1. (a) Evaluate the expressions exactly. (i) Calculate $\left(\frac{3}{2}\right)^2 - 1 + 6$. Step 1: Square $\frac{3}{2}$: $$\left(\frac{3}{2}\right)^2 = \frac{9}{4}$$ Step 2: Substitute and simplify: $$\frac{9}{4} - 1 + 6 = \frac{9}{4} - \frac{4}{4} + \frac{24}{4} = \frac{9 - 4 + 24}{4} = \frac{29}{4}$$ Answer: $\frac{29}{4}$. (ii) Calculate $2.1 \times \frac{10}{7} + 12 \div 1 \frac{3}{5}$. Step 1: Convert mixed number to improper fraction: $$1 \frac{3}{5} = \frac{8}{5}$$ Step 2: Calculate $2.1 \times \frac{10}{7}$: $$2.1 = \frac{21}{10}, \quad \frac{21}{10} \times \frac{10}{7} = \frac{21}{7} = 3$$ Step 3: Calculate $12 \div \frac{8}{5} = 12 \times \frac{5}{8} = \frac{60}{8} = \frac{15}{2}$ Step 4: Add results: $$3 + \frac{15}{2} = \frac{6}{2} + \frac{15}{2} = \frac{21}{2}$$ Answer: $\frac{21}{2}$. 1. (b) Maranda's earnings and savings. (i) She spends $\frac{4}{7}$ of her earnings, so she saves $1 - \frac{4}{7} = \frac{3}{7}$. Convert to percentage: $$\frac{3}{7} \times 100 = 42.857\%$$ (approximately 42.86%). Answer: She saves approximately 42.86% of her monthly salary. (ii) The spending on utility bills, food, and personal items is divided in ratio 5:3:4. Total parts: $5 + 3 + 4 = 12$. Amount spent on personal items: $$\frac{4}{12} \times \frac{4}{7} \times 8316 = \frac{4}{12} \times \frac{4}{7} \times 8316$$ Calculate stepwise: $$\frac{4}{12} = \frac{1}{3}$$ $$\frac{1}{3} \times \frac{4}{7} = \frac{4}{21}$$ $$\frac{4}{21} \times 8316 = \frac{4 \times 8316}{21} = \frac{33264}{21} = 1584$$ Answer: She spends 1584 on personal items. (iii) Monthly savings: $$\frac{3}{7} \times 8316 = \frac{3 \times 8316}{7} = \frac{24948}{7} = 3564$$ Annual savings: $$3564 \times 12 = 42768$$ Answer: Annual savings is 42768. (iv) Compound interest formula: $$A = P \left[1 + \frac{r}{100}\right]^n$$ Given: $P = 42768$, $r = 5$, $n = 2$. Calculate final amount: $$A = 42768 \left(1 + \frac{5}{100}\right)^2 = 42768 \times (1.05)^2 = 42768 \times 1.1025 = 47144.52$$ Interest earned: $$47144.52 - 42768 = 4376.52$$ Answer: Total interest earned after 2 years is approximately 4376.52.