1. **Calculate the simple interest on 12000 for 3 years at 8% per annum.** Simple interest formula: $$SI = P \times r \times t$$ Where $P=12000$, $r=0.08$, $t=3$. Calculate: $$SI = 12000 \times 0.08 \times 3 = 2880$$ 2. **Determine the total amount after 3 years.** Total amount $A = P + SI = 12000 + 2880 = 14880$ 3. **Calculate compound interest on 15000 for 2 years at 10% p.a. compounded annually.** Compound amount formula: $$A = P(1 + r)^t$$ Where $P=15000$, $r=0.10$, $t=2$. Calculate: $$A = 15000(1 + 0.10)^2 = 15000 \times 1.21 = 18150$$ Compound interest $CI = A - P = 18150 - 15000 = 3150$ 4. **Find the percentage increase when price increases from 3500 to 3920.** Percentage increase formula: $$\text{Percentage increase} = \frac{3920 - 3500}{3500} \times 100 = \frac{420}{3500} \times 100 = 12\%$$ 5. **Data Handling: Marks: 4, 6, 7, 8, 10, 12, 14, 15, 16, 18** (a) Calculate mean, median, and mode. - Mean: $$\frac{4 + 6 + 7 + 8 + 10 + 12 + 14 + 15 + 16 + 18}{10} = \frac{110}{10} = 11$$ - Median: Middle two values are 10 and 12, so median is $$\frac{10 + 12}{2} = 11$$ - Mode: No repeating values, so no mode. (b) Box and whisker diagram: (No graph requested, so no plot.) - Minimum = 4 - Q1 (first quartile) = median of first half = median of 4,6,7,8,10 = 7 - Median = 11 - Q3 (third quartile) = median of second half = median of 12,14,15,16,18 = 15 - Maximum = 18 (c) Skewness comment: - Since mean = median = 11 and data is fairly symmetric, the distribution is approximately symmetric (no skew). (d) New mean if 5 marks added to each score: - New mean = old mean + 5 = 11 + 5 = 16