(a) On Sam's first birthday celebration, his... | WAEC SSCE - General Mathematics - 2021 (Essay)

Question 1 Report

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

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

(b)

In the diagram, ABCD are points on the circle with centre O. If $|AB| = |BC|$ and $\angle ADC = 50^\circ$, find $\angle BAD$.

Answer

(a) Compound interest. $\$1000$ at $4\%$ per annum, from the 1st birthday until age 4 is 3 years of growth (multiplier $1.04$ each year):

End of yr 2: $\frac{104}{100}\times1000=\$1040.00$; yr 3: $\frac{104}{100}\times1040=\$1081.60$; yr 4: $\frac{104}{100}\times1081.60=\$1124.86$.

\[A=1000\Big(1+\tfrac{4}{100}\Big)^{3}=1000(1.04)^{3}=\mathbf{\$1124.86}.\]

(b) Circle geometry. $A,B,C,D$ lie on a circle centre $O$, $|AB|=|BC|$, $\angle ADC=50^{\circ}$, and $AC$ subtends $\angle ADC$ with $\angle ACD=90^{\circ}$ (angle in a semicircle, $AD$ a diameter).

In $\triangle ACD$: $\angle CAD=180^{\circ}-50^{\circ}-90^{\circ}=40^{\circ}$.

$ABCD$ is cyclic, so $\angle ABC=180^{\circ}-\angle ADC=130^{\circ}$. Since $|AB|=|BC|$, $\triangle ABC$ is isosceles with $\angle BAC=\angle BCA$:

\[2\angle BAC+130^{\circ}=180^{\circ}\Rightarrow\angle BAC=25^{\circ}.\]

\[\angle BAD=\angle CAD+\angle BAC=40^{\circ}+25^{\circ}=\mathbf{65^{\circ}}.\]

Read lesson note on Modular Arithmetic (WAEC)

Read lesson note on Coordinate Geometry (WAEC)

Answer Details

(a) Compound interest. $\$1000$ at $4\%$ per annum, from the 1st birthday until age 4 is 3 years of growth (multiplier $1.04$ each year):

End of yr 2: $\frac{104}{100}\times1000=\$1040.00$; yr 3: $\frac{104}{100}\times1040=\$1081.60$; yr 4: $\frac{104}{100}\times1081.60=\$1124.86$.

\[A=1000\Big(1+\tfrac{4}{100}\Big)^{3}=1000(1.04)^{3}=\mathbf{\$1124.86}.\]

In $\triangle ACD$: $\angle CAD=180^{\circ}-50^{\circ}-90^{\circ}=40^{\circ}$.

$ABCD$ is cyclic, so $\angle ABC=180^{\circ}-\angle ADC=130^{\circ}$. Since $|AB|=|BC|$, $\triangle ABC$ is isosceles with $\angle BAC=\angle BCA$:

\[2\angle BAC+130^{\circ}=180^{\circ}\Rightarrow\angle BAC=25^{\circ}.\]

\[\angle BAD=\angle CAD+\angle BAC=40^{\circ}+25^{\circ}=\mathbf{65^{\circ}}.\]

Read lesson note on Modular Arithmetic (WAEC)

Read lesson note on Coordinate Geometry (WAEC)

Modular Arithmetic

Coordinate Geometry

View Answer

(a) On Sam's first birthday celebration, his grandfather deposited an amount of $1,000.00 in a bank at compound interest of 4% per annum. Find how much is i...

Download The App On Google Playstore

(a) On Sam's first birthday celebration, his grandfather deposited an amount of $1,000.00 in a bank at compound interest of 4% per annum. Find how much is i...

Related Questions

Download The App On Google Playstore