1991 - JAMB Mathematics Past Questions and Answers - page 3
21
If g(x) = x2 + 3x + 4, find g(x + 1) - g(x)
A
(x + 2)
B
2(x + 2)
C
(2x + 1)
D
(x2 + 4)
correct option: b
g(x) = x2 + 3x + 4
= g(x + 1) = (x + 1)^2 + 3(x + 1) + 4
= x2 + 1 + 2x + 3x + 3 + 4
= x2 + 5x + 8
g(x + 1) - g(x) = x2 + 5x + 8 - (x2 + 3x + 4)
= x2 + 5x + 8 - x2 + 3x + 4
= 2x + 4
= 2(x + 2)
Users' Answers & Comments= g(x + 1) = (x + 1)^2 + 3(x + 1) + 4
= x2 + 1 + 2x + 3x + 3 + 4
= x2 + 5x + 8
g(x + 1) - g(x) = x2 + 5x + 8 - (x2 + 3x + 4)
= x2 + 5x + 8 - x2 + 3x + 4
= 2x + 4
= 2(x + 2)
22
Factorize m3 - 2m2 - m + 2
A
(m2 + 1)(m - 2)
B
(m - 1)(m + 1)(m + 2)
C
(m - 2)(m + 1)(m - 1)
D
(m2 + 2)(m - 1)
correct option: c
m3 - 2m2 - m + 2
Let f(m) = m3 - 2m2 - m2 + 2
= f(1)
= 1 - 2 - 2 + 2 = 0
∴ m - 1 is factor \(\frac{m^3 - 2m^2 - m^2 + 2}{m - 1}\)
= m2 - m - 2
= (m - 1)m2 - m - 2
= (m - 1)(m + 1)(m - 2)
Users' Answers & CommentsLet f(m) = m3 - 2m2 - m2 + 2
= f(1)
= 1 - 2 - 2 + 2 = 0
∴ m - 1 is factor \(\frac{m^3 - 2m^2 - m^2 + 2}{m - 1}\)
= m2 - m - 2
= (m - 1)m2 - m - 2
= (m - 1)(m + 1)(m - 2)
23
Factorize 1 - (a - b)2
A
(1 - a - b)(1 - a + b)
B
(1 + a - b)(1 - a + b)
C
(1 - a + b)(1 - a + b)
D
(1 + a + b)(1 + a + b)
correct option: b
1 - (a - b)2 = [1 + (a - b)][1 - a + b]
= (1 + a - b)(1 - a + b)
Users' Answers & Comments= (1 + a - b)(1 - a + b)
24
Which of the following is a factor of rs + tr - pt - ps?
A
(p - s)
B
(s - p)
C
r - p)
D
r + p)
correct option: c
rs + tr - pt - ps = rs - ps - tr - pt
= (r - p)s + (r - p)t
= (r - p)(s + t),
hence r - p is a factor
Users' Answers & Comments= (r - p)s + (r - p)t
= (r - p)(s + t),
hence r - p is a factor
25
Find the two values of y which satisfy the simultaneous equation 3x + y = 8, x2 + xy = 6
A
-1 and 5
B
-5 and 1
C
1 and 5
D
1 and 1
correct option: a
Users' Answers & Comments26
Find the range of values of x which satisfy the inequality \(\frac{x}{2}\) + \(\frac{x}{3}\) + \(\frac{x}{4}\) < 1
A
x < \(\frac{12}{13}\)
B
x < 13
C
x < 9
D
\(\frac{13}{12}\)
correct option: a
\(\frac{x}{2}\) + \(\frac{x}{3}\) + \(\frac{x}{4}\)< 1
= \(\frac{6x + 4x + 3x < 12}{12}\)
i.e. 13 x < 12 = x < \(\frac{12}{13}\)
Users' Answers & Comments= \(\frac{6x + 4x + 3x < 12}{12}\)
i.e. 13 x < 12 = x < \(\frac{12}{13}\)
27
Find the positive number n, such that thrice its square is equal to twelve times the number
A
1
B
2
C
3
D
4
28
What is the nth term of the progression 27, 9, 3,......?
A
27\(\frac{1}{3}\) n - 1
B
3n + 2
C
27 + 18(n - 1)
D
27 + 6(n - 1)
correct option: a
Given 27, 9, 3,......this is a G.P
r = \(\frac{9}{27}\)
= \(\frac{1}{3}\)
T = arn - 1
= 27\(\frac{1}{3}\) n - 1
Users' Answers & Commentsr = \(\frac{9}{27}\)
= \(\frac{1}{3}\)
T = arn - 1
= 27\(\frac{1}{3}\) n - 1
29
Solve the equation (x - 2) (x - 3) = 12
A
2, 3
B
3, 6
C
-1, 6
D
1, -6
correct option: c
(x - 2) (x - 3) = 12
x2 - 3x - 2x + 6 = 12
x2 - 5x - 6 = 0
(x - 1)(x - 6) = 0
x = -1 or 6
Users' Answers & Commentsx2 - 3x - 2x + 6 = 12
x2 - 5x - 6 = 0
(x - 1)(x - 6) = 0
x = -1 or 6
30
Simplify \(\frac{\sqrt{1 + x} + \sqrt{x}}{\sqrt{1 + x} - \sqrt{x}}\)
A
-2x - 2\(\sqrt{x (1 + x)}\)
B
1 + 2x + 2\(\sqrt{x (1 + x)}\)
C
\(\sqrt{x (1 + x)}\)
D
1 + 2x - 2\(\sqrt{x (1 + x)}\)
correct option: b
Users' Answers & Comments