WAEC 2019 · Paper 2 · Q4

(a)
If $\log_{10} a = 1.3010$ and $\log_{10} b = 1.4771$ , find the value of $ab$ .
(b)
In the diagram, $O$ is the centre of the circle, $ABE$ is a straight line, $\angle ACB = 39^\circ$ and $\angle CBE = 62^\circ$ . Find: (i) the interior angle $AOC$ ; (ii) angle $BAC$ .
Separate values with commas, e.g. 3, −2

Worked solution (try it first)

(a)

Add the logs to multiply: $\log_{10}(ab) = 1.3010 + 1.4771 = 2.7781$ .
So $ab = 10^{2.7781} \approx 600$ .
(In fact $\log 20 = 1.3010$ and $\log 30 = 1.4771$ , so $ab = 20 \times 30 = 600$ .)

(b)(i)

$ABE$ is a straight line, so $\angle ABC = 180^\circ - 62^\circ$
$= 118^\circ$ .
The angle at the centre is twice the angle at the circumference on the same arc, so the reflex angle $AOC = 2 \times 118^\circ = 236^\circ$ , and the interior angle $AOC = 360^\circ - 236^\circ = 124^\circ$ .

(ii)

In triangle $ABC$ : $\angle BAC = 180^\circ - 39^\circ - 118^\circ$
$= 23^\circ$ .

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