1990 - JAMB Mathematics Past Questions and Answers - page 1
1
Simplify 4\(\frac{3}{4}\) - 6\(\frac{1}{4}\)
A
-7\(\frac{7}{8}\)
B
\(\frac{-2}{7}\)
C
\(\frac{-10}{21}\)
D
\(\frac{10}{21}\)
correct option: b
4\(\frac{3}{4}\) - 6\(\frac{1}{4}\)
\(\frac{19}{4}\) - \(\frac{25}{4}\)............(A)
\(\frac{21}{5}\) - \(\frac{5}{4}\).............(B)
Now work out the value of A and the value of B and then find the value \(\frac{A}{B}\)
A = \(\frac{19}{4}\) - \(\frac{25}{4}\)
= \(\frac{-6}{4}\)
B = \(\frac{21}{5}\) x \(\frac{5}{20}\)
= \(\frac{105}{20}\)
= \(\frac{21}{4}\)
But then \(\frac{A}{B}\) = \(\frac{-6}{4}\)
\(\frac{21}{4}\) = \(\frac{-6}{4}\) \(\div\) \(\frac{21}{4}\)
= \(\frac{-6}{4}\) x \(\frac{4}{21}\)
= \(\frac{-24}{84}\)
= \(\frac{-2}{7}\)
Users' Answers & Comments\(\frac{19}{4}\) - \(\frac{25}{4}\)............(A)
\(\frac{21}{5}\) - \(\frac{5}{4}\).............(B)
Now work out the value of A and the value of B and then find the value \(\frac{A}{B}\)
A = \(\frac{19}{4}\) - \(\frac{25}{4}\)
= \(\frac{-6}{4}\)
B = \(\frac{21}{5}\) x \(\frac{5}{20}\)
= \(\frac{105}{20}\)
= \(\frac{21}{4}\)
But then \(\frac{A}{B}\) = \(\frac{-6}{4}\)
\(\frac{21}{4}\) = \(\frac{-6}{4}\) \(\div\) \(\frac{21}{4}\)
= \(\frac{-6}{4}\) x \(\frac{4}{21}\)
= \(\frac{-24}{84}\)
= \(\frac{-2}{7}\)
2
The H.C.F. of a2bx + ab2x and a2b - b2 is
A
b
B
a + b
C
b(a \(\div\) b)
D
abx(a2 - b2)
correct option: b
a2bx + ab2x; a2b - b2
abx(a + b); b(a2 - b2)
b(a + b)(a + b)
∴ H.C.F. = (a + b)
Users' Answers & Commentsabx(a + b); b(a2 - b2)
b(a + b)(a + b)
∴ H.C.F. = (a + b)
3
Correct 241.34(3 x 10-3)2 to 4 significant figures
A
0.0014
B
0.001448
C
0.0022
D
0.002172
correct option: d
first work out the expression and then correct the answer to 4 s.f = 241.34..............(A)
(3 x 103)2............(B)
= 32x
= \(\frac{1}{10^3}\) x \(\frac{1}{10^3}\)
(Note that x2 = \(\frac{1}{x^3}\))
= 24.34 x 32 x \(\frac{1}{10^6}\)
= \(\frac{2172.06}{10^6}\)
= 0.00217206
= 0.002172(4 s.f)
Users' Answers & Comments(3 x 103)2............(B)
= 32x
= \(\frac{1}{10^3}\) x \(\frac{1}{10^3}\)
(Note that x2 = \(\frac{1}{x^3}\))
= 24.34 x 32 x \(\frac{1}{10^6}\)
= \(\frac{2172.06}{10^6}\)
= 0.00217206
= 0.002172(4 s.f)
4
At what rate would a sum of N100.00 deposited for 5 years raise an interest of N7.50?
A
1\(\frac{1}{2}\)%
B
2\(\frac{1}{2}\)%
C
1.5%
D
25%
correct option: c
Interest I = \(\frac{PRT}{100}\)
∴ R = \(\frac{100 \times 1}{100 \times 5}\)
= \(\frac{100 \times 7.50}{500 \times 5}\)
= \(\frac{750}{500}\)
= \(\frac{3}{2}\)
= 1.5%
Users' Answers & Comments∴ R = \(\frac{100 \times 1}{100 \times 5}\)
= \(\frac{100 \times 7.50}{500 \times 5}\)
= \(\frac{750}{500}\)
= \(\frac{3}{2}\)
= 1.5%
5
Three children shared a basket of mangoes in such a way that the first child took \(\frac{1}{4}\) of the mangoes and the second \(\frac{3}{4}\) of the remainder. What fraction of the mangoes did the third child take?
A
\(\frac{3}{16}\)
B
\(\frac{7}{16}\)
C
\(\frac{9}{16}\)
D
\(\frac{13}{16}\)
correct option: a
You can use any whole numbers (eg. 1. 2. 3) to represent all the mangoes in the basket.
