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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