2017 - WAEC Mathematics Past Questions and Answers - page 2

\(\frac{3}{4}\) (3x - 2) < \(\frac{1}{2}\); \(\frac{3}{4}\) (3x - 2) > - \(\frac{1}{4}\)

3(3x - 2) < 2; 3(3x - 2) > -1

9x - 6 < 2; 9x - 6 > -1

9x < 8; 9x > 5

x < \(\frac{5}{9}\); x > \(\frac{8}{9}\)

3x - (p - x) - ( r - p)

= 3x - p + x - r + p

= 4x - r

lac = \(\frac{\theta}{360}\) x 2\(\pi\)r

7.5 = \(\frac{\theta}{360}\) x 2 x \(\frac{22}{7}\) x 7.5

7.5 = \(\frac{330\theta}{2520}\)

\(\theta\) = \(\frac{7.5}{0.1309}\)

\(\theta\) = 57.29

\(\theta\) = 57 \(^o\)

Volume of a cylinder = \(\pi r^2h\)

40\(\pi cm^3\) = \(\pi. 4^2h\)

40\(cm^3\) = 16h

h = 2.5cm/sec

In 4 seconds, 2.5cm x 4

= 10cm

Vol of a cubiod = L x b x h

v = 13cm  x 10cm x 70cm

= 9100cm

Since it is half-filled = \(\frac{9100}{2}\)cm

= 4550cm

4550cm \(\to\) 4.55 litres

T.S.A of hemisphere = 3\(\pi r^2\)

vol of hemisphere = \(\frac{2}{3} \pi r^2\)

3\(\pi r^2\) = \(\frac{2}{3} \pi r^2\)

3 = \(\frac{2}{3} \pi r\)

9 = 2r

r = \(\frac{9}{2}\)

r = 4.5cm

Gradient = m = \(\frac{y_2 - y_1}{x_2 - x_1}\)

= \(\frac{-2 -1}{2 + 1}\)

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

= -1

\(\sqrt{(x_2 - x_1)^2 + (y_2 - Y_1)^2}\)

= \(\sqrt{(2 - 2)^2 + (5 - 3)^2}\)

= \(\sqrt{0^2 + 2^2}\)

= \(\sqrt{4}\)

= 2 units