1992 - WAEC Mathematics Past Questions and Answers - page 1
77ten = 1001101two
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.
Error = 4.25 - 4.10 = 0.15
% error = \(\frac{0.15}{4.25} \times 100%\)
= \(\frac{15}{\frac{17}{4}} = \frac{15 \times 4}{17}\)
= \(3\frac{9}{17} %\)
The nth term of a sequence is given by 3.2\(^{n-2}\). Write down the first three terms of the sequence.
\(T_n = 3. 2^{n - 2} \
T_{1} = 3. 2^{1 - 2} = 3. 2^{-1} \
T_1 = \frac{3}{2} \)
\(T_2 = 3. 2^{2 - 2} \
T_2 = 3. 2^0 = 3\)
\(T_3 = 3. 2^{3 - 2} = 3. 2^1 \
T_3 = 6\)
The first 3 terms of the sequence are \(\frac{3}{2}\), 3 and 6.
Simplify: \((\frac{16}{81})^{\frac{1}{4}}\)
\((\frac{16}{81})^{\frac{1}{4}}\)
= \(((\frac{2}{3})^{4})^{\frac{1}{4}}\)
= \(\frac{2}{3}\)
Evaluate \(\log_{10} 25 + \log_{10} 32 - \log_{10} 8\)
\(\log_{10} 25 + \log_{10} 32 - \log_{10} 8\)
= \(\log_{10} (\frac{25 \times 32}{8})\)
= \(\log_{10} 100 \)
= 2
Factorize the expression 2y\(^2\) + xy - 3x\(^2\)
2y\(^2\) + xy - 3x\(^2\)
2y\(^2\) + 3xy - 2xy - 3x\(^2\)
y(2y + 3x) - x(2y + 3x)
= (y - x)(2y + 3x)
Construct a quadratic equation whose roots are \(-\frac{1}{2}\) and 2.
If x = \(-\frac{1}{2}\) and 2; then
\(x + \frac{1}{2} = 0\) and \(x - 2 = 0\)
\(\implies (x + \frac{1}{2})(x - 2) = 0\)
\(x^2 - 2x + \frac{1}{2}x - 1 = 0\)
\(x^2 - \frac{3}{2}x - 1 = 0\)
\(2x^2 - 3x - 2 = 0\)
Write as a single fraction \(\frac{1}{1 - x} + \frac{2}{1 + x}\)
\(\frac{1}{1 - x} + \frac{2}{1 + x}\)
= \(\frac{(1 + x) + 2(1 - x)}{(1 - x)(1 + x)}\)
= \(\frac{1 + x + 2 - 2x}{1 - x^2}\)
= \(\frac{3 - x}{1 - x^2}\)
What must be added to the expression x\(^2\) - 18x to make it a perfect square?
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.
\(x^2 - 18x + (\frac{-18}{2})^2\)
= \(x^2 - 18x + 81\)
Solve the equation \(\frac{m}{3} + \frac{1}{2} = \frac{3}{4} + \frac{m}{4}\)
\(\frac{m}{3} + \frac{1}{2} = \frac{3}{4} + \frac{m}{4}\)
\(\frac{m}{3} - \frac{m}{4} = \frac{3}{4} - \frac{1}{2}\)
\(\frac{m}{12} = \frac{1}{4}\)
\(4m = 12 \implies m = 3\)