1994 - WAEC Mathematics Past Questions and Answers - page 3

The points of intersection of the curve and the line are at x = -2 and x = 2.

\(\therefore\) (x + 2) = 0; (x - 2) = 0.

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

\(x^2 - 4 = 0\)

2p\(^2\) - 2 

2(p\(^2\) - 1)

= 2(p + 1)(p - 1)

x = 3; x = \(\frac{2}{3}\).

(x - 3)(x - \(\frac{2}{3}\)) = 0

\(x^2 - \frac{2x}{3} - 3x + 2 = 0\)

\(x^2 - \frac{11x}{3} + 2 = 0\)

\(3x^2 - 11x + 6 = 0\)

\(x^2 + 6x = 0\)

\(x(x + 6) = 0\)

\(x = 0\) or \(x = -6\)

\(6x^2 + 7xy - 5y^2\)

= \(6x^2 + 10xy - 3xy - 5y^2\)

= \(2x(3x + 5y) - y(3x + 5y)\)

= \((2x - y)(3x + 5y)\)

\(\frac{r}{6} = \sin 60 \)

\(r = 6 \sin 60\)

= \(6 \times \frac{\sqrt{3}}{2}\)

= \(3\sqrt{3}\)

Chord = 2r = \( 2 \times 3\sqrt{3}\)

= \(6\sqrt{3}\)

Volume of cuboid = length x breadth x height

12.5 x 20 x h = 1000

250h = 1000

h = 4 cm

Length of arc = \(\frac{\theta}{360} \times 2\pi r\)

= \(\frac{75}{360} \times 2 \times \frac{22}{7} \times 3.5\)

= \(4.583 cm\)

\(\approxeq\) 4.6 cm (to 2 sig. figs)