2021 WAEC Mathematics Theory (a) On Sam's first birthday celebration, his grandfather deposited an amount of S 1,000.00 in...

(a) On Sam's first birthday celebration, his grandfather deposited an amount of S 1,000.00 in a bank compound at 4 % interest annually.

Find how much is in the account if Sam is 4 years old.

(b) In the diagram above, ABCD are points on the circle centre O. If |AB| = |BC| and ∠ADC= 50°, find ∠BAD.

(a) Amount at end of the 2nd year = $\frac{104}{100}$ x $1000

= $1,040.00

Amount at end of 3rd year = $\frac{104}{100}$ x $1040

= $1,081.60

Amount at end of 4th year = $\frac{104}{100}$ x $1081.6

= $1,124.86

(b) ∠ADC + ∠DCA+ ∠CAD = 180°

50° + 90°+ ∠CAD = 180°

∠CAD = (180 - 140)°

= 40

∠ADC + ∠ABC = 180°

50° + ∠ABC = 180°

∠ABC =130°

∠BAC+ ∠BCA + ∠ABC = 180°

But ∠BAC = ∠BCA

2∠BAC+ ∠130° = 180°

2 ∠BAC=50°

∠BAC = 25°

∠BAD = ∠CAD + ∠BAC

= 40°+25° = 65°

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