iGCSE Mathematics (0580) - C1.13 Percentages- Exam Style Questions Paper 3- New Syllabus
▶️ Answer/Explanation
First, calculate Ali’s total investment using the compound interest formula.
$\text{Ali’s Total} = 2950 \times (1 + \frac{12}{100})^3$
$\text{Ali’s Total} = 2950 \times 1.12^3 = 4144.50$
Next, calculate Bob’s total investment using the simple interest formula.
$\text{Bob’s Interest} = \frac{3000 \times 12 \times 3}{100} = 1080$
$\text{Bob’s Total} = 3000 + 1080 = 4080$
Finally, comparing the final amounts: $\$4144.50$ is clearly greater than $\$4080$, showing Ali has the larger investment.
✅ Answer: Ali’s total (\$4144.50) is shown to be greater than Bob’s total (\$4080).
▶️ Answer/Explanation
(a)
First, calculate the absolute financial profit made: $\$4.64 – \$3.20 = \$1.44$.
The percentage profit formula is the profit divided by original cost price, all multiplied by 100.
$\frac{1.44}{3.20} \times 100 = 45\%$.
✅ Answer: 45
(b)
Use the standard volume formula for a cone shape: $V = \frac{1}{3}\pi r^2 h$.
Substitute the given measurements: $900 = \frac{1}{3} \times \pi \times r^2 \times 8$.
Rearrange to solve for the unknown variable: $r^2 = \frac{900 \times 3}{8\pi} \approx 107.43$.
Take the square root of this value to find the final radius length: $r = \sqrt{107.43} \approx 10.4\text{ cm}$.
✅ Answer: 10.4 (or 10.36…)