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