If the first child takes \(\frac{1}{4}\) it will remain 1 - \(\frac{1}{4}\) = \(\frac{3}{4}\)
Next, the second child takes \(\frac{3}{4}\) of the remainder
which is \(\frac{3}{4}\) i.e. find \(\frac{3}{4}\) of \(\frac{3}{4}\)
= \(\frac{3}{4}\) x \(\frac{3}{4}\)
= \(\frac{9}{16}\)
the fraction remaining now = \(\frac{3}{4}\) - \(\frac{9}{16}\)
= \(\frac{12 - 9}{16}\)
= \(\frac{3}{16}\)
Users' Answers & CommentsIf the first child takes \(\frac{1}{4}\) it will remain 1 - \(\frac{1}{4}\) = \(\frac{3}{4}\)
Next, the second child takes \(\frac{3}{4}\) of the remainder
which is \(\frac{3}{4}\) i.e. find \(\frac{3}{4}\) of \(\frac{3}{4}\)
= \(\frac{3}{4}\) x \(\frac{3}{4}\)
= \(\frac{9}{16}\)
the fraction remaining now = \(\frac{3}{4}\) - \(\frac{9}{16}\)
= \(\frac{12 - 9}{16}\)
= \(\frac{3}{16}\)
6
Simplify and express in standard form \(\frac{0.00275 \times 0.0064}{0.025 \times 0.08}\)
A
8.8 x 10-1
B
8.8 x 10-2
C
8.8 x 10-3
D
8.8 x 103
correct option: c
\(\frac{0.00275 \times 0.0064}{0.025 \times 0.08}\)
Removing the decimals = \(\frac{275 \times 64}{2500 \times 800}\)
= \(\frac{88}{10^4}\)
88 x 10-4 = 88 x 10-1 x 10-4
= 8.8 x 10-3
Users' Answers & CommentsRemoving the decimals = \(\frac{275 \times 64}{2500 \times 800}\)
= \(\frac{88}{10^4}\)
88 x 10-4 = 88 x 10-1 x 10-4
= 8.8 x 10-3
7
three brothers in a business deal share the profit at the end of a contact. The first received \(\frac{1}{3}\) of the profit and the second \(\frac{2}{3}\) of the remainder. If the third received the remaining N12000.00 how much profit did they share?
A
N60 000.00
B
N54 000.00
C
N48 000.00
D
N42 000.00
correct option: b
use "T" to represent the total profit. The first receives \(\frac{1}{3}\) T
remaining, 1 - \(\frac{1}{3}\)
= \(\frac{2}{3}\)T
The seconds receives the remaining, which is \(\frac{2}{3}\) also
\(\frac{2}{3}\) x \(\frac{2}{3}\) x \(\frac{4}{9}\)
The third receives the left over, which is \(\frac{2}{3}\)T - \(\frac{4}{9}\)T = (\(\frac{6 - 4}{9}\))T
= \(\frac{2}{9}\)T
The third receives \(\frac{2}{9}\)T which is equivalent to N12000
If \(\frac{2}{9}\)T = N12, 000
T = \(\frac{12 000}{\frac{2}{9}}\)
= N54, 000
Users' Answers & Commentsremaining, 1 - \(\frac{1}{3}\)
= \(\frac{2}{3}\)T
The seconds receives the remaining, which is \(\frac{2}{3}\) also
\(\frac{2}{3}\) x \(\frac{2}{3}\) x \(\frac{4}{9}\)
The third receives the left over, which is \(\frac{2}{3}\)T - \(\frac{4}{9}\)T = (\(\frac{6 - 4}{9}\))T
= \(\frac{2}{9}\)T
The third receives \(\frac{2}{9}\)T which is equivalent to N12000
If \(\frac{2}{9}\)T = N12, 000
T = \(\frac{12 000}{\frac{2}{9}}\)
= N54, 000
8
Simplify \(\sqrt{160r^2}\) + \(\sqrt{71r^4}\) + \(\sqrt{100r^2}\)
A
9r2
B
12\(\sqrt{3r}\)
C
13r
D
\(\sqrt{13r}\)
correct option: c
\(\sqrt{160r^2 + 71r^4 + 100r^8}\)
Simplifying from the innermost radical and progressing outwards we have the given expression
\(\sqrt{160r^2 + 71r^4 + 100r^8}\) = \(\sqrt{160r^2 + 81r^4}\)
\(\sqrt{160r^2 + 9r^2}\) = \(\sqrt{169r^2}\)
= 13r
Users' Answers & CommentsSimplifying from the innermost radical and progressing outwards we have the given expression
\(\sqrt{160r^2 + 71r^4 + 100r^8}\) = \(\sqrt{160r^2 + 81r^4}\)
\(\sqrt{160r^2 + 9r^2}\) = \(\sqrt{169r^2}\)
= 13r
9
Simplify \(\sqrt{27}\) + \(\frac{3}{\sqrt{3}}\)
A
4\(\sqrt{3}\)
B
\(\frac{4}{\sqrt{3}}\)
C
3\(\sqrt{3}\)
D
\(\frac{\sqrt{3}}{4}\)
correct option: a
Users' Answers & Comments10
Simplify 3 log69 + log612 + log664 - log672
A
5
B
7776
C
log631
D
(7776)6
correct option: a
3 log69 + log612 + log664 - log672
= log693 + log612 + log664 - log672
log6729 + log612 + log664 - log672
log6(729 x 12 x 64) = log6776
= log665 = 5 log66 = 5
N.B: log66 = 1
Users' Answers & Comments= log693 + log612 + log664 - log672
log6729 + log612 + log664 - log672
log6(729 x 12 x 64) = log6776
= log665 = 5 log66 = 5
N.B: log66 = 1