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
