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