If {X: 2 d- x d- 19; X integer} and 7 + x = 4 (mod 9), find the highest value of x
Answer
(C)
15
2
The sum 11011\(_2\), 11111\(_2\) and 10000\(_2\) is 10m10n0\(_2\). Find the value of m and n.
Answer
(C)
m = 0, n = 1
3
A trader bought an engine for $15,000.00 outside Nigeria. If the exchange rate is $0.075 to N1.00, how much did the engine cost in Naira?
Answer
(B)
N200,000.00
4
If \(\frac{27^x \times 3^{1 - x}}{9^{2x}} = 1\), find the value of x.
Answer
(B)
\(\frac{1}{2}\)
5
Find the 7th term of the sequence: 2, 5, 10, 17, 26,...
Answer
(C)
50
6
Given that logx 64 = 3, evaluate x log\(_2\)8
Answer
(C)
12
7
If 2n = y, Find 2\(^{(2 + \frac{n}{3})}\)
Answer
(A)
4y\(^\frac{1}{3}\)
8
Factorize completely: 6ax - 12by - 9ay + 8bx
Answer
(B)
(3a + 4b)(2x - 3y)
9
Find the equation whose roots are \(\frac{3}{4}\) and -4
Answer
(C)
4x2 + 13x - 12 = 0
10
If m = 4, n = 9 and r = 16., evaluate \(\frac{m}{n}\) - 1\(\frac{7}{9}\) + \(\frac{n}{r}\)
Answer
(D)
- \(\frac{37}{48}\)
11
Adding 42 to a given positive number gives the same result as squaring the number. Find the number
Answer
(C)
7
12
Ada draws the graph of y = x2 - x - 2 and y = 2x - 1 on the same axes. Which of these equations is she solving?
Answer
(B)
x2 - 3x - 1 = 0
13
The volume of a cone of height 3cm is 38\(\frac{1}{2}\)cm3. Find the radius of its base. [Take \(\pi = \frac{22}{7}\)]
Answer
(B)
3.5cm
14
The dimension of a rectangular tank are 2m by 7m by 11m. If its volume is equal to that of a cylindrical tank of height 4cm, calculate the base radius of the cylindrical tank. [Take \(\pi = \frac{22}{7}\)]
Answer
(C)
3\(\frac{1}{2}\)m
15
In the diagram, O is the centre. If PQ//RS and ∠ONS = 140°, find the size of ∠POM.
Answer
(A)
40o
16
In the diagram, PTR is a tangent to the centre O. If angles TON = 108°, Calculate the size of angle PTN
Answer
(B)
126o
17
In the diagram, PQ//RT, QR//Su,
Answer
(B)
132o
18
In the diagram, O is the centre, \(\bar{RT}\) is a diameter, < PQT = 33\(^o\) and <TOS = 76\(^o\). Using the diagram, calculate the value of angle PTR.
Answer
(C)
57o
19
In the diagram, O is the centre, \(\bar{RT}\) is a diameter, < PQT = 33\(^o\) and < TOS = 76\(^o\). Using the diagram, find the size of angle PRS.
Answer
(B)
71o
20
\(\begin{array}{c|c}
x & 0 & 1\frac{1}{4} & 2 & 4\\
\hline
y & 3 & 5\frac{1}{2} & &
\end{array}\)
The table given shows some values for a linear graph. Find the gradient of the line
Answer
(B)
2
21
PQRS is square. If x is the midpoint of PQ, Calculate correct to the nearest degree, <SPX
Answer
(C)
63o
22
The angle of elevation of an aircraft from a point K on the horizontal ground 30\(\alpha\). If the aircraft is 800m above the ground, how far is it from K?
Answer
(D)
1,600.00m
23
The population of students in a school is 810. If this is represented on a pie chart, calculate the sectoral angle for a class of 72 students
Answer
(A)
32o
24
The scores of twenty students in a test are as follows: 44, 47, 48, 49, 50, 51, 52, 53, 53, 54, 58, 59, 60, 61, 63, 65, 67, 70, 73, 75. Find the third quartile.
Answer
(C)
64
25
Score
0 - 4
5 - 9
10 - 14
Frequency
2
1
2
The table shows the distribution of the scores of some students in a test. Calculate the mean scores.
Answer
(D)
7.0
26
The probability that kebba, Ebou and Omar will hit a target are \(\frac{2}{3}\), \(\frac{3}{4}\) and \(\frac{4}{5}\) respectively. Find the probability that only Kebba will hit the target.
Answer
(C)
\(\frac{1}{30}\)
27
In the diagram, VW//YZ, |WX| = 6cm, |XY| = 16cm, |YZ| = 20cm and |ZX| = 12cm. Calculate |VX|
Answer
(D)
8cm
28
Tom will be 25 years old in n years' time. If he is 5 years younger than Bade, find Bade's present age.
Answer
(A)
(30 - n)years
29
If \(\frac{\sqrt{2} + \sqrt{3}}{\sqrt{3}}\) is simplified as m + n\(\sqrt{6}\), find the value of (m + n)
Answer
(C)
1\(\frac{1}{3}\)
30
In the given diagram, \(\bar{QT}\) and \(\bar{PR}\) are straight lines, < ROS = (3n - 20), < SOT = n, < POL = m and < QOL is a right angle. Find the value of n.
Answer
(A)
35o
31
Make K the subject of the relation T = \(\sqrt{\frac{TK - H}{K - H}}\)
Answer
(A)
K = \(\frac{H(T^2 - 1)}{T^2 - T}\)
32
Which of the following is used to determine the mode of a grouped data?
Answer
(D)
Histogram
33
The area of a rhombus is 110 cm\(^2\). If the diagonals are 20 cm and (2x + 1) cm long, find the value of x.
A farmer uses \(\frac{2}{5}\) of his land to grow cassava, \(\frac{1}{3}\) of the remaining for yam and the rest for maize. Find the part of the land used for maize
Answer
(B)
\(\frac{2}{5}\)
36
The rate of consumption of petrol by a vehicle varies directly as the square of the distance covered. If 4 litres of petrol is consumed on a distance of 15km. how far would the vehicle go on 9 litres of petrol?
Answer
(A)
22\(\frac{1}{2}\)km
37
A trader bought 100 oranges at 5 for N40.00 and sold them at 20 for N120.00. Find the profit or loss percent
Answer
(D)
25% loss
38
Describe the shaded portion in the diagram
Answer
(A)
P' \(\cap\) Q \(\cap\) R'
39
Find the value of p if \(\frac{1}{4}\)p + 3q = 10 and 2p - q = 7
