cameroon gce O level June 2024 additional mathematics paper 2
cameroon gce O level June 2024 additional mathematics paper 2
SECTION A: PURE MATHEMATICS
THIS SECTION IS COMPULSORY TO ALL CANDIDATES
(ANSWER ALL QUESTIONS)
1. (i) Find the value(s) of x for which for which (log3 x )2 – 4(log3 x ) + 3 = 0. (4 marks)
(ii) Given that the roots of the quadratic equation 2*2 – 3x — 5 = 0 are a and /?,
a) find the values of a + /? and a/?.
b) write down another quadratic equation with integral coefficients whose roots are – a and – /?. (3 marks)
(1 mark)
2. (i) Find the number of ways of arranging the letters of the word ARRANGING. (4 marks)
(ii) Write down the first three terms in ascending powers ofjc in the binomial expansion of (1 — 2x ) \
simplifying each term. (4 marks)
3. During a meeting of women in a church, 24 women sat on the first row, 21 in the second row and 18 in the
third row. Given that the sitting arrangement continues in the same pattern and no row was skipped,
find,
a) the number of women who sat on the 5th row.
b) Show that no woman sat on the 9th row.
c) Find the total number of women who attended the meeting.
(i) The binary operation * is defined over the set G = {1,3, 5, 7} where * denotes multiplication
modulo 8.
a) Copy and complete the table below for ( G, *).
b) State the identity element
(ii) A linear transformation T is given by
T: (x, y) —> (2x + y, x + 2y)
a) State the transformation matrix represented by T.
b) Find the image of the point P(1, 3) under T.
c) Find the equation of the invariant line under T.
(i) A man sells x cups of patched groundnuts and y cups of patched com during break in a certain
school as shown in the inequality diagram below.
From the diagram,
a) write down three inequalities in terms of x and y that satisfy the unshaded region.
If he must sell both patched groundnuts and patched corn and that a cup of
patched groundnut cost 125 francs and a cup of patched corn cost 50 francs,
b) find the maximum expenditure that can be incurred by the man.
(ii) The points A and B has coordinates (—2,5) and (3, —1) respectively.
Find
a) the gradient of the straight line AB,
b) the equation of the straight line joining the points AB.
(2 marks)
(2 marks)
6. (i) Solve for 0, in the range 0° < 0 360°, the equation cos 20 = 1 (3 marks)
(ii) The function f\x ) is defined by f (x ) = sin*+ cosx, where 0 < x 2n.
a) Copy and complete the table below. (3 marks)
x 0 n n 37T n 57T 3n In 2n
b) draw Taking the graph Icm toof represent y = f ( x )^ radians units on the x-axis and 2cm to represent I unit on the y-axis,
c) write down the minimum value of/OO-
(2 marks)
(1 mark)
7. The vector equations of the lines and l 2 are :
r = l – j +W – j )
r = 4/ + (a +1)7 respectively, where X and a are constants,
lind.
a) The value of a given that / ] a n d l2 intersect.
Ilenee find,
b) the position vector of their point of intersection
c) the angle between / j a n d l 2
