If the value of \(\pi\) is taken to be \(\frac{22}{7}\), the area of a semi-circle of diameter 42m is
Answer
(E)
693m2
4
(3.2)2 - (1.8)2 equals
Answer
(A)
7.0
5
In \(\bigtriangleup\)PQR, PQ = 10cm, QR = 8cm and RP = 6cm, the perpendicular RS is drawn from R to PQ. Find the length of RS
Answer
(E)
4.8cm
6
After getting a rise of 15%, a man's new monthly salary is N345. How much per month did he earn before the increase?
Answer
(C)
N300
7
In base ten, the number 101101 (base 2) equals
Answer
(C)
45
8
The annul profits of a transport business were divided between the partners A and B in the ratio 3 : 5. If B received N3000 more than A, the total profit was
Answer
(C)
N12000
9
x is directly proportional to y and inversely proportional to z. If x = 9 when y = 24 and z = 8, what is the value of x when y = 5 and z = 6?
Answer
(D)
2\(\frac{1}{2}\)
10
The solution of the equation x2 - 2x = 8 is
Answer
(B)
x = -2 or 4
11
A trader goes to Ghana for y days with y cedis. For the first x days, he spends X cedis per day. The amount he has to spend per day for the rest of his stay is
Answer
(E)
\(\frac{Y - Xx}{y - x}\) cedis
12
Multiply (3x + 5y + 4z) by (2x - 3y + z)
Answer
(A)
6x2 + xy - 15y2 + 4z2 + 11xz - 7yz
13
A square of cardboard is taped at the perimeter by a piece of ribbon 20cm long. What is the area of the board?
Answer
(C)
25sq.cm
14
Rationalize the denominator of the expression \(\frac{6 + 2\sqrt{5}}{4 - 3\sqrt{6}}\)
A steel ball of radius 1 cm is dropped into a cylinder of radius 2cm and height 4cm. If the cylinder is now filled with water, what is the volume of the water in the cylinder?
A ladder resting on a vertical wall makes an angles whose tangent is 2.4 with the ground. If the distance between the foot of the ladder and the wall is 50cm, What is the length of the ladder?
Answer
(E)
1.3m
19
Simplify 2\(\frac{5}{12}\) - 1\(\frac{7}{8}\) x \(\frac{6}{5}\)
Answer
(A)
\(\frac{1}{6}\)
20
One of the following statements is wrong. Which is it?
Answer
(C)
If two triangles are similar then they are also congurent
21
PQRS is a cyclic quadrilateral with PQ as diameter of the circle. If < PQS = 15o find < QRS
Answer
(D)
105o
22
Make c the subject of the equation a(b + c) + \(\frac{5}{d}\) - 2 = 0
Answer
(B)
c = \(\frac{2d - 5 - abd}{ad}\)
23
Which of the following values of the variable x, (a)x = 0, (b)x = -3, (c)x = 9, satisfy the inequalities 0 < \(\frac{x + 3}{x - 1}\) < 2?
Answer
(B)
(c)
24
On each market day Mrs. Bassey walks to the market from her home at a steady speed. This journey normally takes her 2 hours to complete. She finds, however, that by increasing her usual speed by 1 km/hr she can save 20 minutes. Find her usual speed in km/hr
Answer
(C)
5
25
Solve the simultaneous linear equations: 2x + 5y = 11, 7x + 4y = 2
Answer
(C)
x = \(\frac{-34}{27}\), y = \(\frac{73}{27}\)
26
If x\(^3\) - 12x - 16 = 0 has x = -2 as a solution then the equation has
Answer
(C)
3 roots with two equal and the third different
27
Find the value of (4\(^{\frac{1}{2}}\))\(^6\)
Answer
(E)
64
28
Find the value of log\(_{10}\)\(\frac{1}{40}\), given that log10\(_4\) = 0.6021
Answer
(C)
-1.6021
29
12 men complete a job in 9 days. How many men working t the same rate would be required to complete the job in 6 days?
Answer
(B)
18
30
For the set of numbers 2, 3, 5, 6, 7, 7, 8
Answer
(E)
the mean is less than the median
31
Simplify \(\frac{1 - x^2}{x - x^2}\), where x \(\neq\) 0
Answer
(C)
\(\frac{1 + x}{x}\)
32
A cylinder of height h and radius r is open at one end. Its surface area is
Answer
(C)
2\(\pi\)rh + \(\pi\)r2
33
An arc of circle of radius 2cm subtends an angle of 60º at the centre. Find the area of the sector
Answer
(A)
\(\frac{2 \pi}{3}\)cm2
34
What is the greatest straight line distance between two vertices (corners) of a cube whose sides are 2239cm long?
Answer
(D)
\(\sqrt{3}\) x 2239cm
35
What is log\(_7{(49^a)}\) - log\(_{10}^{(0.01)}\)?
Answer
(D)
2a + 2
36
The size of a quantity first doubles and then increases by a further 16%. After a short time its size decreases by 16%. What is the net increases in size of the quantity?
Answer
(C)
200%
37
The following table relates the number of objects f corresponding to a certain size x. What is the average size of an object?
\(\begin{array}{c|c} f & 1 & 2 & 3 & 4 & 5 \\ \hline x & 1 & 2 & 4 & 8 & 16\end{array}\)
Answer
(D)
\(\frac{43}{5}\)
38
If y = x\(^2\) - 2x - 3, find the least value of y and the corresponding value of x
Answer
(D)
x = 1, y = -4
39
A father is now three times as old as his son. Twelve years ago he was six times as old as his son. How old are the son and the father?
Answer
(E)
20 and 60
40
If \(\sqrt{3^{\frac{1}{x}}}\) = \(\sqrt{9}\) then the value of x is:
Answer
(E)
\(\frac{1}{2}\)
41
A man is standing in the corridor of a 10-storey building and looking down at a tall tree in front of the building. He sees the top of the tree at angle of depression of 30o. If the tree is 200m tall and the man's eyes are 300m above the ground, calculate the angle of depression of the foot tree as seen by the man
Answer
(B)
60o
42
In the figure, \(\bigtriangleup\) ABC are in adjacent planes. AB = AC = 5cm, BC = 6cm and o then AE is equal to
Answer
(B)
2\(\sqrt{3}\)
43
In this figure, PQRS is a parallelogram, PS = PT and < PST = 55\(^o\). The size of <PQR is
Answer
(D)
110o
44
If O is the centre of the circle, < POS equls
Answer
(E)
150o
45
In the figure, PQ and QR are chords of the circle PQR. QRS is a straight line and PR is equal to RS, < PSR is 20o. What is the size of <POQ.
Answer
(C)
80o
46
In the figure, PQ is parallel to SQ ; QS bisets < PSQ, < PQS is 65o and < RPS is 20o. What is the size of < PRS?
Answer
(D)
30o
47
(Numbers indicate the lengths of the sides of the triangles) If the area of \(\bigtriangleup\) PQR is k2sq. units what is the area of the shades portion?
Answer
(A)
\(\frac{5}{9}\)k2 sq. units
48
In the parallelogram PQRS, PE is perpendicular to QR. Find the area of the parallelogram.
