WAEC 2021 · Paper 2 · Q13

(a)
On Sam's first birthday celebration, his grandfather deposited an amount of $1,000.00 in a bank compounded at $4\%$ interest annually. Find how much is in the account if Sam is 4 years old.
(b)
In the diagram, $A$ , $B$ , $C$ , $D$ are points on the circle centre $O$ , with $AD$ a diameter. If $|AB| = |BC|$ and $\angle ADC = 50^\circ$ , find $\angle BAD$ .

Worked solution (try it first)

(a)

From his first birthday to when he is 4 is 3 years.
Compound interest at $4\%$ : $1000 \times 1.04^3 = 1000 \times 1.124864$
$\approx 1124.86$ , so the account holds $1,124.86.

(b)

Join $AC$ .
$AD$ is a diameter, so $\angle ACD = 90^\circ$ (angle in a semicircle) and $\angle CAD = 180^\circ - 90^\circ - 50^\circ$
$= 40^\circ$ .
$ABCD$ is cyclic, so $\angle ABC = 180^\circ - \angle ADC$
$= 130^\circ$ .
$|AB| = |BC|$ , so triangle $ABC$ is isosceles: $\angle BAC = \frac{180^\circ - 130^\circ}{2}$
$= 25^\circ$ .
$\angle BAD = \angle BAC + \angle CAD$
$= 25^\circ + 40^\circ$
$= 65^\circ$ .

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