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