# 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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