If x is negative, what is the range of values of x within which \(\frac{x + 1}{3}\) > \(\frac{1}{X + 3}\)
Answer
(B)
-4 < x < -3
21
A binary operation \(\ast\) is defined on a set of real numbers by x \(\ast\) y = xy for all real values of x and y. If x \(\ast\) 2 = x. Find the possible values of x
Answer
(A)
0, 1
22
If k + 1; 2k - 1, 3k + 1 are three consecutive terms of a geometric progression, find the possible values of the common ratio
Answer
(B)
-1, \(\frac{5}{3}\)
23
A man's initial salary is N540.00 a month and increases after each period of six months by N36.00 a month. Find his salary in the eighth month of the third year
Answer
(C)
N720.00
24
A rectangular polygon has 150o as the size of each interior angle. How many sides has the polygon?
Answer
(A)
12
25
Calculate the length in cm. of the arc of a circle of diameter 8cm which subtends an angle of 22\(\frac{1}{2}\)o at the centre of the circle
Answer
(D)
\(\frac{\pi}{2}\)
26
The three sides of an isosceles triangle are length of lengths (x + 3), (2x + 3), (2x - 3) respectively. Calculate x.
Answer
(D)
6
27
find the radius of a sphere whose surface area is 154cm2 (\(\pi = \frac{22}{7}\))
Answer
(B)
3.50cm
28
Find the area of the sector of a circle with radius 3m, if the angle of the sector is 60o
Answer
(C)
4.7m2
29
The angle between latitudes 30oS and 13oN is
Answer
(C)
43o
30
If sin \(\theta\) = cos \(\theta\), find \(\theta\) between 0o and 360o
Answer
(A)
45o, 225o
31
If two angles of a triangle are 30° each and the longest side is 10cm. Calculate the length of each of the other sides.
Answer
(D)
\(\frac{10\sqrt{3}}{3}\)cm
32
Quantities in the proportions 1, 4, 6, 7 are to be represented in a pie chart. Calculate the angle of the sector with proportion 7
Answer
(D)
140o
33
The following marks were obtained by twenty students in an examination: 53, 30, 70, 84, 59, 43, 90, 20, 78, 48, 44, 60, 81, 73, 50, 37, 67, 68, 64, 52. Find the numbers of students who scored at least 50 marks
Answer
(D)
14
34
\(\begin{array}{c|c} Weight(s) & 0 -10 & 10 - 20 & 20 - 30 & 40 - 50\\ \hline \text{Number of coconuts} & 10 & 27 & 19 & 6 & 2\end{array}\)
Estimate the mode of the frequency distribution above
Answer
(C)
16.8g
35
The mean of the ages of ten secondary school pupils is 16 but when the age of their teacher is added to it the men becomes 19. Find the age of the teacher
Answer
(D)
49
36
\(\begin{array}{c|c} Class & Frequency\\ \hline 1 - 5 & 2\\6 - 10 & 4\\11 - 15 & 5\\16 - 20 & 2 \\ 21 - 25 & 3\\26 - 30 & 2\\31 - 35 & 1\\36 - 40 & 1 \end{array}\)
Find the median of the observation in the table given
Answer
(D)
14.5
37
A number is selected at random between 20 and 30, both numbers inclusive. Find the probability that the number is a prime
Answer
(A)
\(\frac{2}{11}\)
38
Calculate the standard deviation of the following data: 7, 8, 9, 10, 11, 12, 13.
Answer
(A)
2
39
The chances of three independent events X, Y, Z occurring are \(\frac{1}{2}\), \(\frac{2}{3}\), \(\frac{1}{4}\) respectively. What are the chances of Y and Z only occurring?
Answer
(C)
\(\frac{1}{12}\)
40
The shaded portion in the venn diagram is
Answer
(C)
x \(\cap\) yo \(\cap\) z
41
The figure represents the graphs of y = x(2 - x) and y = (x - 1)(x - 3). What are the x-coordinates of P, Q and F respectively?
Answer
(D)
1, 2, 3
42
PQRST is a regular pentagon and PQVU is a rectangle with U and V lying on TS and SR respectively as shown in the diagram. Calculate TUP
Answer
(B)
54o
43
In the diagram, PQRS is a circle with O as centre and PQ||RT. If RTS = 32°. Find PSQ
Answer
(C)
58o
44
In the diagram, O is the centre of the circle and POQ a diameter. If POR = 96o, find the value of ORQ.
Answer
(B)
48o
45
In the diagram, QP//ST:PQR = 34o qrs = 73o and Rs = RT. Find SRT
Answer
(B)
102o
46
In the figure, PT is tangent to the circle at U and QU/RS if TUR = 35º and SRU = 50º find x
Answer
(A)
95o
47
In the diagram, QPS = SPR, PR = 9cm. PQ = 4cm and QS = 3cm, find SR.
Answer
(A)
6\(\frac{3}{4}\)cm
48
In the figure, the line segment ST is tangent to two circles at S and T. O and Q are the centres of the circles wih OS = 5cm. QT = 2cm and OR = 14cm. Find ST
Answer
(B)
12.9cm
49
In the figure, the area of the square of the square PQRS is 100cm2. If the ratio of the area of the square TUYS to the area of the area of the square XQVU is 1 : 16, Find YR
