speed of B , after the collision. (7)

Question 4 (***+)
A light elastic spring AB , of natural length 2 m , has its end A attached to a fixed
point on a horizontal ceiling and a particle, of mass 3 kg , is attached to the other end
of the spring, B , with the particle hanging in equilibrium.

The modulus of elasticity of the spring is 100 g N

The particle is then pulled vertically downwards, so that AB = 2.15 m , and released
from rest.

Determine the length of AB when the particle first comes to instantaneous rest. (12 )

Created by T. Madas
 Created by T. Madas

Question 5 (***)

A
B

50 m
25m
1200m

The figure above shows the path of a cyclist on a section of a road from A to B ,
where the distance AB is 1200 m .

The cyclist leaves point A at the top of a hill with a speed V ms −1 and descends a
vertical distance of 50 m to the bottom of the hill. He then ascends a vertical distance
of 25 m to the top of another hill at point B .

The cyclist takes 110 s to travel from A to B and is assumed to be working at the
constant rate of 40 W , throughout the motion.

The combined mass of the cyclist and his bike is 80 kg.

The cyclist and his bike are modelled as a single particle subject to a constant non
gravitational resistance of 20 N, throughout the motion.

Show that speed of the cyclist at B is V ms −1 . (10 )

Created by T. Madas
 Created by T. Madas

Question 6 (***+)

P 4 ms −1
θ

I Ns

A particle P of mass 0.5 kg is moving in a straight line with speed 4 ms −1 .

An impulse of magnitude I Ns is applied to P , acting at an acute angle θ to the

direction of motion of P , as shown in the figure above.

After the impulse was applied, P is moving with speed 8 ms −1 in a direction which
is inclined by an acute angle α to its original direction of motion.

Given that sin α = 3 , determine the value of I and the value of θ . ( 9)

5

Question 7 (****)
Three small smooth spheres A , B and C , are resting on a straight line, and in that
order, on a horizontal surface.

The respective masses of A , B and C , are m , 3m and 7 m .

A is project towards B with speed u and a direct collision takes place.

The coefficient of restitution between A and B is 0.5 .

The coefficient of restitution between B and C is e .

If there is a second collision between A and B , find the range of possible values of e .
(14 )

Created by T. Madas
 Created by T. Madas

Question 8 (**+)

2u
m 4m
ψ
L
θ
A B

5u

Two smooth uniform spheres A and B have equal radii, and their respective masses
are m and 4m . The spheres are moving on a smooth horizontal plane when they
collide obliquely, with their centres at impact defining the straight line L , as shown in
the figure above.

Immediately before the collision, A is moving with speed 5u at an acute angle θ to

L and B is moving with speed 2u at an acute angle ψ to L .

It is further given that cos θ = 0.2 , cosψ = 0.75 and the coefficient of restitution
between the two spheres is 0.5 .

a) Determine, in terms of m and u , the magnitude of the impulse on A due to

the collision. (7)

b) Express the kinetic energy gained by A in the collision, as a percentage of its

initial kinetic energy. ( 3)

Created by T. Madas