1993 - JAMB Mathematics Past Questions and Answers - page 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
A
0, 1
B
1, 2
C
2, 2
D
0, 2
correct option: a
x \(\ast\) y = xy
x \(\ast\) 2 = x2
x \(\ast\) 2 = x
∴ x2 - x = 0
x(x - 1) = 0
x = 0 or 1
Users' Answers & Commentsx \(\ast\) 2 = x2
x \(\ast\) 2 = x
∴ x2 - x = 0
x(x - 1) = 0
x = 0 or 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
A
0, 8
B
-1, \(\frac{5}{3}\)
C
2, 3
D
1, -1
correct option: b
Users' Answers & Comments23
A man's initial salary is N540.00 a month and increases after each period of six months by N36.oo a month. Find his salary in the eighth month of the third year
A
N828.00
B
N756.00
C
N720.00
D
N684.00
correct option: c
Initial salary = N540
increment = N36 (every 6 months)
Period of increment = 2 yrs and 6 months
amount(increment) = N36 x 5 = N180
The man's new salary = N540 = N180
= N720.00
Users' Answers & Commentsincrement = N36 (every 6 months)
Period of increment = 2 yrs and 6 months
amount(increment) = N36 x 5 = N180
The man's new salary = N540 = N180
= N720.00
24
A rectangular polygon has 150o as the size of each interior angle. How many sides has the polygon?
A
12
B
10
C
9
D
8
correct option: a
A rectangular polygon has each interior angle to be 150o
let the polygon has n-sides
therefore, Total interior angle 150 x n = 150n
hence 150n = (2n - 4)90
150n = 180n - 360
360 = (180 - 150)n
30n = 360
n = 12
Users' Answers & Commentslet the polygon has n-sides
therefore, Total interior angle 150 x n = 150n
hence 150n = (2n - 4)90
150n = 180n - 360
360 = (180 - 150)n
30n = 360
n = 12
25
Calculate the length in cm. of the area of a circle of diameter 8cm which subtends an angle of 22\(\frac{1}{2}\)o at the centre of the circle
A
2\(\pi\)
B
\(\pi\)
C
\(\frac{2}{3}\)
D
\(\frac{\pi}{2}\)
correct option: d
Diameter = 8cm
∴ Radius = 4cm
Length of arc = \(\frac{\theta}{360}\) x 2 \(\pi\)r but Q = 22\(\frac{1}{2}\)
∴ Length \(\frac{22\frac{1}{2}}{360}\) x 2 x \(\pi\) x 4
= \(\frac{22\frac{1}{2} \times 8\pi}{360}\)
= \(\frac{180}{360}\)
= \(\frac{\pi}{2}\)
Users' Answers & Comments∴ Radius = 4cm
Length of arc = \(\frac{\theta}{360}\) x 2 \(\pi\)r but Q = 22\(\frac{1}{2}\)
∴ Length \(\frac{22\frac{1}{2}}{360}\) x 2 x \(\pi\) x 4
= \(\frac{22\frac{1}{2} \times 8\pi}{360}\)
= \(\frac{180}{360}\)
= \(\frac{\pi}{2}\)
26
The three sides of an isosceles triangle are length of lengths (x + 3), (2x + 3), (2x - 3) respectively. Calculate x.
A
5
B
1
C
3
D
6
correct option: d
2x + 3 \(\neq\) 2x - 3 for any value of x
∴ for the \(\bigtriangleup\) to be isosceles, either
2x - 3 = x + 3 or 2x + 3 = x + 3
solve the two equations we arrive at
x = 6 or x = 0
When x = 6, the sides are 9, 15, 9
When x = 0, the sides are 3, 4, -3 since lengths of a \(\bigtriangleup\)can never be negative then the value of x = 6
Users' Answers & Comments∴ for the \(\bigtriangleup\) to be isosceles, either
2x - 3 = x + 3 or 2x + 3 = x + 3
solve the two equations we arrive at
x = 6 or x = 0
When x = 6, the sides are 9, 15, 9
When x = 0, the sides are 3, 4, -3 since lengths of a \(\bigtriangleup\)can never be negative then the value of x = 6
27
find the radius of a sphere whose surface area is 154cm2 (\(\pi = \frac{22}{7}\))
A
7.00cm
B
3.50cm
C
3.00cm
D
1.75cm
correct option: b
Surface area = 154cm2 (area of sphere)
4\(\pi\)r2 = 154
r\(\sqrt{\frac{154}{4\pi}}\)
= 3.50cm
Users' Answers & Comments4\(\pi\)r2 = 154
r\(\sqrt{\frac{154}{4\pi}}\)
= 3.50cm
28
Find the area of the sector of a circle with radius 3m, if the angle of the sector is 60o
A
4.0m2
B
1m2
C
4.7m2
D
5.0m2
correct option: c
Area of sector
\(\frac{\theta}{360}\) x \(\pi\)r2, \(\theta\) = 60o, r = 3m
= \(\frac{60}{360}\) x \(\frac{12}{7}\) x 3 x 3
\(\frac{1}{6}\) x \(\frac{22}{7}\) x 9
= \(\frac{33}{7}\)
= 4.7m2
Users' Answers & Comments\(\frac{\theta}{360}\) x \(\pi\)r2, \(\theta\) = 60o, r = 3m
= \(\frac{60}{360}\) x \(\frac{12}{7}\) x 3 x 3
\(\frac{1}{6}\) x \(\frac{22}{7}\) x 9
= \(\frac{33}{7}\)
= 4.7m2
29
The angle between latitudes 30oS and 13oN is
A
17o
B
33o
C
43o
D
53o
correct option: c
The angle between 2 latitudes one in northern hemisphere and the other in southern hemisphere and the other in southern hemisphere is the sum of their latitudes.
∴ Total angle difference = (30 + 13) = 43o
Users' Answers & Comments∴ Total angle difference = (30 + 13) = 43o
30
If sin \(\theta\) = cos \(\theta\), find \(\theta\) between 0o and 360o
A
45o, 225o
B
135o, 315o
C
45o, 315o
D
135o, 225o
correct option: c
sin \(\theta\) = cos \(\theta\) 0 \(\leq\) \(\theta\) \(\leq\) 360o
The acute angle where sin \(\theta\) = cos \(\theta\) = 45o
But at the fourth Quadrant Cos \(\theta\) = +ve
at the 4th quadrant, value with respect to Q is
(360 - Q) where Q = acute angle
(360 - 45) = 315o
The two solution are 45o, 315o
Users' Answers & CommentsThe acute angle where sin \(\theta\) = cos \(\theta\) = 45o
But at the fourth Quadrant Cos \(\theta\) = +ve
at the 4th quadrant, value with respect to Q is
(360 - Q) where Q = acute angle
(360 - 45) = 315o
The two solution are 45o, 315o