2007 - JAMB Mathematics Past Questions and Answers - page 3
21
Make L the subject of the formula if d = \(\sqrt{\frac{42W}{5L}}\)
A
\(\frac{1}{d}\sqrt{\frac{42W}{5}}\)
B
\(\frac{42}{5dW}\)
C
\(\sqrt{\frac{42W}{5d}}\)
D
\(\frac{42W}{5d^2}\)
correct option: d
d = \(\sqrt{\frac{42W}{5L}}\), square both sides
= d2 = \(\frac{42W}{5L}\)
cross multiply: 5d2L = 42W
divide both sides by 5d2
L = \(\frac{42W}{5d^2}\)
Users' Answers & Comments= d2 = \(\frac{42W}{5L}\)
cross multiply: 5d2L = 42W
divide both sides by 5d2
L = \(\frac{42W}{5d^2}\)
22
The nth term of the sequence \(\frac{3}{2}\), 3, 7, 16, 35, 74, ..., is
A
3.2n - 2
B
5.2n - 2 - n
C
\(\frac{3}{2}\)n
D
\(\frac{3}{2}\) n - 2
correct option: b
T1 = \(\frac{3}{2}\) = \(\frac{5}{2}\) - 1
T2 = 3 = 5 - 3
T3 = 7 = 10 - 3 = 5.2 - 3
T4 = 16 = 20 - 4 = 5.22 - 4
T5 = 35 = 40 - 5 = 5.23 - 5
T6 = 74 = 80 - 6 = 5.24 - 6
Tn = 5.2n - 2 - n
Users' Answers & CommentsT2 = 3 = 5 - 3
T3 = 7 = 10 - 3 = 5.2 - 3
T4 = 16 = 20 - 4 = 5.22 - 4
T5 = 35 = 40 - 5 = 5.23 - 5
T6 = 74 = 80 - 6 = 5.24 - 6
Tn = 5.2n - 2 - n
23
Evaluate\(\begin{pmatrix} 3 & -2 \ -7 & 5\end{pmatrix}\) + 2\(\begin{pmatrix} -2 & 4 \ 3 & -1\end{pmatrix}\)
A
\(\begin{pmatrix}-1 & 6 \ -1 & 3\end{pmatrix}\)
B
\(\begin{pmatrix} 3 & 4 \ -2 & 6\end{pmatrix}\)
C
\(\begin{pmatrix} -1 & 6 \ 1 & 3\end{pmatrix}\)
D
\(\begin{pmatrix} 3 & 4 \ 2 & 6\end{pmatrix}\)
correct option: a
\(\begin{pmatrix} 3 & -2 \ -7 & 5\end{pmatrix}\) + 2\(\begin{pmatrix} -2 & 4 \ 3 & -1\end{pmatrix}\) = \(\begin{pmatrix} 3 & -2 \ -7 & 5\end{pmatrix}\) + \(\begin{pmatrix} -4 & 8 \ 6 & -2\end{pmatrix}\)
= \(\begin{pmatrix} 3 & -4 \ -7 & 6\end{pmatrix}\) + 2\(\begin{pmatrix} -2 & 8 \ 5 & -2\end{pmatrix}\)
= \(\begin{pmatrix}-1 & 6 \ -1 & 3\end{pmatrix}\)
Users' Answers & Comments= \(\begin{pmatrix} 3 & -4 \ -7 & 6\end{pmatrix}\) + 2\(\begin{pmatrix} -2 & 8 \ 5 & -2\end{pmatrix}\)
= \(\begin{pmatrix}-1 & 6 \ -1 & 3\end{pmatrix}\)
24
Given: p = {1, 3, 5, 7, 9, 11} and Q = {2, 4, 6, 8, 10, 12}. Determine the relationship between P and Q
A
P = Q
B
P \(\supset\) Q
C
p ∩ Q = \(\phi\)
D
Q ∪ P
correct option: c
p = {1, 3, 5, 7, 9, 11}, Q = {2, 4, 6, 8, 10, 12}
p ∩ Q = \(\phi\)
Users' Answers & Commentsp ∩ Q = \(\phi\)
25
simplify \(\frac{3}{5}\) \(\div\) (\(\frac{2}{7}\) x \(\frac{4}{3}\) \(\div\) \(\frac{4}{9}\))
