In a class of 40 students, 32 offer mathematics, 24 offer Physics, and 4 offer neither Mathematics nor Physics. How many offer both Mat
ematics and Physics?
A cinema hall contains a certain number of people. If 22\(\frac{1}{2}\)% are children, 47\(\frac{1}{2}\)% are men and 84 are women, find the number of men in the hall.
Answer
(D)
133
9
If \(\frac{9^{2x-1}}{27^{x+1}} = 1\), find the value of x.
Answer
(B)
5
10
The sum of four numbers is 1214\(_5\). What is the average expressed in base five?
Answer
(B)
141
11
Given:
U = {Even numbers between 0 and 30}
P = {Multiples of 6 between 0 and 30}
Q = {Multiples of 4 between 0 and 30}
Find (P∪Q)c
Answer
(A)
{2, 10, 14, 22, 26}
12
x varies directly as the product of u and v and inversely as their sum. If x = 3 when u = 3 and v = 1, what is the value of x if u = 3 and v = 3?
Answer
(C)
6
13
Find the range of the value of x satisfying the inequalities 5 + x \(\leq\) 8 and 13 + x \(\geq\) 7
Answer
(C)
-6 \(\leq\) x \(\leq\) 3
14
The graph of the function y = x\(^2\) + 4 and a straight line PQ are drawn to solve the equation x\(^2\) - 3x + 2 = 0. What is the equation of PQ?
Answer
(B)
y = 3x + 2
15
The length a person can jump is inversely proportional to his weight. If a 20 kg person can jump 1.5 m, find the constant of proportionality
Answer
(B)
30
16
Find the value of x and y respectively if 3x - 5y + 5 = 0 and 4x - 7y + 8 = 0
Answer
(D)
5, 4
17
Three consecutive terms of a geometric progression are given as n-2, n and n+3. Find the common ratio
Answer
(D)
3/2
18
Triangle OPQ above is the solution of the inequalities
Answer
(A)
x + 1 ≥ 0, y + x ≤ 0, y - x ≥ 0
19
Factorize completely 4abx - 2axy -12b2x + 6bxy
Answer
(A)
2x(a - 3b)(2b - y)
20
The sum of the first n terms of an arithmetic progression is 252. If the first term is -16 and the last term is 72, find the number of terms in the series
Answer
(D)
9
21
A trapezium has two parallel sides of length 5cm and 9cm. If the area is 21cm2, find the distance between the parallel sides
Answer
(A)
3 cm
22
The locus of a point P which moves on one side only of a straight line XY so that ∠XPY = 90o is
Answer
(B)
a semicircle
23
Find the slope of the curve y = 2x\(^2\) + 5x - 3 at (1, 4).
Answer
(D)
9
24
Evaluate \(\int^{3} _{2}(x^2 - 2x)dx\)
Answer
(C)
4/3
25
If y = 3 sin(-4x), dy/dx is
Answer
(C)
-12 cos (-4x)
26
Determine the maximum value of y = 3x2 - x3
Answer
(C)
4
27
By how much is the mean of 30, 56, 31, 55, 43 and 44 less than the median?
Answer
(C)
0.33
28
The range of 4, 3, 11, 9, 6, 15, 19, 23, 27, 24,21 and 16 is
Answer
(D)
24
29
Find the mean of the distribution above
Answer
(C)
3
30
On a pie chart, there are four sectors of which three angles are 45°, 90° and 135°. If the smallest sector represents N28.00, how much is the largest sector?
Answer
(B)
N84.00
31
If \(^{n}P_{3} - 6(^{n}C_{4}) = 0\), find the value of n.
Answer
(C)
7
32
Find the number of committees of three that can be formed consisting of two men and one woman from four men and three women
Answer
(C)
18
33
A bag contains 5 blacks balls and 3 red balls. Two balls are picked at random without replacement. What is the probability that a black and red balls are picked?
Answer
(A)
15/28
34
The result of tossing a fair die 120 times is summarized above. Find the value of x
Answer
(B)
20
35
An aeroplane flies due north from airport P to Q and then flies due east R. If Q is equidistant from P and R, find the bearing of P and R
Answer
(C)
225o
36
An arc of a circle subtends an angle of 30° on the circumference of a circle of radius 21cm. Find the length of the arc.
Answer
(B)
22cm
37
Find the equation of the locus of a point P(x,y) which is equidistant from Q(0,0) and R(2,1).
Answer
(A)
4x + 2y = 5
38
In the diagram above, PQ is parallel to RS. What is the value of α + β + γ?
Answer
(A)
360o
39
XYZ is a circle with center O and a radius 7cm. Find the area of the shaded region.
Answer
(D)
14cm2
40
In the diagram above, PQR is a straight line and PS is a tangent to the circle QRS with /PS/ = /SR/ and ∠SPR = 40°. Find ∠PSQ
