A trader bought goats for N4000 each. He sold them for N180,000 at a loss of 25%. How many goats did he buy?
Answer
(A)
60
7
If dy/dx = 2x - 3 and y = 3 when x = 0, find y in terms of x.
Answer
(D)
x2 - 3x + 3
8
Find the derivative of \(y = \sin^{2} (5x)\) with respect to x.
Answer
(A)
10 sin 5x cos 5x
9
The slope of the tangent to the curve y = 3x\(^2\) - 2x + 5 at the point (1, 6) is
Answer
(A)
4
10
Evaluate \(\int \sin 3x \mathrm d x\)
Answer
(C)
(-1/3) cos 3x + c
11
A circle with radius 5cm has its radius increasing at the rate of 0.2m/s. What will be the corresponding increase in the area?
Answer
(A)
2π
12
If \(y = x^2 - \frac{1}{x}\). find dy/dx
Answer
(D)
2x + (1/x2)
13
Solve for x in the equation x\(^3\) - 5x\(^2\) - x + 5 = 0
Answer
(A)
1, - 1, or 5
14
The time taken to do a piece of work is inversely proportional to the number of men employed. if it takes 45 men to do a piece of work in 5 days, how long will it take 25 men?
Answer
(D)
9 days
15
Find the range of values of x for which \(\frac{(x+2)}{4}\) -\(\frac{2x-3}{3}\) < 4
Answer
(A)
x > -6
16
Find the maximum value of y in the equation y = 1 - 2x - 3x\(^2\)
Answer
(D)
4/3
17
If the 9th term of an A.P is five times the 5th term, find the relationship between a and d.
Answer
(C)
a + 3d = 0
18
Make r subject of the formula given that \(\frac{x}{r+a}=\frac{a}{r}\)
Answer
(A)
\(\frac{a^{2}}{(x-a)}\)
19
The inverse function f(x) = 3x + 4 is
Answer
(A)
(x-4)/3
20
If -2 is the solution of the equation 2x + 1 - 3c = 2c + 3x - 7, find the value of c.
Answer
(C)
2
21
The binary operation * is defined on the set of integers p and q by p*q = pq + p + q. Find 2 * (3 * 4).
Answer
(A)
59
22
The sum to infinity of the series: 1 + (1/3) + (1/9) + (1/27) + ... is
Answer
(D)
3/2
23
If x varies directly as √n and x = 9 when n = 9, find x when n = (17/9)
Answer
(D)
√17
24
A chord of a circle subtends an angle of 120° degrees at the centre of a circle of diameter 4√3 cm. Calculate the area of the major sector.
Answer
(D)
8 π cm2
25
If tan θ = 4/3, calculate sin\(^2\) θ - cos\(^2\) θ.
Answer
(C)
7/25
26
Find the equation of the set of points which are equidistant from the parallel lines x = 1 and x = 7
Answer
(C)
x = 4
27
A bucket is 12 cm in diameter at the top, 8 cm in diameter at the bottom and 4 cm deep. Calculate its volume.
Answer
(A)
304π/3 cm3
28
The sum of the interior angles of a polygon is 20 right angles. How many sides does the polygon have?
Answer
(A)
12
29
Find the coordinates of the mid-point of x and y intercepts of the line 2y = 4x - 8
Answer
(B)
(1, -2)
30
A hunter 1.6 m tall, views a bird on top of a tree at an angle of 45°. if the distance between the hunter and the tree is 10.4 m, find the height of the tree.
Answer
(B)
12. 0 m
31
A solid hemisphere has a radius of 7 cm. Find the total surface area.
Answer
(B)
462 cm2
32
Find the value of a if the line 2y - ax + 4 = 0 is perpendicular to the line y + (x/4) - 7 = 0
Answer
(C)
8
33
The locus of a point P which is equidistant from two given points S and T is
Answer
(A)
the perpendicular bisector of ST
34
Find the mean of the data: 7, -3, 4, -2, 5, -9, 4, 8, -6, 12
Answer
(D)
2
35
The range of the data: k+2, k-3, k+4, k-2, k, k-5, k+3, k-1, and k+6 is
Answer
(B)
11
36
The probability of a student passing any exam is 2/3. If the student takes three exams, what is the probability that he will not pass any of them?
Answer
(D)
1/27
37
The acres for rice, pineapple, cassava, cocoa, and palm oil in a certain district are given respectively as 2, 5, 3, 11, and 9. What is the angle sector for cassava in a pie chart?
Answer
(C)
36°
38
How many three-digit numbers can be formed from 32564 without repeating any of the digits?
Answer
(D)
60
39
The mean of a set of six numbers is 60. If the mean of the first five is 50, find the sixth number in the set.
Answer
(D)
110
40
Calculate the mean deviation of the set of numbers 7, 3, 14, 9, 7, and 8.
Answer
(D)
7/3
41
In the diagram above , XZ is the diameter of the circle XZW, with center O and radius 15/2 cm. If XY = 12 cm, find the area of the triangle XYZ
Answer
(A)
54 cm2
42
The venn diagram above shows the numbers of students offering music and history in a class of 80 students. If a student is picked at random from the class, what is the probability that he offers Music only?
Answer
(D)
0.25
43
In the diagram above, PST is a straight line, PQ = QS = RS. If ∠RST = 72o, find x
Answer
(D)
24o
44
In the diagram above are two concentric circles of radii r and R respectively with center O. If r = 2/3R, express the area of the shaded portion in terms of π and R
Answer
(D)
5/9πR2
45
In the diagram above, a cylinder is summounted by a hemisphere bowl. Calculate the volume of the solid.
