Find the coordinates of the midpoint of line PQ given P(-3, 4) and Q(5, 6).
إجابة
(D)
(1, 5)
8
Given that Cos A = \(\frac{12}{13}\) for 0 ≤ A ≤ 90º, find Tan A.
إجابة
(A)
\(\frac{5}{12}\)
9
Which of the following angles cannot be constructed using a protractor, a compass, and a sharpened pencil?
إجابة
(C)
145°
10
Find the number of permutations of the letters of the word SCHOOL.
إجابة
(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.
إجابة
(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.
إجابة
(C)
1070kg
13
Find the sum of the entries in the inverse of \(\begin{bmatrix} 1 & 2 \\ 3 & 5 \end{bmatrix}\)
إجابة
(B)
-1
14
A varies directly as b\(^2\) when A = 4, b = 1. Find A when b = 2
إجابة
(C)
16
15
If I is a 2 × 2 identity matrix, find the determinant of the matrix.
إجابة
(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.
إجابة
(C)
3
17
The mean of the numbers 0, x + 2, 3x + 6, and 4x + 8 is 4, find the value of x.
إجابة
(C)
0
18
Obtain the equation of a straight line passing through (3, 15) whose slope = 3\(\frac{1}{5}\).
إجابة
(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?
إجابة
(A)
\(\frac{17}{30}\)
22
Calculate the interior angle of a 5 - sided regular polygon
إجابة
(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
إجابة
(B)
\(\frac{8}{15}\)
24
Find the probability of getting an even number in a single throw of a six-sided die.
إجابة
(C)
\(\frac{1}{2}\)
25
Integrate y = 4x\(^3\) + 2x + cos x.
إجابة
(B)
x\(^4\) + x\(^2\) + sin x + C
26
Simplify - log\(_{10}\) 0.00001.
إجابة
(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.
إجابة
(C)
8cm
28
Find the limit of y = \(\frac{(x^3 - 2x^2 + 6x - 12)}{(x - 2)}\) as x goes to 2.
إجابة
(B)
10
29
The second and fifth terms of a G.P are 1 and \(\frac{1}{8}\) respectively. Find the common ratio
إجابة
(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
إجابة
(B)
# 500,000
31
Given the progression 3, 5, 7, 9,.... . . . find an expression for the (n - 2)\(^{th}\) term of the progression.
إجابة
(D)
\(2n - 3\)
32
Find the derivatives of y = sin 4x
إجابة
(D)
4cos4x
33
If A = \(\frac{\theta}{360}\)\(\pi r^2\), make \(\theta\) the subject of the formula
إجابة
(C)
\( \theta = \frac{360A}{\pi r^2} \)
34
What is the minimum value of y = 2 - 4x - 2x\(^2\)
إجابة
(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
إجابة
(B)
pq
36
Given the construction in the figure above. What is X\(\hat{Y}\)Z
إجابة
(A)
60º
37
Convert 137 to base 5
إجابة
(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
إجابة
(A)
68
39
The word HANDIER can be arranged in how many ways
إجابة
(D)
5040
40
From the table above, estimate the mode of the distribution.
إجابة
(D)
34.5
41
Find the value of t for which (\(\frac{1}{2}\))\(^{t - 1}\) = 64
إجابة
(B)
-5
42
If 54\(_{ten}\) = X\(_{four}\), find the value of X to 3 decimal point
إجابة
(B)
312\(_{four}\)
43
Integrate the function y = 3x\(^2\) + 2x - 5 with respect to x.
إجابة
(A)
x\(^3\) + x\(^2\) - 5x + C
44
Express \(\sqrt[4]{0.16}\) in standard form
إجابة
(A)
2 \(\times 10^{-\frac{1}{2}}\)
45
Solve x\(^2\) + 3x - 4 ≤ 0
إجابة
(D)
\(- 4 \leq x \leq 1\)
46
Solve for y in \(\sqrt{75}\) - \(\sqrt{12}\) + \(\sqrt{27}\) = y\(\sqrt{3}\)
إجابة
(D)
\(6\sqrt{3}\)
47
If cos \(\theta\) = \(\frac{\text{x}}{\text{y}}\), find tan \(\theta\) in terms of x and y
إجابة
(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
