2011 - JAMB Mathematics Past Questions and Answers - page 1
1
If 2q35 = 778, find q
A
2
B
1
C
4
D
O
correct option: a
2q35 = 778
2 x 52 + q x 51 + 3 x 50 = 7 x 81 + 7 x 80
2 x 25 + q x 5 + 3 x 1 = 7 x 8 + 7 x 1
50 + 5q + 3 = 56 + 7
5q = 63 - 53
q = \(\frac{10}{5}\)
q = 2
Users' Answers & Comments2 x 52 + q x 51 + 3 x 50 = 7 x 81 + 7 x 80
2 x 25 + q x 5 + 3 x 1 = 7 x 8 + 7 x 1
50 + 5q + 3 = 56 + 7
5q = 63 - 53
q = \(\frac{10}{5}\)
q = 2
2
Simplify \(\frac{3\frac{2}{3} \times \frac{5}{6} \times \frac{2}{3}}{\frac{11}{15} \times \frac{3}{4} \times \frac{2}{27}}\)
A
\(5\frac{2}{3}\)
B
30
C
\(4\frac{1}{3}\)
D
50
correct option: d
\(\frac{3\frac{2}{3} \times \frac{5}{6} \times \frac{2}{3}}{\frac{11}{15} \times \frac{3}{4} \times \frac{2}{27}}\)
\(\frac{\frac{11}{3} \times \frac{5}{6} \times \frac{2}{3}}{\frac{11}{15} \times \frac{3}{4} \times \frac{2}{27}}\)
\(\frac{110}{54} \div \frac{66}{1620}\)
50
Users' Answers & Comments\(\frac{\frac{11}{3} \times \frac{5}{6} \times \frac{2}{3}}{\frac{11}{15} \times \frac{3}{4} \times \frac{2}{27}}\)
\(\frac{110}{54} \div \frac{66}{1620}\)
50
3
A man invested N5,000 for 9 months at 4%. What is the simple interest?
A
N150
B
N220
C
N130
D
N250
correct option: a
S.I. = \(\frac{P \times R \times T}{100}\)
If T = 9 months, it is equivalent to \(\frac{9}{12}\) years
S.I. = \(\frac{5000 \times 4 \times 9}{100 \times 12}\)
S.I. = N150
Users' Answers & CommentsIf T = 9 months, it is equivalent to \(\frac{9}{12}\) years
S.I. = \(\frac{5000 \times 4 \times 9}{100 \times 12}\)
S.I. = N150
4
If the numbers M, N, Q are in the ratio 5:4:3, find the value of \(\frac{2N - Q}{M}\)
A
2
B
3
C
1
D
4
correct option: c
M:N:Q == 5:4:3
i.e M = 5, N = 4, Q = 3
Substituting values into equation, we have...
\(\frac{2N - Q}{M}\)
= \(\frac{2(4) - 3}{5}\)
= \(\frac{8 - 3}{5}\)
= \(\frac{5}{5}\)
= 1
Users' Answers & Commentsi.e M = 5, N = 4, Q = 3
Substituting values into equation, we have...
\(\frac{2N - Q}{M}\)
= \(\frac{2(4) - 3}{5}\)
= \(\frac{8 - 3}{5}\)
= \(\frac{5}{5}\)
= 1
5
Simplify \((\frac{16}{81})^{\frac{1}{4}} \div (\frac{9}{16})^{-\frac{1}{2}}\)
A
\(\frac{2}{3}\)
B
\(\frac{1}{2}\)
C
\(\frac{8}{9}\)
D
\(\frac{1}{3}\)
correct option: b
\((\frac{16}{81})^{\frac{1}{4}} \div (\frac{9}{16})^{-\frac{1}{2}}\)
\((\frac{16}{81})^{\frac{1}{4}} \div (\frac{16}{9})^{\frac{1}{2}}\)
\((\frac{2^4}{3^4})^{\frac{1}{4}} \div (\frac{4^2}{3^2})^{\frac{1}{2}}\)
\(\frac{2^{4 \times \frac{1}{4}}}{3^{4 \times \frac{1}{4}}} \div \frac{4^{2 \times \frac{1}{2}}}{3^{2 \times \frac{1}{2}}}\)
\(\frac{2}{3} \div \frac{4}{3}\)
\(\frac{2}{3} \times \frac{3}{4}\)
\(\frac{2}{4}\)
\(\frac{1}{2}\)
Users' Answers & Comments\((\frac{16}{81})^{\frac{1}{4}} \div (\frac{16}{9})^{\frac{1}{2}}\)
\((\frac{2^4}{3^4})^{\frac{1}{4}} \div (\frac{4^2}{3^2})^{\frac{1}{2}}\)
\(\frac{2^{4 \times \frac{1}{4}}}{3^{4 \times \frac{1}{4}}} \div \frac{4^{2 \times \frac{1}{2}}}{3^{2 \times \frac{1}{2}}}\)
\(\frac{2}{3} \div \frac{4}{3}\)
\(\frac{2}{3} \times \frac{3}{4}\)
\(\frac{2}{4}\)
\(\frac{1}{2}\)
6
If log318 + log33 - log3x = 3, Find x.
