Master’s Degree and Internship Program
of the African Business Education Initiative for Youth (ABE Initiative)
(3rd Batch)
Examination for Mathematics (45 min.)
Note:
1. Rules of Examination
 Do not leave the room without proctor’s permission.
 Do not take this question booklet out of the room.
 No calculators are allowed.
 Show all your work in blank spaces and write your answers in the
space provided.
2. Instruction for the Question booklet
 Do not open this question booklet until instructed.
 Do not remove the staples from this booklet.
 After being instructed, write your registration number and name in
the space provided below.
 If your question booklet is missing any pages, raise your hand.
 This question booklet consists of 2 parts (Part1 and Part 2). You are
requested to answer all the questions.
Registration No.
Name
(Type A)
Part 1
Write down your answer for each question.
(1) Calculate 4 − {1 − (2 − 6) − 7}.
Answer:
(2) Calculate
×
−
÷ −
6
.
Answer:
(3) Calculate 4
×
÷2
.
Answer:
2 =8
(4) Solve 2x − 8 = 1 + 5x for x.
Answer:
x = −3
(5) Solve x + y − 24 = 0 and −2x − 6y + 4 = 0 for x and y.
Answer:
x = 35, y = −11
Answer:
x = −15, 3
(6) Solve 45 − x + 5x = 17x for x.
(7) Suppose that the average of the five values, {−1, 2, 1 − 2x, x, 5}, is equal
to x. Find the value of x.
Answer:
x=
Part 2
Write down your answer for each question.
(8) Find the region of x satisfying
≤ 1.
Answer:
(9) Solve 10
−1 ≤ x ≤ 3
= 1.
Answer:
x = 0,2
(10) Find the region of x satisfying log (2x − 1) < 0.
Answer:
< 𝑥< 1
(11) Find the positive value of n satisfying
2
= 63
Answer:
n=6
(12) Find the first-derivative of y = x [ln(x) − 1]. Note that ln (x) is the log of x
with the base of the exponential, e, which is approximately equal to 2.718.
Answer:
y = ln (x)
(13) Find the definite integral:
√𝑥 dx
Answer:
(14) Let A =
x−1
1
1 − 2x
. Suppose the determinant of A is zero, so that A
2
is not invertible. Solve for x
Answer:
x=
(15) Assume that 0 < 𝜃 < 𝜋. Solve the following equation for θ.
1
= 2√3tanθ − 2
(cosθ)
Answer:
θ = π/3
(16) There are 5 boys and 6 girls in the math class. Find the number of ways the
instructor can select a team of 3 students from the class. The team consists
of 1 boy and 2 girls.
Answer: C × C = ×
×
×
= 75