2012 - WAEC Mathematics Past Questions and Answers - page 3

y = 8\(\sqrt{m}\); log y = log 8\(\sqrt{m}\)

log y = log 8 + log \(\sqrt{m}\)

log y = log 2³ + log m^{\(\frac{1}{2}\)}

log y = 3 log 3 + \(\frac{1}{2}\) log m

x + 0.4y = 3...(i)

y = \(\frac{1}{2}\)x

x = 2y

x - 2y = 0....(ii)

solve simultaneously; x + 0.4y

= 3 - x - 2y = 0

2.4 = 3

y = \(\frac{3 \times 10}{2.4 \times 10} \)

= \(\frac{30}{24} = \frac{5}{4}\)

x - 2(\(\frac{5}{4}\)) = 0

x - \(\frac{5}{2}\) = 0

x = \(\frac{5}{2}\)

x + y = \(\frac{5}{2} + \frac{5}{4}\)

\(\frac{10 + 5}{4} = \frac{15}{4}\)

= 3\(\frac{3}{4}\)

(\(\frac{x -y}{y}\)); \(\frac{3}{1} - \frac{x y}{y}\)

= \(\frac{3y - (x - y)}{y}\)

= \(\frac{3y - x + y}{y}\)

= \(\frac{4y - x}{y}\)

prime factor of 210 = 2, 3, 5, 7

prime numbers less than 10 = 2, 3, 5 , 7

let the total amount be Nx i.e (\(\frac{1}{4}\))x + (\(\frac{1}{3}\))x + 72,000 = x

\(\frac{x}{4} + \frac{x}{4} + 72,000 = x\)

\(\frac{3x + 4x + 86,400}{12} = x\)

cross multiply to clear fraction

12x = 3x + 4x + 86,400

12x - 7x = 86,400

5x = 86,400

x - \(\frac{86,400}{5}\) = 172,800

amount spent on food = \(\frac{1}{4} \times 172,800\)

= N43,200

(\(\frac{27}{125}\))^{-\(\frac{1}{3}\)} x (\(\frac{4}{9}\))^{\(\frac{1}{2}\)}

= (\(\frac{3^3}{5^3}\))^{-\(\frac{1}{3}\)}_{-\(\frac{1}{3}\)} x (\(\frac{3^2}{3^2}\))^{\(\frac{1}{2}\)} _{-\(\frac{1}{2}\)}

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

= \(\frac{\frac{1}{3}}{\frac{1}{5}} \times \frac{2}{3}\)

\(\frac{1}{3} \times \frac{5}{1} \times {2}{3} = \frac{10}{9}\)

Sum = (n - 2)180

1800 = (n - 2)180

divide both sides by 180^o

\(\frac{1800}{180}\) = (n - 2)\(\frac{180}{180}\)

10 = n - 2

10 + 2 = n

n = 12

(\(\frac{m}{2} - 1\frac{1}{4}\))(m + \(\frac{2}{3}\))

(\(\frac{m}{2} - \frac{3}{2}\))(\(\frac{m}{1} + \frac{2}{3}\))

= \(\frac{m^2}{3} + \frac{3m}{6} - \frac{6}{6}\)

= \(\frac{2m - 9m}{6}\)

= \(\frac{-7m}{6}\)

= 1\(\frac{1}{6}\)