FORM THREE 2 HOURS
Section A. multiple choice questions. Circle the correct letter.
1) When the expression 2 x (5−3 x) is expanded the coefficient of x is:
a) 10 b) 4 c) −6 d) 16
2
2) Given that ( 5 x−3 ) ( x+ 2 ) ≡ 5 x −kx−6 , the value of k is:
a) 10 b) −3 c) 7 d) −7
3) The order of the matrix ( 3 0 −6 ) is:
a) 3 ×1 b) 3 ×3 c) 1 ×3 d) 1 ×1
4) The leading diagonal of the matrix (−24 16) has elements:
a)−2∧6 b) −2∧1 c) 1∧4 d) 1∧6
5) The adjoint of the matrix (−53 −12 ) is:
a) (−13 −5
2 ) b) (
5 3)
2 1
c) (−31 5
−2 ) (−25
d)
1
−3 )
Section B. show all steps in your working
1) Factorise the following
a) 5 m2−20
b) n2 −16
c) x 2−6 x +8
2) Solve the following quadratic equations using the indicated method
a) By factorization: x 2+ 5 x +6=0
b) Using the quadratic formular: 3 x 2+7 x −6=0
3) Solve the pair of simultaneous equations
{a+5
a+ b=50
b=74
4) Given the matrices P= ( 14 x−1
5 )
and Q=
1 −3
2y 5 ( )
. Find the values of x and y for which
P=Q
5) Given the matrix M = (42 53). Find:
a) The determinant of M
b) The adjugate of M
c) Hence the inverse of M
Section C
Three friends Michael, Peter and John bought a plot for 2,800,000 fcfa from a man who agreed to be
paid 65 % of its value as initial deposit.
a) Calculate the initial deposit.
The deposit is paid by Michael, Peter and John in the ratio 5 :3 :2 respectively.
b) Determine the amount paid by Peter.
Given that 91000 fcfa is to be paid as processing fee for the documents.
c) Find the percentage of the initial deposit needed to process the document.
d) Calculate the balance expected to be paid to the man.
LOWER SIXTHS 2 HOURS
SECTION A
1) Use prove by mathematical induction to prove that:
n
a) ∑ 2 r−1=2n−1
i=1
2 2 2 2 n
b) 1 +2 +3 +…+n = ( n+1)(2n+ 1)
6
2) The sum of the first six terms of an arithmetic progression is 72 and the second term is seven
times the fifth term.
a) Find the first term and the common difference
b) Find the sum of the first ten terms.
3) a) given that A={2 , 3 , 4 , 5 } and B={ x : x is even }. Show that A is not a subset of B .
b)Given the sets A , B∧ξ defined as:
A={1 , 2, 5 , 7 }, B={2 ,3 , 6 , 7 } and ξ={1 ,2 , 3 , 4 , 5 , 6 ,7 ,8 , 9 , 10 }. Find
i) A
c
ii) A ∩ B iii) A ∪ B iv) A ∖ B v) n(B)
Section B
1) Given that f ( θ )=sin θ−√ 3 cos θ.
π
a) Express f (θ) in the form r sin(θ−λ) where r >0 and 0< λ< .
2
Hence,
1
b) Find the maximum and minimum values of (6 marks)
f ( θ ) +3
2) Prove the following
sin 3 A−sin A
a) =tan 3 A (3 marks)
cos 3 A +cos A
cos θ sin θ
b) + =cos θ +sin θ (3 marks)
1−tanθ 1+cot θ
c) sin 3 θ=3 sin θ−4 sin3 θ (3 marks)
3) Solve the equation cos 4 x +cos 2 x=0 for 0° ≤ x ≤ 360° (5 marks)
FORM FOUR 2 HOURS
Section A. multiple choice questions. Circle the correct letter. (1 mark each)
()
2
3 2
1) Simplify: 1− of
4 3
1 1 2 1
a) b) c) d)
2 9 3 6
6
2) Express to three decimal places
25
a) 2.4 b) 2.40 c) 0.240 d) 0.24
3) Which of these numbers is to three significant figures and two decimal places?
a) 10.45 b) 5.23 c) 25.02 d) 0.023
2
4) The coefficient of x in −2 x (1−3 x) is:
a) 1 b) −2 c) −3 d) 6
5) When expanded (x−1)(1−x ) gives:
a) −x 2+ 2 x−1 b) −x 2−2 x−1 c) x 2−2 x+1 d) x 2−2 x−1
6) The number 0.06 ×1.14 in standard form is:
a) 6.84 × 102 b) 6.84 × 10−3 c) 6.84 × 10−2 d) 6.84 × 103
7) Base 10 numbers are called ----------------- numbers
a) Binary b) decimal c) pental d) octal
8) In the number 25 ,
a) 1 is the power b) the exponent is 0 c) the index is 0 d) the base is 1
2 2
9) Factorise ( 4 a+3) −(3 a−2)
a) (a+ 1)(a+5) b) (a−5)(7 a−1) c) (a+ 5)(7 a+1) d) a (7 a+1)
0.00275 ×0.00064
10) Simplify and express I standard form
0.02 ×0.08
a) 1.1 ×10−4 b) 1.1 ×10 4
c) 1.1 ×10−3 d) 1.1 ×103
Section B. show all steps in your working.
1) Solve the following quadratic equations using the indicated method.
a) x 2−5 x+ 6=0 by factorization (3 marks)
2
b) 2 x +11 x +15=0 using the quadratic formular (3 marks)
2) The functions g and h are defined on R , the set of real numbers as follows:
g : x ⟼ x + 2 and h : x ⟼ x +2, find
2
a) g(2)
b) h−1 (x)
c) hg (x) (7 marks)
3) If A={0 , 2 , 4 } and B={1, 5 }, find the Cartesian product B× A and A × A (4 marks)
4) Given the number 46315
a) Round off the number to 1 significant figure
b) Calculate the absolute error
c) Calculate the relative error
Hence
d) Determine the percentage error (4 marks)
Section C
A woman bought a piece of land in the year 2010 at 2,500,000 fcfa . An amount worth 5 % of the
buying price was paid to prepare a deed conveyance, 35000 fcfa was used for food and 16000 fcfa used
for drinks on the day of purchase of the piece of land.
Find
a) The amount used to prepare the deed of conveyance (3 marks)
b) The total amount used on the day of purchase of the piece of land (2 marks)
Given that she was expected to pay an annual land task of 1 % and that she also pursued a land
title at an amount worth 10 % of the cost of piece of land. Calculate
c) The amount paid as annual land tax (2 marks)
d) The total amount spent to own the piece of land in 2010. (3 marks)
