WAEC 2013 · Paper 2 · Q1✱✱

(a)
Evaluate $\left(1 - \frac{63}{64}\right)^{-\frac12} \times 2^{-1}$ .
(b)
The interior angle of a regular polygon is $108^\circ$ greater than the exterior angle. How many sides has the polygon?

Worked solution (try it first)

(a)

Work out the bracket first: $1 - \frac{63}{64} = \frac{1}{64}$ .
A negative power means turn the fraction upside down: $\left(\frac{1}{64}\right)^{-\frac12} = 64^{\frac12}$ .
A power of $\frac12$ is a square root: $64^{\frac12} = 8$ .
In the same way, $2^{-1} = \frac12$ .
Multiply: $8 \times \frac12 = 4$ .
The value is 4.

(b)

Let the exterior angle be $e$ .
The interior angle is then $e + 108^\circ$ .
An interior angle and its exterior angle make a straight line: $e + (e + 108^\circ) = 180^\circ$ .
So $2e = 72^\circ$ , which gives $e = 36^\circ$ .
The exterior angles of any polygon add up to $360^\circ$ , so the number of sides is $360^\circ \div 36^\circ = 10$ .
The polygon has 10 sides.

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