An arc of a circle of radius 7.5cm is 7.5cm long. Find, correct to the nearest degree, the angle which the arc subtends at the centre of the circle. [Take \(\pi = \frac{22}{7}\)]
Answer
(B)
57\(^o\)
14
Water flows out of a pipe at a rate of 40\(\pi cm^2\) per seconds into an empty cylinder container of base radius 4cm. Find the height of water in the container after 4 seconds.
Answer
(A)
10 cm
15
The dimensions of water tank are 13cm, 10cm and 70cm. If it is half-filled with water, calculate the volume of water in litres
Answer
(A)
4.55 litres
16
If the total surface area of a solid hemisphere is equal to its volume, find the radius
Answer
(B)
4.5cm
17
Which of the following is true about parallelogram?
Answer
(C)
opposite angles are equal
18
Calculate the gradient (slope) of the joining points (-1, 1) and (2, -2)
Answer
(A)
-1
19
If P(2,3) and Q)2, 5) are points on a graph, calculate the length PQ
Answer
(D)
2 units
20
A bearing of 320\(^o\) expressed as a compass bearing is
Answer
(B)
N 40\(^o\) W
21
Given that cos 30\(^o\) = sin 60\(^o\) = \(\frac{3}{2}\) and sin 30\(^o\) = cos 60\(^o\) = \(\frac{1}{2}\), evaluate \(\frac{tan 60^o - 1}{1 - tan 30^o}\)
Answer
(C)
\(\sqrt{3}\)
22
The average age of a group of 25 girls is 10year. If one girl, aged 12 years and 4 months joins the group, find the new average age of the group
Answer
(A)
10.1 years
23
In what number base was the addition 1 + nn = 100, where n > 0, done?
Three exterior angles of a polygon are 30\(^o\), 40\(^o\) and 60\(^o\). If the remaining exterior angles are 46\(^o\) each, name the polygon.
Answer
(C)
octagon
26
Simplify the expression \(\frac{a^2 b^4 - b^2 a^4}{ab(a + b)}\)
Answer
(D)
\(ab^2 - a^2b\)
27
Find the 6th term of the sequence \(\frac{2}{3} \frac{7}{15} \frac{4}{15}\),...
Answer
(A)
-\(\frac{1}{3}\)
28
The roots of a quadratic equation are \(\frac{-1}{2}\) and \(\frac{2}{3}\). Find the equation.
Answer
(B)
\(6x^2 - x - 2 = 0\)
29
Make x the subject of the relation d = \(\sqrt{\frac{6}{x} - \frac{y}{2}}\)
Answer
(D)
x = \(\frac{12}{2d^2 + y}\)
30
Consider the statements: p it is hot, q: it is raining
Which of the following symbols correctly represents the statement "It is raining if and only if it it is cold"?
Answer
(D)
q \(\iff\) \(\sim\)p
31
Given that t = \(2 ^{-x}\), find \(2 ^{x + 1}\) in terms of t.
Answer
(A)
\(\frac{2}{t}\)
32
Two bottles are drawn with replacement from a crate containing 8 Coke, 12 Fanta, and 4 Sprite bottles. What is the probability that the first is coke and the second is not coke?
Answer
(C)
\(\frac{2}{9}\)
33
If the simple interest on a certain amount of money saved in a bank for 5 years at 2\(\frac{1}{2}\)% annum is N500.00, calculate the total amount due after 6 years at the same rate
Answer
(D)
N4,600.00
34
Calculate the variance of 2, 3, 3, 4, 5, 5, 5, 7, 7 and 9
Answer
(D)
4.2
35
A circular pond of radius 4m has a path of width 2.5m round it. Find, correct to two decimal places, the area of the path. [Take\(\frac{22}{7}\)]
Answer
(D)
82.50\(m^2\)
36
Fig. 1 and Fig. 2 are the addition and multiplication tables respectively in modulo 5. Use these tables to solve the equation (n \(\oplus 4\))
Answer
(C)
3
37
The diagram shows a circle centre O. if <STR = 29º and < RST = 46º, Calculate the value of <STO.
Answer
(B)
15\(^o\)
38
In the diagram, XY is a straight line. <POX = <POQ and <ROY = <QOR. Find the value of <POQ + <ROY.
Answer
(B)
90\(^o\)
39
The diagram shows a circle O. If < ZYW = 33\(^o\) , find < ZWX
Answer
(B)
57\(^o\)
40
In the diagram, PQ and PS are tangents to the circle O. If PSQ = m, <SPQ = n and <SQR = 33\(^o\), find the value of (m + n)
Answer
(B)
123\(^o\)
41
Marks
0
1
2
3
4
5
Frequency
7
4
18
12
8
11
The table gives the distribution of marks obtained by a number of pupils in a class test. Using this information, Find the median of the distribution
Answer
(B)
3
42
Marks
0
1
2
3
4
5
Frequency
7
4
18
12
8
11
The table gives the distribution of marks obtained by a number of pupils in a class test. Using this information, find the first quartile
Answer
(C)
2.0
43
In a class of 45 students, 28 offer chemistry and 25 offer Biology. If each student offers at least one of the two subjects, calculate the probability that a student selected at random from the class the class offers chemistry only.
Answer
(B)
\(\frac{4}{9}\)
44
In the diagram, NQ//TS, <RTS = 50\(^o\) and <PRT = 100\(^o\). Find the value of <NPR
Answer
(B)
130\(^o\)
45
A stationary boat is observed from a height of 100m. If the horizontal distance between the observer and the boat is 80m, calculate, correct to two decimal places, the angles of depression of the boat from point of observation
