# 1992 - WAEC Mathematics Past Questions & Answers - page 1

1
Convert 77 to a number in base two
A
1001 101
B
111001
C
100110
D
10101
CORRECT OPTION: a
$$\begin{array}{c|c} 2 & 77 \ \hline 2 & 38 R1 \ 2 & 19 R0 \ 2 & 9 R1 \ 2 & 4 R1 \ 2 & 2 R0 \ 2 & 1 R0 \ & 0 R1\end{array}$$

77ten = 1001101two
2

A bricklayer measured the length of a wall and obtained 4.10m. If the actual length of the wall is 4.25m, find his percentage error.

A
3 9/17%
B
3 27/41%
C
15%
D
35 5/17%
CORRECT OPTION: a

Error = 4.25 - 4.10 = 0.15

% error = $$\frac{0.15}{4.25} \times 100%$$

= $$\frac{15}{\frac{17}{4}} = \frac{15 \times 4}{17}$$

= $$3\frac{9}{17} %$$

3

The nth term of a sequence is given by 3.2$$^{n-2}$$. Write down the first three terms of the sequence.

A
2/3, 0, 6
B
3/2, 3, 6,
C
2/3, 3, 8/3
D
2/3, 3/4, 6
CORRECT OPTION: b

$$T_n = 3. 2^{n - 2} \ T_{1} = 3. 2^{1 - 2} = 3. 2^{-1} \ T_1 = \frac{3}{2}$$

$$T_2 = 3. 2^{2 - 2} \ T_2 = 3. 2^0 = 3$$

$$T_3 = 3. 2^{3 - 2} = 3. 2^1 \ T_3 = 6$$

The first 3 terms of the sequence are $$\frac{3}{2}$$, 3 and 6.

4

Simplify: $$(\frac{16}{81})^{\frac{1}{4}}$$

A
8/27
B
1/3
C
4/9
D
2/3
CORRECT OPTION: d

$$(\frac{16}{81})^{\frac{1}{4}}$$

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

= $$\frac{2}{3}$$

5

Evaluate $$\log_{10} 25 + \log_{10} 32 - \log_{10} 8$$

A
0.2
B
2
C
100
D
409
CORRECT OPTION: b

$$\log_{10} 25 + \log_{10} 32 - \log_{10} 8$$

= $$\log_{10} (\frac{25 \times 32}{8})$$

= $$\log_{10} 100$$

= 2

6

Factorize the expression 2y$$^2$$ + xy - 3x$$^2$$

A
2y (y + x) - 3x2
B
(2y - x)(2y + x)
C
(3x - 2y(x - y)
D
(2y + 3) x (y - x)
CORRECT OPTION: d

2y$$^2$$ + xy - 3x$$^2$$

2y$$^2$$ + 3xy - 2xy - 3x$$^2$$

y(2y + 3x) - x(2y + 3x)

= (y - x)(2y + 3x)

7

Construct a quadratic equation whose roots are $$-\frac{1}{2}$$ and 2.

A
3x2-3x+2=0
B
3x2+3x-2=0
C
2x2+3x-2=0
D
2x2-3x+2=0
CORRECT OPTION: e

If x = $$-\frac{1}{2}$$ and 2; then

$$x + \frac{1}{2} = 0$$ and $$x - 2 = 0$$

$$\implies (x + \frac{1}{2})(x - 2) = 0$$

$$x^2 - 2x + \frac{1}{2}x - 1 = 0$$

$$x^2 - \frac{3}{2}x - 1 = 0$$

$$2x^2 - 3x - 2 = 0$$

8

Write as a single fraction $$\frac{1}{1 - x} + \frac{2}{1 + x}$$

A
$$\frac{x + 3}{1 - x^2}$$
B
$$\frac{3 - x}{(1 - x)^2}$$
C
$$\frac{3 - x}{1 + x^2}$$
D
$$\frac{3 - x}{(1 + x)^2}$$
CORRECT OPTION: e

$$\frac{1}{1 - x} + \frac{2}{1 + x}$$

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

= $$\frac{1 + x + 2 - 2x}{1 - x^2}$$

= $$\frac{3 - x}{1 - x^2}$$

9

What must be added to the expression x$$^2$$ - 18x to make it a perfect square?

A
3
B
9
C
36
D
72
CORRECT OPTION: e

x$$^2$$ - 18x to be a perfect square.

$$(\frac{b}{2})^2$$ is added to ax$$^2$$ + bx + c in order to make it a perfect square.

$$x^2 - 18x + (\frac{-18}{2})^2$$

= $$x^2 - 18x + 81$$

10

Solve the equation $$\frac{m}{3} + \frac{1}{2} = \frac{3}{4} + \frac{m}{4}$$

A
-3
B
-2
C
2
D
3
CORRECT OPTION: d

$$\frac{m}{3} + \frac{1}{2} = \frac{3}{4} + \frac{m}{4}$$

$$\frac{m}{3} - \frac{m}{4} = \frac{3}{4} - \frac{1}{2}$$

$$\frac{m}{12} = \frac{1}{4}$$

$$4m = 12 \implies m = 3$$

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