1990 JAMB Mathematics Past Questions & Answers - page 1

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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


Solution
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 \(\frac{4}{21}\)

= \(\frac{-24}{84}\)

= \(\frac{-2}{7}\)

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


Solution
a2bx + ab2x; a2b - b2

abx(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


Solution
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)

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


Solution
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%

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


Solution
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 = \(\frac{3}{4}\) - \(\frac{9}{16}\)

= \(\frac{12 - 9}{16}\)

= \(\frac{3}{16}\)

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


Solution
\(\frac{0.00275 \times 0.0064}{0.025 \times 0.08}\)

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

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


Solution
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

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


Solution
\(\sqrt{160r^2 + 71r^4 + 100r^8}\)

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

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



10
Simplify 3 log69 + log612 + log664 - log672
A 5
B 7776
C log631
D (7776)6


Correct Option: A


Solution
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

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