A
\(\frac{6}{7}\)
B
\(\frac{4}{5}\)
C
\(\frac{7}{10}\)
D
\(\frac{21}{6}\)
correct option: c
\(\frac{3}{5}\) \(\div\) (\(\frac{2}{7}\) x \(\frac{4}{3}\) \(\div\) \(\frac{4}{9}\)) = \(\frac{2}{3}\) \(\div\) (\(\frac{2}{7}\) x \(\frac{4}{3}\) x \(\frac{9}{4}\))
= \(\frac{3}{5}\) \(\div\) \(\frac{6}{7}\)
= \(\frac{3}{5}\) x \(\frac{7}{6}\)
= \(\frac{7}{10}\)
Users' Answers & Comments= \(\frac{3}{5}\) \(\div\) \(\frac{6}{7}\)
= \(\frac{3}{5}\) x \(\frac{7}{6}\)
= \(\frac{7}{10}\)
26
A man made a profit of 5% when he sold an article for N60,000.00. How much would he have to sell the article to make a profit of 26%?
A
N65,000
B
N68,000
C
N70,000
D
N72,000
correct option: d
Let the cost price be C. For the profit of 5%, selling price = 105% C = N60,000
therefore C = \(\frac{100}{105}\) x N60,000
For a profit of 26%, the selling price = 126%C
= \(\frac{126}{100}\)C x \(\frac{100}{105}\) x N60,000
= N72,000
Users' Answers & Commentstherefore C = \(\frac{100}{105}\) x N60,000
For a profit of 26%, the selling price = 126%C
= \(\frac{126}{100}\)C x \(\frac{100}{105}\) x N60,000
= N72,000
27
Find the value of x for which 2(32x - 1) = 162
A
\(\frac{3}{2}\)
B
\(\frac{1}{2}\)
C
\(\frac{5}{2}\)
D
\(\frac{2}{5}\)
correct option: c
2(32x - 1) = 162, 32x - 1 = 81
= 34
2x - 1 = 4 , 2x = 5
x = \(\frac{5}{2}\)
Users' Answers & Comments= 34
2x - 1 = 4 , 2x = 5
x = \(\frac{5}{2}\)
28
Evaluate 101122 - 10122
A
1100002
B
11000002
C
110002
D
1102
correct option: b
101122 - 10122 = (1011 - 101)2 (1011 + 101)4
= 1102 x 100002
= 11000002
Users' Answers & Comments= 1102 x 100002
= 11000002
29
Find y, if \(\sqrt{12} - \sqrt{147}\) + y\(\sqrt{3}\) = 0
A
3
B
7
C
1
D
5
correct option: d
\(\sqrt{12} - \sqrt{147}\) + y\(\sqrt{3}\) = 0
\(\sqrt{4 \times 3 } - \sqrt{49 \times 3}\) + y\(\sqrt{3}\) = 0
y - 5 = 0
y = 5
Users' Answers & Comments\(\sqrt{4 \times 3 } - \sqrt{49 \times 3}\) + y\(\sqrt{3}\) = 0
y - 5 = 0
y = 5
30
Evaluate \(\frac{(0.5625)^2 - (0.4375)^2}{0.04}\)
A
0.131
B
3.11
C
3.12
D
3.13
correct option: d
\(\frac{(0.5625)^2 - (0.4375)^2}{0.04}\) = \(\frac{(0.5625 - 0.4375)(0.5625 - 0.4375)}{0.04}\)
= \(\frac{0.1250 \times 1}{0.04}\)
= \(\frac{12.50}{0.04}\)
Users' Answers & Comments= \(\frac{0.1250 \times 1}{0.04}\)
= \(\frac{12.50}{0.04}\)