Find the coordinates of the midpoint of line PQ given P(-3, 4) and Q(5, 6).
Відповідь
(D)
(1, 5)
8
Given that Cos A = \(\frac{12}{13}\) for 0 ≤ A ≤ 90º, find Tan A.
Відповідь
(A)
\(\frac{5}{12}\)
9
Which of the following angles cannot be constructed using a protractor, a compass, and a sharpened pencil?
Відповідь
(C)
145°
10
Find the number of permutations of the letters of the word SCHOOL.
Відповідь
(B)
360
11
Y is partly constant and partly varies as x. When x = 3, y = 7 and when x = 5, y = 11. Find the constants of variation.
Відповідь
(B)
1,2
12
The average weight of 15 iron bars is 1000 kg. If the heaviest iron bar is removed, the average weight is reduced by 5 kg. Find the weight in kg of the heaviest iron bar.
Відповідь
(C)
1070kg
13
Find the sum of the entries in the inverse of \(\begin{bmatrix} 1 & 2 \\ 3 & 5 \end{bmatrix}\)
Відповідь
(B)
-1
14
A varies directly as b\(^2\) when A = 4, b = 1. Find A when b = 2
Відповідь
(C)
16
15
If I is a 2 × 2 identity matrix, find the determinant of the matrix.
Відповідь
(A)
1
16
The determinant of the matrix \(A = \begin{pmatrix} -2 & 3 & 1 \\ p & 2 & 1 \\ 1 & 4 & 2\end{pmatrix}\) is -5. Find the value of p.
Відповідь
(C)
3
17
The mean of the numbers 0, x + 2, 3x + 6, and 4x + 8 is 4, find the value of x.
Відповідь
(C)
0
18
Obtain the equation of a straight line passing through (3, 15) whose slope = 3\(\frac{1}{5}\).
Відповідь
(C)
5y - 16x - 27 = 0
19
A car dealer bought a used car for ₦270,000 and spent ₦70,000 to refurbish it. He later sold the car for ₦490,000. What was the percentage profit?
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?
Відповідь
(A)
\(\frac{17}{30}\)
22
Calculate the interior angle of a 5 - sided regular polygon
Відповідь
(C)
108º
23
A banker spent \(\frac{1}{5}\) of his salary on shirts, \(\frac{1}{3}\) of the remainder on transport, and kept the rest for contingencies. What fraction was left
Відповідь
(B)
\(\frac{8}{15}\)
24
Find the probability of getting an even number in a single throw of a six-sided die.
Відповідь
(C)
\(\frac{1}{2}\)
25
Integrate y = 4x\(^3\) + 2x + cos x.
Відповідь
(B)
x\(^4\) + x\(^2\) + sin x + C
26
Simplify - log\(_{10}\) 0.00001.
Відповідь
(C)
5
27
The chord of a circle of radius 17 cm is 30 cm long. Calculate the distance of the chord from the centre of the circle.
Відповідь
(C)
8cm
28
Find the limit of y = \(\frac{(x^3 - 2x^2 + 6x - 12)}{(x - 2)}\) as x goes to 2.
Відповідь
(B)
10
29
The second and fifth terms of a G.P are 1 and \(\frac{1}{8}\) respectively. Find the common ratio
Відповідь
(C)
\(\frac{1}{2}\)
30
An amount of # 600,000.00 was realized when a principal y was saved for 5% simple interest for 4 years, find the value of y
Відповідь
(B)
# 500,000
31
Given the progression 3, 5, 7, 9,.... . . . find an expression for the (n - 2)\(^{th}\) term of the progression.
Відповідь
(D)
\(2n - 3\)
32
Find the derivatives of y = sin 4x
Відповідь
(D)
4cos4x
33
If A = \(\frac{\theta}{360}\)\(\pi r^2\), make \(\theta\) the subject of the formula
Відповідь
(C)
\( \theta = \frac{360A}{\pi r^2} \)
34
What is the minimum value of y = 2 - 4x - 2x\(^2\)
Відповідь
(A)
4
35
If the probability of death is q and the probability of survival is p, find the probability of one death and one survival in an accident involving two persons
Відповідь
(B)
pq
36
Given the construction in the figure above. What is X\(\hat{Y}\)Z
Відповідь
(A)
60º
37
Convert 137 to base 5
Відповідь
(A)
\( 1022_5 \)
38
P is partly constant and varies partly as Q. If P = 32 when Q = 16 and P = 20 when Q = 12, find P when Q = 28
Відповідь
(A)
68
39
The word HANDIER can be arranged in how many ways
Відповідь
(D)
5040
40
From the table above, estimate the mode of the distribution.
Відповідь
(D)
34.5
41
Find the value of t for which (\(\frac{1}{2}\))\(^{t - 1}\) = 64
Відповідь
(B)
-5
42
If 54\(_{ten}\) = X\(_{four}\), find the value of X to 3 decimal point
Відповідь
(B)
312\(_{four}\)
43
Integrate the function y = 3x\(^2\) + 2x - 5 with respect to x.
Відповідь
(A)
x\(^3\) + x\(^2\) - 5x + C
44
Express \(\sqrt[4]{0.16}\) in standard form
Відповідь
(A)
2 \(\times 10^{-\frac{1}{2}}\)
45
Solve x\(^2\) + 3x - 4 ≤ 0
Відповідь
(D)
\(- 4 \leq x \leq 1\)
46
Solve for y in \(\sqrt{75}\) - \(\sqrt{12}\) + \(\sqrt{27}\) = y\(\sqrt{3}\)
Відповідь
(D)
\(6\sqrt{3}\)
47
If cos \(\theta\) = \(\frac{\text{x}}{\text{y}}\), find tan \(\theta\) in terms of x and y
Відповідь
(A)
\(\frac{\sqrt{y^2 - x^2}}{x}\)
48
Given that \(P = \begin{pmatrix} 1 & 3 \\ 2 & -5 \end{pmatrix}\) and Q = \(\begin{pmatrix} 3 & -7 \\ 1 & 2 \end{pmatrix}\) . Find P + 2Q
