WAEC 2020 · Paper 2 · Q1

(a)
Two fractions have the same denominator, 8. The sum of the two fractions is $\frac12$ . If one of the fractions is added to 5 times the other, the result is 2. Find the two fractions.
Separate values with commas, e.g. 3, −2
(b)
If $a = \dfrac{mg - kv^2}{m}$ , find, correct to the nearest whole number, the value of $v$ when $a = 2.8$ , $m = 12$ , $g = 9.8$ and $k = \frac83$ .

Worked solution (try it first)

(a)

Let the two fractions be $\frac x8$ and $\frac y8$ (a different letter for each).
Their sum is $\frac12$ : $\frac x8 + \frac y8 = \frac12$ , so $x + y = 4$ (1).
One added to 5 times the other is 2: $\frac x8 + \frac{5y}{8} = 2$ , so $x + 5y = 16$ (2).
Take (1) from (2): $4y = 12$ , so $y = 3$ and $x = 1$ .
The fractions are $\frac18$ and $\frac38$ .

(b)

First make $v$ the subject.
Multiply by $m$ : $am = mg - kv^2$ .
Rearrange: $kv^2 = mg - am = m(g - a)$ .
So $v^2 = \frac{m(g - a)}{k}$ and $v = \sqrt{\frac{m(g - a)}{k}}$ .
Substitute: $v = \sqrt{\frac{12 \times (9.8 - 2.8)}{\frac83}}$
$= \sqrt{\frac{84 \times 3}{8}}$
$= \sqrt{31.5}$
$\approx 5.61$ .
To the nearest whole number, $v = 6$ .

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