WAEC 2018 · Paper 2 · Q12✱✱

(a)
Mr John paid ₦8,400.00 for ₦1.00 ordinary shares of a company which sold at ₦2.50 per share. If a dividend was declared at 25 kobo per share, how much dividend did he get?
(b)
Using the method of completing the square, solve $\dfrac{1 - x}{x} + \dfrac{x}{1 - x} = \dfrac52$ .
Separate values with commas, e.g. 3, −2

Worked solution (try it first)

(a)

The shares cost ₦2.50 each, so ₦8,400 buys $\frac{8400}{2.50} = 3360$ shares.
The dividend is 25 kobo (₦0.25) per share: $3360 \times 0.25 = 840$ , which is ₦840.00.

(b)

Multiply every term by $2x(1 - x)$ : $2(1 - x)^2 + 2x^2 = 5x(1 - x)$ .
Expand: $2 - 4x + 2x^2 + 2x^2 = 5x - 5x^2$ , so $9x^2 - 9x + 2 = 0$ .
Divide by 9: $x^2 - x = -\frac29$ .
Add $\left(\frac12\right)^2 = \frac14$ to both sides: $\left(x - \frac12\right)^2 = \frac14 - \frac29$
$= \frac{1}{36}$ .
So $x - \frac12 = \pm\frac16$ , giving $x = \frac23$ or $x = \frac13$ .

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