If 2x + y = 7 and 3x - 2y = 3, by how much is 7x greater than 10?
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(C)
7
14
A cylinder of base radius 4cm is open at one end . If the ratio of the area of its base to that of its curved surface is 1:4, calculate the height of the cylinder
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(D)
8cm
15
A headmaster contributes 7% of his income into a fund and his wife contributes 4% of her income. If the husband earns N5,500 per annum (p.a) and the wife earns N4,000 (P.a), find the sum of their annual contribution to the fund
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(C)
N545
16
A car is travelling at an average speed of 80km/hr. Its speed in meters per second (m/s) is
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(B)
22.2m/s
17
Mrs. Kofi sold an article for C7.50 instead of C12.75. Calculate her percentage of error, correct to one decimal place.
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(A)
41.2%
18
In the diagram above, PXR and PYO are two semi-circles with diameters 14cm and 7cm respectively. Find the area of the enclosed region, PXROY correct to the nearest whole number
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(A)
96cm2
19
In the diagram above, PXR and PYO are two semicircles with diameters 14cm and 7cm respectively. Find the perimeter of the region (take \(\pi\) = \(\frac{22}{7}\) )
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(C)
40cm
20
The shaded portion shows the outer boundary
of the half plane defined by the inequality
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(A)
4x + 3y \(\geq\) 6
21
Find the coordinates of point B
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(E)
(11/2, 0)
22
The first term a of an A.P is equal to twice the
common difference d. Find, in terms of d, the 5th
term of the A.P.
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(C)
6d
23
The common ratio of a G.P. is 2. If the 5th term is
greater than the 1st term by 45, find the 5th term,
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(D)
48
24
Two towns, P and Q, are on (4oN 40oW) and (4oN
20oE) respectively. What is the distance between
them, along their line of latitude? (Give your
answer in teems of π and R, the radius of the earth).
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(D)
πR/3
cos4o
25
the graph above is a sketch of
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(B)
y=sinx
26
Given that sin \(\theta\) = -0.9063, where O \(\leq\) \(\theta\) \(\leq\) 270°, find \(\theta\).
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(D)
245o
27
From the top of a cliff, the angle of depression of
a boat on the sea is 60o, if the top of the cliff is
25m above the sea level, calculate the horizontal
distance from the bottom of the cliff to the boat.
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(C)
25√3m/3
28
The angle of elevation of the top of a tree 39m
away from a point on the ground is 30o. Find the height of the tree
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(B)
13√3m
29
In the diagram above, ATR is a tangent at the point T to the circle center O, if ∠TOB = 145°, find ∠TAO
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(D)
55o
30
P={2, 1,3, 9, 1/2}; Q = {1,21/2,3, 7} and R = {5, 4, 21/2}. Find P∪Q∪R
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(E)
(1/2, 1, 2, 21/2, 3, 4, 5, 7, 9)
31
P = {2, 1,3, 9, 1/2}; Q = {1,21/2,3, 7} and R = {5, 4, 21/2}. Find P∩Q∩R
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(B)
∅
32
In a class of 80 students, every student had to study Economics or Geography or both Economics and Geography. lf 65 students studied Economics and 50 studied Geography, how many studied both subjects?
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(C)
35
33
Which of the following is not a measure of dispersion?
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(A)
Mode
34
The mean of 30 observations recorded in an experiment is 5. lf the observed largest value of 34 is deleted, find the mean of the remaining observations
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(B)
4
35
Find the mean of the distribution
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(C)
4.4
36
Find the mode of the distribution
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(D)
5
37
No. of chairs
1
2
3
4
5
6
7
Frequency
2
7
5
4
9
7
6
Find the median of the distribution
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(C)
5
38
If two events are mutually exclusive, their intersection is empty. This means that there are no outcomes that are common to both events. In probability terms, if X and Y are mutually exclusive events, then:
Pr(X ∩ Y) = 0
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(A)
0
39
If events X and Y are mutually exclusive, P(X) = 1/3 and P(Y) = 2/5, P(X∪Y) is
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(D)
11/15
40
A box contains 2 white and 3 blue identical marbles. If two marbles are picked at random, one after the other without replacement, what is the probability of picking two marbles of different colors?
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(B)
3/5
41
Mrs. Jones is expecting a baby. The probability that it will be a boy is 1/2 and probability that the baby will have blue eyes is 1/4. What is the probability that she will have a blue-eyed boy?
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(A)
1/8
42
Which of the following about a rhombus may not be true?
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(A)
The diagonals are equal
43
The angles of a pentagon are x°, 2x°, (x + 60)°, (x + 10)°, (x -10)°. Find the value of x.
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(D)
80
44
In the diagram above, ∠PTQ = ∠URP = 25° and XPU = 4URP. Calculate ∠USQ.
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(D)
130o
45
In a given regular polygon, the ratio of the exterior angle to the interior angles is 1:3. How many side has the polygon?
