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