2007 - JAMB Mathematics Past Questions & Answers - page 7

61
If x10 = 12145 find x
A
124
B
121
C
184
D
180
CORRECT OPTION: c
x10 = 12145
= x10 = 1 x 53 + 2 x 52 + 1 * 51 + 4 x 50
= 1 x 125 + 2 x 25 + 1 x 5 + 4 x 1
= 125 + 50 + 5 + 4
= 184
62
Evaluate \(\frac{(05652 - 04375)^2}{0.04}\) correct to three significant figures
A
3.11
B
3.13
C
0.313
D
3.12
CORRECT OPTION: b
\(\frac{(0.5652 - 0.4375)^2}{0.04}\\ \frac{(0.5625+0.4375)(0.5625-0.4375)}{0.04}\\ \frac{1.000\times 0.125}{0.04}\\ =3.125\\ =3.13\)
63
Find the value of x for which 2(32x-1) = 162
A
5/2
B
3/2
C
2/5
D
1/2
CORRECT OPTION: a
2(32x-1) = 162
32x-1 = 162/2
32x-1 = 81
32x-1 = 32
2x - 1 = 4 (equating the indices)
2x = 5
5/2
x =
64
Simplify \(\frac{3}{5} \div \left(\frac{2}{7} \times \frac{4}{3} \div \frac{4}{9}\right)\)
A
\(\frac{4}{5}\)
B
\(\frac{7}{10}\)
C
\(\frac{6}{6}\)
D
\(\frac{21}{6}\)
CORRECT OPTION: b
\(\frac{3}{5} \div \left(\frac{2}{7} \times \frac{4}{3} \div \frac{4}{9}\right)\\ =\frac{3}{5} \div \left(\frac{2}{7} \times \frac{4}{3} \times \frac{9}{4}\right)\\ =\frac{3}{5} \div \frac{6}{7}\\ =\frac{3}{5} \times \frac{7}{6}\\ =\frac{7}{10}\)
65
If log102 = x, express log1012.5 in terms of x
A
2(1 + x)
B
2 + 3x
C
2(1 - x)
D
2 - 3x
CORRECT OPTION: d
log1012.5 = log10 121/2
= log1025/2
= log1025 - log102
= log1052 - log102
= 2log105 - log102
= 2log1010/2 - log102
= 2(1-x)- x
= 2 - 2x – x
= 2 – 3x
66
A man made a profit of 5% when he sold an article for N60,000.00. How much would he have sell the article to make a profit of 26%
A
N68,000
B
N72,000
C
N65,000
D
N70,000
CORRECT OPTION: b
5% profit = 100 + 5 = 105%
26% profit = 100 + 26 = 126%
∴ 105% → N60,000
1% → 60000/15
126% = 1000/105 x 126/1
=N72,000
67
Given
P = {1, 3, 5, 7, 9, 11}
and Q = {2, 4, 6, 8, 1, 12}. Determine the relationship between P and Q
A
P∩Q = ∅
B
P ⊂ Q
C
Q⊂P
D
P = Q
CORRECT OPTION: a
P = {1, 3, 5, 7, 9, 11}
Q = {2, 4, 6, 8, 1, 12}
P∩Q = {1, 3, 5, 7, 9, 11}∩{2, 4, 6, 8, 1, 12}
= {} = ∅
68
Evaluate 101122 - 10122
A
1100002
B
1102
C
11000002
D
110002
CORRECT OPTION: c
101122 - 10122 = (1x23 + 0x22 + 1x21 + 1x20)2 - (1x22 + 0x21 + 1x22)2
(1x8 + 0x4 + 1x2 + 1x1) 2 - (1x4 + 0x2 + 1x1) 2)
= (8 + 0 + 2 + 1) 2 - (4 + 0 + 1) 2
= 112 - 52
= 16 x 6 = 96
9610 to base 2
2/96 = 48 R 0
2/48 = 24 R 0
2/24 = 12 R 0
2/12 = 6 R 0
2/6 = 3 R 0
2/3 = 1 R 1
2/1 = 0 R 1
11000002
69
If X = {all the perfect squares less than 40}
Y = {all the odd numbers fro, 1 to 15}. Find X ∩ Y.
A
{3, 9}
B
{9}
C
{9, 25}
D
{1, 9}
CORRECT OPTION: d
All the perfect squares < 40
X = {1, 4, 9, 16, 25, 36}
All the odd numbers from 1 to 15
Y = {1, 3, 5, 7, 9, 11, 13, 15}
X ∩ Y = {1, 9}
70
Calculate the length of an arc of a circle diameter 14 cm, which substends an angle of 90o at the center of the circle
A
7π/2 cm
B
7π cm
C
14π cm
D
7π/4 cm
CORRECT OPTION: a
Length of an arc = θ/360 x 2πr
90/360 x 2 x π x 7
= /2
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