1990 - JAMB Mathematics Past Questions and Answers - page 2
11
Simplify (\(\frac{1}{x^{-1}} + \frac{1}{y^{-1}}\))-1
A
\(\frac{x}{y}\)
B
xy
C
\(\frac{x}{y}\)
D
(xy)-1
correct option: c
Simplify (\(\frac{1}{x^{-1}} + \frac{1}{y^{-1}}\))-1 = (\(\frac{1}{x^{-1}} + \frac{1}{y^{-1}}\))-1
= (x + y)-1 = \(\frac{(x)}{y}\)
= \(\frac{x}{y}\)
Users' Answers & Comments= (x + y)-1 = \(\frac{(x)}{y}\)
= \(\frac{x}{y}\)
12
If a = 2, b = -2 and c = -\(\frac{1}{2}\), evaluate (ab2 - bc2)(a2c - abc)
A
2
B
-28
C
-30
D
-34
correct option: d
(ab2 - bc2)(a2c - abc)
[2(2)2 - (- 2x\(\frac{1}{2}\))] [22(-\(\frac{1}{2}\)) - 2(-2)(-\(\frac{1}{2}\))]
[8 = \(\frac{1}{2}\)][-2 - 2] = \(\frac{17}{2}\) x 42
= -34
Users' Answers & Comments[2(2)2 - (- 2x\(\frac{1}{2}\))] [22(-\(\frac{1}{2}\)) - 2(-2)(-\(\frac{1}{2}\))]
[8 = \(\frac{1}{2}\)][-2 - 2] = \(\frac{17}{2}\) x 42
= -34
13
If f(x - 4) = x2 + 2x + 3, Find, f(2)
A
6
B
11
C
27
D
51
correct option: d
f(x - 4) = x2 + 2x + 3
To find f(2) = f(x - 4)
= f(2)
x - 4 = 2
x = 6
f(2) = 62 + 2(6) + 3
= 36 + 12 + 3
= 51
Users' Answers & CommentsTo find f(2) = f(x - 4)
= f(2)
x - 4 = 2
x = 6
f(2) = 62 + 2(6) + 3
= 36 + 12 + 3
= 51
14
Factorize 9(x + y)2 - 4(x - y)2
A
(x + y)(5x + y)
B
(x + y)2
C
(x + 5y)(5x + y)
D
5(x + y)2
correct option: c
9(x + y)2 - 4(x - y)2
Using difference of two squares which says
a2 - b2 = (a + b)(a - b) = 9(x + y)2 - 4(x - y)2
= [3(x + y)]2 - [2(x - y)]-2
= [3(x + y) + 2(x - y) + 2(x - y)][3(x + y) - 2(x - y)]
= [3x +3y + 2x - 2y][3x + 3y - 2x + 2y]
= (5x + y)(x + 5y)
Users' Answers & CommentsUsing difference of two squares which says
a2 - b2 = (a + b)(a - b) = 9(x + y)2 - 4(x - y)2
= [3(x + y)]2 - [2(x - y)]-2
= [3(x + y) + 2(x - y) + 2(x - y)][3(x + y) - 2(x - y)]
= [3x +3y + 2x - 2y][3x + 3y - 2x + 2y]
= (5x + y)(x + 5y)
15
If a2 + b2 = 16 and 2ab = 7.Find all the possible values of (a - b)
A
3, -3
B
2, -2
C
1, -1
D
3, -1
correct option: a
a2 + b2 = 16 and 2ab = 7
To find all possible values = (a - b)2 + b2 - 2ab
Substituting the given values = (a - b)2
= 16 - 7
= 9
(a - b) = \(\pm\)9
= \(\pm\)3
OR a - b = 3, -3
Users' Answers & CommentsTo find all possible values = (a - b)2 + b2 - 2ab
Substituting the given values = (a - b)2
= 16 - 7
= 9
(a - b) = \(\pm\)9
= \(\pm\)3
OR a - b = 3, -3
16
Divide x3 - 2x2 - 5x + 6 by (x - 1)
A
x2 - x - 6
B
x2 - 5x + 6
C
x2 - 7x + 6
D
x2 - 5x - 6
correct option: a
Users' Answers & Comments17
If x + \(\frac{1}{x}\) = 4, find x2 + \(\frac{1}{x^2}\)
A
16
B
14
C
12
D
9
correct option: b
x + \(\frac{1}{x}\) = 4, find x2 + \(\frac{1}{x^2}\)
= (x + \(\frac{1}{x}\))2 = x2 + \(\frac{1}{x^2}\) + 2
x2 + \(\frac{1}{x^2}\) = ( x + \(\frac{1}{x^2}\))2 - 2
= (4)2 - 2
= 16 - 2
= 14
Users' Answers & Comments= (x + \(\frac{1}{x}\))2 = x2 + \(\frac{1}{x^2}\) + 2
x2 + \(\frac{1}{x^2}\) = ( x + \(\frac{1}{x^2}\))2 - 2
= (4)2 - 2
= 16 - 2
= 14
18
What must be added to 4x2 - 4 to make it a perfect square?
A
\(\frac{-1}{x^2}\)
B
\(\frac{1}{x^2}\)
C
1
D
-1
correct option: b
(2x \(\frac{-1}{4}\)2 = 4x2 + \(\frac{1}{x^2}\) - 4
what must be added is +\(\frac{1}{x^2}\)
Users' Answers & Commentswhat must be added is +\(\frac{1}{x^2}\)
19
Find the solution of the equation x - 8\(\sqrt{x}\) + 15 = 0
A
3, 5
B
-3, -5
C
9, 25
D
-9, 25
correct option: c
x - 8\(\sqrt{x}\) + 15 = 0
x + 15 = 8\(\sqrt{x}\)
square both sides = (x + 15)2 = (8 \(\sqrt{x}\)2
x2 + 225 + 30x = 64x
x2 + 225 + 30x - 64x = 0
x2 - 34x + 225 = 0
(x - 9)(x - 25) = 0
x = 9 or 25
Users' Answers & Commentsx + 15 = 8\(\sqrt{x}\)
square both sides = (x + 15)2 = (8 \(\sqrt{x}\)2
x2 + 225 + 30x = 64x
x2 + 225 + 30x - 64x = 0
x2 - 34x + 225 = 0
(x - 9)(x - 25) = 0
x = 9 or 25
20
The perimeter of a rectangular lawn is 24m. If the area of the lawn is 35m2; how wide is the lawn?
A
5cm
B
7m
C
12m
D
14m
correct option: a
Users' Answers & Comments