WAEC Mathematics Past Questions & Answers - Page 63

x +  2x + 2x + (x + $30^o$) + (x + $20^o$) + (x - $10^o$) = (2n - 4) x $90^o$

8x + 50 $^o$ - 10$^o$ = (2 x 6 -4) x 90$^o$

8x + 40$^o$ = 8 x 90$^o$ = 720$^o$

8x = 720$^o$ - 40$^o$ = 680$^o$

x = $\frac{680^o}{8}$

= 85$^o$

Surface area of a sphere = $4 \pi r^2$ $4 \pi r^2$ = $\frac{792}{7}cm^2$ 4 x $\frac{22}{7}$ x $r^2$ = $\frac{792}{7}$ $r^2$ = $\frac{792}{7}$ x $\frac{7}{4 \times 22}$ = 9 r = $\sqrt{9}$ = 3cm Hence, volume of sphere = $\frac{4}{3} \pi r^3$ = $\frac{4}{3} \times \frac{22}{7} \times 3 \times 3 \times 3$ = $\frac{4 \times 22 \times 9}{7}$ $\approx$ = 113.143 = 113$cm^3$ (to the nearest whole number)

Volume of a cylinder = $\pi r^2$h

385 = $\frac{22}{7}$ x $r^2$ x 10

385 x 7 = 22 x $r^2$ x 10

$r^2$ = $\frac{385 \times 7}{22 \times 10}$

= 12.25

r = $\sqrt{12.25}$

= 3.5m

Hence, diameter of tank = 2r

= 2 x 3.5 = 7m

Since the curve cuts the x-axis at x = -2 and x = 3,

(x + 2)(x - 3) = 0

$x^2 - 3x + 2x - 6$ = 0

$x^2 - x - 6$ = 0

Hence, the equation of the curve is

y = $x^2 - x - 6$

$\frac{2 - 18m^2}{1 + 3m}$ = $\frac{2(1 - 9)m^2}{1 + 3m}$

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

= $2(1 - 3m)$