Make m the subject of the relation k = \(\sqrt{\frac{m - y}{m + 1}}\)
Answer
(B)
m = \(\frac{y + k^2}{1 - k^2}\)
14
Find the quadratic equation whose roots are \(\frac{1}{2}\) and -\(\frac{1}{3}\)
Answer
(D)
6x\(^2\) - x - 1 = 0
15
Given that x is directly proportional to y and inversely proportional to Z, x = 15 when y = 10 and Z = 4, find the equation connecting x, y and z
Answer
(A)
x = \(\frac{6y}{z}\)
16
Two buses start from the same station at 9.00am and travel in opposite directions along the same straight road. The first bus travel at a speed of 72 km/h and the second at 48 km/h. At what time will they be 240km apart?
Answer
(C)
11:00 am
17
A solid cuboid has a length of 7 cm, a width of 5 cm, and a height of 4 cm. Calculate its total surface area.
Answer
(B)
166 cm\(^2\)
18
In the diagram, PQ // SR. Find the value of x
Answer
(B)
46
19
Find the equation of the line parallel to 2y = 3(x - 2) and passes through the point (2, 3)
Answer
(C)
y = \(\frac{3}{2} x\)
20
The expression \(\frac{5x + 3}{6x (x + 1)}\) will be undefined when x equals
Answer
(B)
{0, -1}
21
A man is five times as old as his son. In four years' time, the product of their ages would be 340. If the son's age is y, express the product of their ages in terms of y.
In the diagram, XYZ is an equilateral triangle of side 6cm and Y is the midpoint of \(\overline{XY}\). Find tan (< XZT)
Answer
(A)
\(\frac{1}{\sqrt{3}}\)
24
A fence 2.4 m tall, is 10m away from a tree of height 16m. Calculate the angle of elevation of the top of the tree from the top of the fence.
Answer
(B)
53.67\(^o\)
25
Fati buys milk at ₦x per tin sells each at a profit of ₦y. If she sells 10 tins of milk, how much does she receives from the sales?
Answer
(D)
₦10(x + y)
26
If tan y is positive and sin y is negative, in which quadrant would y lie?
Answer
(C)
Third only
27
The dimension of a rectangular base of a right pyramid is 9 cm by 5cm. If the volume of the pyramid is 105 cm\(^3\), how high is the pyramid?
Answer
(D)
7cm
28
Each interior angle of a regular polygon is 168\(^o\). Find the number of sides of the polygon
Answer
(A)
30
29
In the diagram, \(\overline{MN}\)//\(\overline{PQ}\), < MNP = 2x, and < NPQ = (3x - 50)°. Find the value of < NPQ
Answer
(B)
100\(^o\)
30
The length of an arc of a circle of radius 3.5 cm is 1\(\frac{19}{36}\) cm. Calculate, correct to the nearest degree , the angle substended by the centre of the circle. [Take \(\pi = \frac{22}{7}\)]
Answer
(C)
25\(^o\)
31
In the diagram, \(\overline{PU}\)/\(\overline{SR}\), \(\overline{PS}\)/\(\overline{TR}\), \(\overline{QS}\)/\(\overline{UR}\), \(\overline{UR}\) = 15cm, \(\overline{SR}\) = 8 cm, \(\overline{PS}\) = 10 cm and area of △SUR = 24 cm\(^2\). Calculate the area of PTRS.
Answer
(C)
80 cm\(^2\)
32
In the diagram, PQR is a circle with center O. If ∠OPQ = 48°, find the value of M.
Answer
(A)
96\(^o\)
33
The pie chart shows the population of men, women, and children in a city. If the population of the city is 1,800,000, how many men are in the city?
Answer
(C)
355,000
34
The mean of the numbers 15, 21, 17, 26, 18, and 29 is 21. Calculate the standard deviation
Answer
(C)
5
35
Find the sum of the interior angle of a pentagon.
Answer
(C)
540\(^o\)
36
The diameter of a sphere is 12 cm. Calculate, correct of the nearest cm\(^3\), the volume of the sphere, [Take \(\pi = \frac{22}{7}\)]
Answer
(C)
905 cm\(^3\)
37
A box contains 12 identical balls of which 5 are red, 4 blue, and the rest are green. If a ball is selected at random from the box, what is the probability that it is green?
Answer
(D)
\(\frac{1}{4}\)
38
A box contains 12 identical balls of which 5 are red, 4 blue, and the rest are green. If two balls are selected at random one after the other with replacement, what is the probability that both are red?
Answer
(A)
\(\frac{25}{144}\)
39
In the diagram, PQ is a straight line. If m = \(\frac{1}{2}\) (x + y + z), find value of m.
Answer
(B)
60\(^o\)
40
x
6.20
6.85
7.50
y
3.90
5.20
6.50
The points on a linear graph are as shown in the table. Find the gradient (slope) of the line.
Answer
(B)
2
41
In the diagram, O is the center of the circle. \(\overline{PQ}\) and \(\overline{RS}\) are tangents to the circle. Find the value of (M + N).
Answer
(B)
90\(^o\)
42
Which of the following is not a sufficient condition for two triangles to be congruent?
Answer
(D)
SSA
43
A woman received a discount of 20% on a piece of cloth she purchased from a shop. If she paid $525.00, what was the original price?
Answer
(C)
$656.25
44
The interquartile range of distribution is 7. If the 25th percentile is 16, find the upper quartile.
Answer
(C)
23
45
The graph of the equations y = 2x + 5 and y = 2x\(^2\) + x - 1 are shown. Use the information above to answer this question.
