2005 - JAMB Mathematics Past Questions and Answers - page 2
11
A polynomial in x whose zeros are -2, -1 and 3 is
A
x3 - 7x + 6
B
x3 + 7x - 6
C
x3 + 7x + 6
D
x3 - 7x - 6
correct option: d
x = -2, x = -1 and x = 3
∴x+2 = 0, x+1 = 0 and x-3 = 0
Product of the factors
(x+2)(x+1)(x-3) = 0
(x2 + 3x + 2)(x-3)
x(x2 + 3x + 2) -3(x2 + 3x + 2) = 0
x3 + 3x2 + 2x - 3x2 - 9x - 6 = 0
x3 - 7x - 6 = 0
Users' Answers & Comments∴x+2 = 0, x+1 = 0 and x-3 = 0
Product of the factors
(x+2)(x+1)(x-3) = 0
(x2 + 3x + 2)(x-3)
x(x2 + 3x + 2) -3(x2 + 3x + 2) = 0
x3 + 3x2 + 2x - 3x2 - 9x - 6 = 0
x3 - 7x - 6 = 0
12
The time taken to do a piece of work is inversely proportional to the number of men employed. If it takes 30 men to do a piece of work in 6 days, how many men are required to do the work in 4 days?
A
20
B
35
C
45
D
60
correct option: c
t = time taken and N = number of men
t ∝ 1/N
t = K/N
K = Nt
K = 30 * 6
K = 180
∴t = 180/N
4 = 180/N
4N = 180
N = 180/4
45 men
Users' Answers & Commentst ∝ 1/N
t = K/N
K = Nt
K = 30 * 6
K = 180
∴t = 180/N
4 = 180/N
4N = 180
N = 180/4
45 men
13
The weight W kg of a metal bar varies jointly as its length L meters and the square of its diameter d meters. If w = 140 when d = 42/3 and L = 54, find d in terms of W and L.
A
\(\sqrt{\frac{42W}{5L}}\)
B
\(\sqrt{\frac{6L}{42W}}\)
C
\(\frac{42W}{5L}\)
D
\(\frac{5L}{42W}\)
correct option: a
\(W\infty LD^2\W=KLd^2\K=\frac{W}{Ld^2}\=\frac{140}{54}\times\left(4\frac{2}{3}\right)^2 \=\frac{140}{54}\times\left(\frac{14}{3}\right)^2\=\frac{140\times 9}{54\times 14\times 14}\=\frac{5}{42}\∴W=\frac{5}{42Ld^2}\42W=5Ld^2\\frac{42W}{5L}=d^2\d=\sqrt{\frac{42W}{5L}}\)
Users' Answers & Comments14
Find the range of values of x for which 7x - 3 > 25 + 3x
A
x >7
B
x<7
C
x>-7
D
x<-7
15
A
x \(\leq\) 2
B
0 \(\leq\) x \(\leq\) 2
C
-2 \(\leq\) x \(\leq\) 0, x \(\geq\) 2
D
x \(\leq\) -2, 0 \(\leq\) x \(\leq\) 2
correct option: c
Users' Answers & Comments16
If the 7th term of an AP is twice the third term and the sum of the first four terms is 42, find the common difference.
A
6
B
3
C
2
D
1
correct option: b
U7 = a + (7 - 1)d
= a + 6d
U3 = a + (3 - 1)d
= a + 2d
But U7 = 2(U3)
∴a + 6d = 2(a + 2d)
a + 6d = 2a + 4d
2a - a + 4d - 6d = 0
a - 2d = 0 → eqn1
Sn = n/2 (2a + (n - 1)d)
42 = 4/2 (2a + (4 - 1)d)
42 = 2(2a + 3d)
21 = 2a + 3d → eqn2
eqn1 * eqn2 0 = 2a - 4d
21 = 7d
∴d = 21/7
d = 3
Users' Answers & Comments= a + 6d
U3 = a + (3 - 1)d
= a + 2d
But U7 = 2(U3)
∴a + 6d = 2(a + 2d)
a + 6d = 2a + 4d
2a - a + 4d - 6d = 0
a - 2d = 0 → eqn1
Sn = n/2 (2a + (n - 1)d)
42 = 4/2 (2a + (4 - 1)d)
42 = 2(2a + 3d)
21 = 2a + 3d → eqn2
eqn1 * eqn2 0 = 2a - 4d
21 = 7d
∴d = 21/7
d = 3
17
Find the sum of the first 20 terms of the series 8, 12, 16, ....., 96
A
1400
B
1040
C
960
D
920
correct option: b
8, 12, 16, .....96
a = 8, d = 4, l = 96, n = 20
S20 = n/2(a + l)
= 20/2(8 + 96)
= 10 * 104
= 1040
Users' Answers & Commentsa = 8, d = 4, l = 96, n = 20
S20 = n/2(a + l)
= 20/2(8 + 96)
= 10 * 104
= 1040
18
An operation * is defined on the set of real numbers by a * b = ab + 2(a + b + 1). find the identity elements
A
2
B
1
C
-1
D
-2
correct option: c
a * b = ab + 2(a + b + 1)
let e be the identity element
∴ a * e = e * b = a
∴ a * e
ae + 2(a + e + 1) = a
ae + 2a + 2e + 2 = a
ae + 2e = a - 2a = 2
(a + 2)e = -a - 2
e = -(a-2) / (a+2)
e = -(a+2) / (a+2)
e = -1
Users' Answers & Commentslet e be the identity element
∴ a * e = e * b = a
∴ a * e
ae + 2(a + e + 1) = a
ae + 2a + 2e + 2 = a
ae + 2e = a - 2a = 2
(a + 2)e = -a - 2
e = -(a-2) / (a+2)
e = -(a+2) / (a+2)
e = -1
19
A
60o
B
100o
C
120o
D
140o
correct option: c
p + 40o = 100o (exterior ∠ = sum of two interior opp ∠s)
p = 100o - 40o
P = 60o
But q + p = 180o (∠s on a straight line)
q + 60o
q = 180o - 60o
q = 120o
x = q (corresponding ∠)
∴x = 120o
Users' Answers & Commentsp = 100o - 40o
P = 60o
But q + p = 180o (∠s on a straight line)
q + 60o
q = 180o - 60o
q = 120o
x = q (corresponding ∠)
∴x = 120o
20
A
26o
B
43o
C
52o
D
85o
correct option: b
∠GOK = 85o (vertical opposite angle ∠s)
∠EOG + ∠GOK + ∠KOF = 180 (∠s on a straight line)
∠EOg + 85o + 52o = 180o
∠EOG + 137o = 180o
∠EOG = 43o
Users' Answers & Comments∠EOG + ∠GOK + ∠KOF = 180 (∠s on a straight line)
∠EOg + 85o + 52o = 180o
∠EOG + 137o = 180o
∠EOG = 43o