A
1
B
2
C
o
D
3
correct option: b
log\(_{3}^{18}\) + log\(_{3}^{3}\) - log\(_{3}^{x}\) = 3
log\(_{3}^{18}\) + log\(_{3}^{3}\) - log\(_{3}^{x}\) = 3log33
log\(_{3}^{18}\) + log\(_{3}^{3}\) - log\(_{3}^{x}\) = log333
log3(\(\frac{18 \times 3}{X}\)) = log333
\(\frac{18 \times 3}{X}\) = 33
18 x 3 = 27 x X
x = \(\frac{18 \times 3}{27}\)
= 2
Users' Answers & Commentslog\(_{3}^{18}\) + log\(_{3}^{3}\) - log\(_{3}^{x}\) = 3log33
log\(_{3}^{18}\) + log\(_{3}^{3}\) - log\(_{3}^{x}\) = log333
log3(\(\frac{18 \times 3}{X}\)) = log333
\(\frac{18 \times 3}{X}\) = 33
18 x 3 = 27 x X
x = \(\frac{18 \times 3}{27}\)
= 2
7
Rationalize \(\frac{2 - \sqrt5}{3 - \sqrt5}\)
A
\(\frac{1 - \sqrt5}{2}\)
B
\(\frac{1 - \sqrt5}{4}\)
C
\(\frac{ \sqrt5 - 1}{2}\)
D
\(\frac{1 + \sqrt5}{4}\)
correct option: b
\(\frac{2 - \sqrt5}{3 - \sqrt5}\) x \(\frac{3 + \sqrt5}{3 + \sqrt5}\)
\(\frac{(2 - \sqrt5)(3 + \sqrt5)}{(3 - \sqrt5)(3 + \sqrt5)}\) = \(\frac{6 +2\sqrt5 - 3\sqrt5 - \sqrt25}{9 + 3\sqrt5 - 3\sqrt5 - \sqrt25}\)
= \(\frac{6 - \sqrt5 - 5}{9 - 5}\)
= \(\frac{1 - \sqrt5}{4}\)
Users' Answers & Comments\(\frac{(2 - \sqrt5)(3 + \sqrt5)}{(3 - \sqrt5)(3 + \sqrt5)}\) = \(\frac{6 +2\sqrt5 - 3\sqrt5 - \sqrt25}{9 + 3\sqrt5 - 3\sqrt5 - \sqrt25}\)
= \(\frac{6 - \sqrt5 - 5}{9 - 5}\)
= \(\frac{1 - \sqrt5}{4}\)
8
Simplify (\(\sqrt2 + \frac{1}{\sqrt3})(\sqrt2 - \frac{1}{\sqrt3}\))
A
\(\frac{7}{3}\)
B
\(\frac{5}{3}\)
C
\(\frac{5}{2}\)
D
\(\frac{3}{2}\)
correct option: b
(\(\sqrt2 + \frac{1}{\sqrt3})(\sqrt2 - \frac{1}{\sqrt3}\))
\(\sqrt4 - \frac {\sqrt2}{\sqrt3} + \frac {\sqrt2}{\sqrt3} - \frac {1}{\sqrt9}\)
= 2 - \(\frac {1}{3}\)
= \(\frac {16 - 1}{3}\)
= \(\frac{5}{3}\)
Users' Answers & Comments\(\sqrt4 - \frac {\sqrt2}{\sqrt3} + \frac {\sqrt2}{\sqrt3} - \frac {1}{\sqrt9}\)
= 2 - \(\frac {1}{3}\)
= \(\frac {16 - 1}{3}\)
= \(\frac{5}{3}\)
9
Raial has 7 different posters to be hanged in her bedroom, living room and kitchen. Assuming she has plans to place at least a poster in each of the 3 rooms, how many choices does she have?
A
49
B
170
C
21
D
210
correct option: d
The first poster has 7 ways to be arranges, the second poster can be arranged in 6 ways and the third poster in 5 ways.
= 7 x 6 x 5
= 210 ways
or \(\frac{7}{P_3}\) = \(\frac{7!}{(7 - 3)!}\) = \(\frac{7!}{4!}\)
= \(\frac{7 \times 6 \times 5 \times 4!}{4!}\)
= 210 ways
Users' Answers & Comments= 7 x 6 x 5
= 210 ways
or \(\frac{7}{P_3}\) = \(\frac{7!}{(7 - 3)!}\) = \(\frac{7!}{4!}\)
= \(\frac{7 \times 6 \times 5 \times 4!}{4!}\)
= 210 ways
10
Make R the subject of the formula if T = \(\frac {KR^2 + M}{3}\)
A
\(\sqrt\frac{3T - K}{M}\)
B
\(\sqrt\frac{3T - M}{K}\)
C
\(\sqrt\frac{3T + K}{M}\)
D
\(\sqrt\frac{3T - K}{M}\)
correct option: b
T = \(\frac{KR^2 + M}{3}\)
3T = KR2 + M
KR2 = 3T - M
R2 = \(\frac{3T - M}{K}\)
R = \(\sqrt\frac{3T - M}{K}\)
Users' Answers & Comments3T = KR2 + M
KR2 = 3T - M
R2 = \(\frac{3T - M}{K}\)
R = \(\sqrt\frac{3T - M}{K}\)