2001 - WAEC Mathematics Past Questions and Answers - page 2
Evaluate \(\frac{1}{2}+\frac{3}{4}of\frac{2}{5}\div 1\frac{3}{5}\)
\(\frac{1}{2} + (\frac{3}{4} \text{ of } \frac{2}{5}) \div 1\frac{3}{5}\)
= \(\frac{1}{2} + (\frac{3}{4} \times \frac{2}{5}) \div \frac{8}{5}\)
= \(\frac{1}{2} + \frac{3}{10} \div \frac{8}{5}\)
= \(\frac{1}{2} + (\frac{3}{10} \times \frac{5}{8})\)
= \(\frac{1}{2} + \frac{3}{16}\)
= \(\frac{11}{16}\)
∴ 4x - x = 36; 3x = 36; x = 12
The son is 12 years and the father is 12 x 4 = 48.
The sum of their ages (12 + 48) years = 60years
Given that y = px + q and y = 5 when x = 3, while y = 4 when x = 2, find the value of p and q.
y = px + q
5 = 3p + q ... (i)
4 = 2p + q ... (ii)
(i) - (ii) : p = 1
\(\therefore\) 5 = 3(1) + q
\(\implies\) q = 5 - 3 = 2
(p, q) = (1, 2)
Evaluate \(\frac{x^2 + x - 2}{2x^2 + x -3}\) when x = -1
\(\frac{x^2 + x - 2}{2x^2 + x - 3}\)
= \(\frac{x^2 + 2x - x - 2}{2x^2 + 3x - 2x - 3}\)
= \(\frac{x(x + 2) - 1(x + 2)}{x(2x + 3) - 1(2x + 3)}\)
= \(\frac{(x - 1)(x + 2)}{(x - 1)(2x + 3)}\)
= \(\frac{x + 2}{2x + 3}\)
At x = -1,
= \(\frac{-1 + 2}{2(-1) + 3}\)
= \(\frac{1}{1}\)
= 1
Factorize \(6x^2 + 7x - 20\)
\(6x^2 + 7x - 20\)
= \(6x^2 + 15x - 8x - 20\)
= \(3x(2x + 5) - 4(2x + 5)\)
= \((3x - 4)(2x + 5)\)
Simplify \(\frac{2x-1}{3}-\frac{x+3}{2}\)
\(\frac{2x - 1}{3} - \frac{x + 3}{2}\)
= \(\frac{2(2x - 1) - 3(x + 3)}{6}\)
= \(\frac{4x - 2 - 3x - 9}{6}\)
= \(\frac{x - 11}{6}\)
If \(\frac{y-3}{2}<\frac{2y-1}{3}\), which of the following is true?
\(\frac{y - 3}{2} < \frac{2y - 1}{3}\)
\(3(y - 3) < 2(2y - 1)\)
\(3y - 9 < 4y - 2\)
\(3y - 4y < -2 + 9\)
\(-y < 7\)
\(y > -7\)
if \(\frac{4m+3n}{4m-3n}=\frac{5}{2}\), find the ratio m:n
\(\frac{4m + 3n}{4m - 3n} = \frac{5}{2}\)
\(5(4m - 3n) = 2(4m + 3n)\)
\(20m - 15n = 8m + 6n\)
\(20m - 8m = 6n + 15n\)
\(12m = 21n\)
\(\frac{21}{12} = \frac{m}{n}\)
\(m : n = 7 : 4\)
∴2x^2 + kx - 14 = 2x^2 - 3x - 14\)
equating coefficient K = -3
which of the following is not quadratic expression?
A quadratic equation is an equation of the second order. The highest power in the equation is 2.