### cameroon gce A level June 2024 pure mathematics with mechanics 1

cameroon gce A level June 2024 pure mathematics with mechanics 1

SECTION A: PURE MATHEMATICS

A small sphere of mass 0.6 kg is moving on a

horizontal table with a speed of 10 m s-1 when

it collides with a fixed smooth wall perpendicular

to the table surface. It rebounds with a speed of

-1

. The coefficient of restitution between

40.

-1 3 4

M is

A -18

B -8

C 0

D 18

is

— m s

the sphere and the wall is

A 4

3

SECTION B: MECHANICS

The position vector of a particle at time t seconds

is r. where r = [(t 2 +l)i+ t3j ] m The ve|ocity

of the particle when f = 2 is

A (4i+ 6j)ms-1

B (4! — 12j)ms-1

C (2i + 12j)m s-1

D (4i+ 12j)m s_1

B 5

36. 3

C 1

53

D

4

Three particles of masses 5 kg, 3 kg and m kg lie

on the y-axis at the points (0,4), (0,2) and (0, 5)

respectively. The center of mass of the system is

at the point (0,4). The value of m is

A 5

B 4

C 6

D 7

41.

37. The extension a force ot 20 N produces in a spring

of natural length 5 m whose modulus of elasticity

is 150 N is

3

A – m

2 3

B – rn

A— car m swheel -1. Itsofangular radius speed ^ m isinmoving rad s-1at is a speed of

3

\

AB

53

C

4 42.

C – in

D – m

3 2

3

38. The velocity of a particle A relative to another B is

(7i+ 5j) m s'”1. Given that the velocity of A is

(8i+ 6j) m s'”1. The velocity of B is

A (15i+llj) m s”1

B (—i — j) m s_1

C (H- j) ms”1

D (15i — llj) m s_1

3

D 25

3

43. A car accelerates uniformly from a velocity of

10 m s”1 to 60 m s _1 in 6 seconds on a straight

road. The distance it covered is

Given that A and B are events with P(A) = 7,

P( A U B ) =\ and P( A n B ) = ± .

P(.A\B ) =

A i

2

B –

3

C –

6

D –

A 150 m

B 200 m

C 210 m

D 215 m

39.

A box contains ten green and six white marbles. A

marble is chosen at random, its colour noted and it

is not replaced. This process is repeated once. The

probability that the marbles chosen are of the same

colour is

°gvy — 2 and x y = 125, then the values of

x and y are respectively

A 3 and 9

B 9 and 3

C 5 and 25

D 25 and 5

B p <—> q

C pVq

D p A q

J* ) j

Given the lines

r = 3i – 2j + 4k + d(4i + 2j- 3k)

r = i + 3j + k + 5(8i + 4j- 6k)

r = 2i + 6j + 2k + /?(i – 4j + 4k)

r = 4i + 12j + 4k – ji( » + 3j + k) .

Which pair of lines are parallel?

A L| and L2

B Li and Lj

C L2 and L4

D L2 and L2

8.

L, :

L? :

The vertical asymptotes of the curve

1

(x-2)(x+3)

A x = 3, x = -2

B x = 2, x = —3

C x = —3, x = — 2

D x = 2, x = 3

The engine of a car of mass 1 ,200 kg works at a

constant rate of 69 kW up a road inclined at an

angle sin-1 Q) to the horizontal. Given that the

non-gravitational resistance to the motion of the

car is 300 N and taking g as 10 m s “ 2, the

maximum speed of the car is

15 m s

B 25 ms”1

30 m s

22 ms”1

45. 48.

A -l M 3N

B N

\

C -l \

Q

X

.52 N

The work done by a force F = (i- 2j- 4k) N

which moves its point of application from a point

A with position vector rA = (3i – 4j) m to another

point B with position vector rB = (—i — 6k) m is

46.

40 *N\a

44 »

9 N

Fie- 3

A 47 .!

B 36.1

C 12.1

D -6 J

The angle 0 which AB makes with the floor is

given by

A’

tan tan 0 0 ==-^

sm 0 = -4

sin 0= –

A particle decelerating to rest has its speed v m s- I

at time / seconds given by

v = 6/ – – /V

2

The deceleration of the particle when v = 10 is

4ms”2

B 10ms”2

C -10ms ”2

D —4ms”2

47.

4

c

A 4

A particle of mass of 14 kg rests on smooth

horizontal table. It is connected by a light

incxtcnsible string passing over a smooth pulley

fixed at the edge of the table to a particle of mass 6

kg which hangs freely.

Given that the acceleration of the system is

3 m s“2 when it is released from rests, the force

exerted by the string on the pulley is

49.

A 42v/2 N

B 82V2 N

C 42 N

D 82 N (

so. A smooth sphere A of mass 6 kg travelling at 4

collides directly witl\ a smooth sphere /1 of mass 3 kg

travelling at 2 m s 1 in the opposite direction, ( liven

that the speed ol B alter impact is 2 m s’1, the kinetic

energy of /1 alter impact is

m s

A 6.1

It 12.1

C 50.1

I ) 13.5 .1y = are L4 :

When the polynomial p( x) = a x 3 4- 5x 2 + 2x —

8 is divided by ( x — 1), the remainder is -3 .

a =

4.

A relation R defined on a non-empty set S is called

a partial order it R is

A Reflexive, symmetric and antisymmetric

B Reflexive, anti-symmetric and

transitive

C Reflexive, symmetric and transitive

D Symmetric, anti-symmetric and

transitive

9.

A -4

B -2

C 2

D 3

(x+l)2+3

5. The set of values of x for which < 0

(x+3)(x-2)

10.

IS

00

‘ A [x : x < —3 or x > 2}

B [ x ‘ x —3 or x > 2)

C [x : — 3 x < 2}

D {x : —3 < x < 2}

v-1 m

If = 10, then m =

7 =1

A 10

B 5

C 15

D 7

6. A function f: DS US is defined by

4/y + 4x, i f x < 1 4x – /? 2 – 4 i f x > 1 .

If f(x) has a limit at x = 1, the value of /? is

A 2

B 1

C 3

D -2

f(*) = j The first order differential equation obtained

from the function y = A x + In x is

A

X’

Y = y 4- lnx + 1

B ^x£==y-y -!n x \

### cameroon gce A level June 2024 pure mathematics with mechanics 1