Find the simple interest rate percent per annum at which N1,000 accumulates to N1,240 in 3 years
Răspuns
(B)
8%
7
If U = (s, p, i, e, n, d, o, u, r), X = (s, p, e, n, d) Y = (s, e, n, o, u), Z = (p, n, o, u, r) find X ∩( Y ∪ Z)
Răspuns
(C)
(s, p, n, e)
8
A survey of 100 students in an institution shows that 80 students speak Hausa and 20 students speak Igbo, while only 9 students speak both language. How many students speak neither Hausa nor Igbo?
Răspuns
(B)
9
9
If the function f(fx) = x3 + 2x2 + qx - 6 is divisible by x + 1, find q
Find the minimum value of X2 - 3x + 2 for all real values of x
Răspuns
(A)
-\(\frac{1}{4}\)
12
Make F the subject of the formula t = \(\sqrt{\frac{v}{\frac{1}{f} + \frac{1}{g}}}\)
Răspuns
(B)
\(\frac{gt^2}{gv-t^2}\)
13
What value of g will make the expression 4x2 - 18xy + g a perfect square?
Răspuns
(D)
\(\frac{18y^2}{4}\)
14
Find the value of k if \(\frac{5 + 2r}{(r + 1)(r - 2)}\) expressed in partial fraction is \(\frac{k}{r - 2}\) + \(\frac{L}{r + 1}\) where K and L are constants
Răspuns
(A)
3
15
Let f(x) = 2x + 4 and g(x) = 6x + 7 here g(x) > 0. Solve the inequality \(\frac{f(x)}{g(x)}\) < 1
Răspuns
(C)
x > - \(\frac{3}{4}\)
16
Find the range of values of x which satisfies the inequality 12x2 < x + 1
Răspuns
(A)
-\(\frac{1}{4}\) < x < \(\frac{1}{3}\)
17
Sn is the sum of the first n terms of a series given by Sn = n\(^2\) - 1. Find the nth term
Răspuns
(D)
2n - 1
18
The nth term of a sequence is given \(3^{1 - n}\), find the sum of the first three terms of the sequence.
Răspuns
(A)
\(\frac{13}{9}\)
19
Two binary operations \(\ast\) and \(\oplus\) are defines as m \(\ast\) n = mn - n - 1 and m \(\oplus\) n = mn + n - 2 for all real numbers m, n.
Find the value of 3 \(\oplus\) (4 \(\ast\) 5)
Răspuns
(C)
54
20
If X \(\ast\) Y = X + Y - XY, find x when (x \(\ast\) 2) + (x \(\ast\) 3) = 68
Răspuns
(D)
-21
21
Determine x + y if \(\begin{pmatrix} 2 & -3 \\ -1 & 4 \end{pmatrix}\) \(\begin{pmatrix} x \\ y \end{pmatrix}\) = \(\begin{pmatrix}-1 \\ 8 \end{pmatrix}\)
Răspuns
(C)
7
22
Find the non-zero positive value of x which satisfies the equation \(\begin{vmatrix} x & 1 & 0 \\ 1 & x & 1 \\ 0 & 1 & x\end{vmatrix}\) = 0
Răspuns
(D)
√2
23
Each of the base angles of a isosceles triangle is 58° and the verticles of the triangle lie on a circle. Determine the angle which the base of the triangle subtends at the centre of the circle.
Răspuns
(A)
128o
24
A chord of a circle of a diameter 42cm subtends an angle of 60o at the centre of the circle. Find the length of the mirror arc
Răspuns
(A)
22cm
25
An arc of a circle subtends an angle 70o at the centre. If the radius of the circle is 6cm, calculate the area of the sector subtended by the given angle.(\(\pi\) = \(\frac{22}{7}\))
Răspuns
(A)
22cm2
26
A cone with a sector angle of 45° is cut out of a circle of radius r cm. Find the base radius of the cone.
Răspuns
(C)
\(\frac{r}{8}\) cm
27
The angle between the positive horizontal axis and a given line is 135o. Find the equation of the line if it passes through the point (2,3)
Răspuns
(C)
x + y = 5
28
A point P moves so that its equidistant from point L and M. If LM is16cm, find the distance of P from LM when P is 10cm from L
Răspuns
(D)
6cm
29
Find the distance between the point Q (4,3) and the point common to the lines 2x - y = 4 and x + y = 2
Răspuns
(D)
√13
30
The angle of elevation of a building from a measuring instrument placed on the ground is 30o. If the building is 40m high, how far is the instrument from the foot of the building?
Răspuns
(D)
40√3m
31
In a triangle XYZ, if < ZYZ is 60, XY = 3cm and YZ = 4cm, calculate the length of the sides XZ.
Răspuns
(B)
√13cm
32
Differentiate \(\frac{6x^3 - 5x^2 + 1}{3x^2}\) with respect to x
Răspuns
(C)
2 - \(\frac{2}{3x^3}\)
33
\(\frac{d}{dx}\) cos(3x\(^2\) - 2x) is equal to
Răspuns
(D)
-(6x - 2)sin(3x2 - 2x)
34
Integrate \(\frac{1}{x}\) + cos x with respect to x
Răspuns
(C)
x - sin x + k
35
If \(y = x(x^4 + x + 1)\), evaluate \(\int \limits_{0} ^{1} y \mathrm d x\).
Răspuns
(B)
1
36
Ages
20
25
30
35
40
45
Number of people
3
5
1
1
2
3
Find the median age of the frequency distribution in the table above.
Răspuns
(B)
25
37
Find the difference between the range and the variance of the following set of numbers 4, 9, 6, 3, 2, 8, 10, 5, 6, 7 where \(\sum d^2\) = 60
Răspuns
(A)
2
38
In a basket of fruits, there are 6 grapes, 11 bananas and 13 oranges, if one fruit is chosen at random, what is the probability that the fruit is either a grape or a banana?
Răspuns
(A)
\(\frac{17}{30}\)
39
A number is selected at random between 10 and 20, both numbers inclusive. Find the probability that the number is an even number
Răspuns
(C)
\(\frac{6}{11}\)
40
Find the standard derivation of the following data -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5
