A trader bought goats for N4000 each. He sold them for N180,000 at a loss of 25%. How many goats did he buy?
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(A)
60
7
If dy/dx = 2x - 3 and y = 3 when x = 0, find y in terms of x.
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(D)
x2 - 3x + 3
8
Find the derivative of \(y = \sin^{2} (5x)\) with respect to x.
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(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
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(A)
4
10
Evaluate \(\int \sin 3x \mathrm d x\)
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(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?
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(A)
2π
12
If \(y = x^2 - \frac{1}{x}\). find dy/dx
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(D)
2x + (1/x2)
13
Solve for x in the equation x\(^3\) - 5x\(^2\) - x + 5 = 0
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(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?
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(D)
9 days
15
Find the range of values of x for which \(\frac{(x+2)}{4}\) -\(\frac{2x-3}{3}\) < 4
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(A)
x > -6
16
Find the maximum value of y in the equation y = 1 - 2x - 3x\(^2\)
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(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.
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(C)
a + 3d = 0
18
Make r subject of the formula given that \(\frac{x}{r+a}=\frac{a}{r}\)
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(A)
\(\frac{a^{2}}{(x-a)}\)
19
The inverse function f(x) = 3x + 4 is
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(A)
(x-4)/3
20
If -2 is the solution of the equation 2x + 1 - 3c = 2c + 3x - 7, find the value of c.
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(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).
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(A)
59
22
The sum to infinity of the series: 1 + (1/3) + (1/9) + (1/27) + ... is
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(D)
3/2
23
If x varies directly as √n and x = 9 when n = 9, find x when n = (17/9)
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(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.
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(D)
8 π cm2
25
If tan θ = 4/3, calculate sin\(^2\) θ - cos\(^2\) θ.
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(C)
7/25
26
Find the equation of the set of points which are equidistant from the parallel lines x = 1 and x = 7
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(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.
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(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?
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(A)
12
29
Find the coordinates of the mid-point of x and y intercepts of the line 2y = 4x - 8
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(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.
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(B)
12. 0 m
31
A solid hemisphere has a radius of 7 cm. Find the total surface area.
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(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
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(C)
8
33
The locus of a point P which is equidistant from two given points S and T is
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(A)
the perpendicular bisector of ST
34
Find the mean of the data: 7, -3, 4, -2, 5, -9, 4, 8, -6, 12
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(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
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(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?
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(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?
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(C)
36°
38
How many three-digit numbers can be formed from 32564 without repeating any of the digits?
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(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.
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(D)
110
40
Calculate the mean deviation of the set of numbers 7, 3, 14, 9, 7, and 8.
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(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
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(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?
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(D)
0.25
43
In the diagram above, PST is a straight line, PQ = QS = RS. If ∠RST = 72o, find x
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(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
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(D)
5/9πR2
45
In the diagram above, a cylinder is summounted by a hemisphere bowl. Calculate the volume of the solid.
