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})

V = L x B x H

V = \(2x \times x \times x = 2x^3\)

= 54cm3

i.e. 2x3 = 54

x3 = \(\frac{54}{2}\) = 27

x = 3\(\sqrt{27}\)

x = 3

L = 2x i.e. 2 x 3 = 6cm

B = x i.e. x = 3cm

H = x i.e. x = 3cm

but A = 2(LB + LH + BH) = 2(6 x 3) + (6 x 3) + (3 x 3) = 2(18 + 18 + 9) = 2(45)

= 90cm2