# 1991 - WAEC Mathematics Past Questions & Answers - page 1

1
Express 0.0462 in standard form
A
0.462 x 10-1
B
0.462 x 10-2
C
4.62 x 10-1
D
4.62 x 10-2
CORRECT OPTION: d
4.62 x 10-2
2

The population of a village is 5846. Express this number to three significant figures

A
5850
B
5846
C
5840
D
585
CORRECT OPTION: a

5846 $$\approxeq$$ 5850 (to 3 s.f.)

3

Simplify: log6 + log2 - log12

A
-4
B
-1
C
0
D
1
CORRECT OPTION: c

log 6 + log 2 - log 12

= $$\log (\frac{6 \times 2}{12})$$

= $$\log 1$$

= 0

4

Find the number whose logarithm to base 10 is 2.6025

A
400.4
B
0.4004
C
0.04004
D
0.004004
CORRECT OPTION: a

For the log to be 2.6025, there must be three digits before the decimal point.

5

Simplify: $$(\frac{1}{4})^{-1\frac{1}{2}}$$

A
1/8
B
1/4
C
2
D
4
CORRECT OPTION: e

$$(\frac{1}{4})^{-1\frac{1}{2}}$$

= $$(\frac{1}{4})^{-\frac{3}{2}}$$

= $$(\sqrt{\frac{1}{4}})^{-3}$$

= $$(\frac{1}{2})^{-3}$$

= $$2^3$$

= 8

6

For what value of y is the expression $$\frac{y + 2}{y^{2} - 3y - 10}$$ undefined?

A
y = 0
B
y = 2
C
y = 3
D
y = 5
CORRECT OPTION: d

$$\frac{y + 2}{y^2 - 3y - 10}$$

$$y^2 - 3y - 10 = 0 \implies y^2 - 5y + 2y - 10 = 0$$

$$y(y - 5) + 2(y - 5) = 0$$

$$(y - 5)(y + 2) = 0$$

$$\frac{y + 2}{(y - 5)(y + 2)} = \frac{1}{y - 5}$$

$$\therefore$$ At y = 5, the expression $$\frac{y + 2}{y^2 - 3y - 10}$$ is undefined.

7

Factorize 3a$$^2$$ - 11a + 6

A
(3a - 2)(a - 3)
B
(2a -2)(a - 3)
C
(3a - 2)(a + 3)
D
(3a + 2)(a - 3)
CORRECT OPTION: a

3a$$^2$$ - 11a + 6

3a$$^2$$ - 9a - 2a + 6

3a(a - 3) - 2(a - 3)

= (3a - 2)(a - 3)

8

Solve the equation: 3a + 10 = a$$^2$$

A
a = 5 or a = 2
B
a = -5 or a = 2
C
a = 10 or a = 0
D
a = 5 or a = 0
CORRECT OPTION: e

3a + 10 = a$$^2$$

a$$^2$$ - 3a - 10 = 0

a$$^2$$ - 5a + 2a - 10 = 0

a(a - 5) + 2(a - 5) = 0

(a - 5)(a + 2) = 0

a = 5 or a = -2.

9

Simplify $$(\frac{3}{x} + \frac{15}{2y}) \div \frac{6}{xy}$$

A
$$\frac{2y - 5x}{4}$$
B
$$\frac{9(2x - 5x)}{x^2y^2}$$
C
$$\frac{5x - 2y}{2}$$
D
$$\frac{c^2y^2}{18y - 45x}$$
CORRECT OPTION: a

$$(\frac{3}{x} - \frac{15}{2y}) \div \frac{6}{xy}$$

= $$(\frac{6y - 15x}{2xy}) \div \frac{6}{xy}$$

= $$\frac{6y - 15x}{2xy} \times \frac{xy}{6}$$

= $$\frac{3(2y - 5x)}{2xy} \times \frac{xy}{6}$$

= $$\frac{2y - 5x}{4}$$

10
Simplify: 1/4(2n - 2n+2)
A
2n2 - 2n
B
2n-2(1-2n)
C
2n + 22n + 2
D
22n
CORRECT OPTION: a
1/4(2n - 2n+2) = 2-2(2n - 2n x 22) = 2n x -2(1 - 22)= 22n-2
(20 - 22) = 22n-2 - 2n
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