1. (a) (i) Calculate the exact value of $1 \frac{4}{5} - 1 \frac{3}{2} \frac{2}{5}$. Step 1: Convert mixed numbers to improper fractions. $1 \frac{4}{5} = \frac{9}{5}$ $1 \frac{3}{2} \frac{2}{5}$ seems ambiguous; assuming it means $1 \frac{3}{2} + \frac{2}{5}$ or $1 \frac{3}{5} + \frac{2}{5}$, but likely a typo. Assuming the problem is $1 \frac{4}{5} - 1 \frac{3}{5} \frac{2}{5}$, which is unclear. Since the problem is ambiguous, let's interpret it as $1 \frac{4}{5} - 1 \frac{3}{5} - 2 \frac{2}{5}$. Step 2: Convert all to improper fractions: $1 \frac{4}{5} = \frac{9}{5}$ $1 \frac{3}{5} = \frac{8}{5}$ $2 \frac{2}{5} = \frac{12}{5}$ Step 3: Calculate $\frac{9}{5} - \frac{8}{5} - \frac{12}{5} = \frac{9 - 8 - 12}{5} = \frac{-11}{5} = -2 \frac{1}{5}$. (ii) Calculate $\sqrt{1.5625} + (0.32)^2$. Step 1: Calculate $\sqrt{1.5625}$. $\sqrt{1.5625} = 1.25$ Step 2: Calculate $(0.32)^2$. $(0.32)^2 = 0.1024$ Step 3: Add the results. $1.25 + 0.1024 = 1.3524$ (b) Determine the better buy between 350 ml at 4.20 and 450 ml at 5.13. Step 1: Calculate cost per ml for each size. $\text{Cost per ml for 350 ml} = \frac{4.20}{350} = 0.012$ $\text{Cost per ml for 450 ml} = \frac{5.13}{450} \approx 0.0114$ Step 2: Compare costs. Since 0.0114 < 0.012, the 450 ml carton is the better buy. (c) Faye borrowed 9600 at 8% compound interest. (i) Calculate interest for the first year. Formula: $\text{Interest} = \text{Principal} \times \text{Rate}$ $= 9600 \times 0.08 = 768$ (ii) Calculate amount owed at the beginning of the second year after repaying 4368. Step 1: Calculate total amount after first year. $9600 + 768 = 10368$ Step 2: Subtract repayment. $10368 - 4368 = 6000$ (iii) Calculate interest on remaining balance for second year. $6000 \times 0.08 = 480$ Final answers: 1. (a)(i) $-2 \frac{1}{5}$ 1. (a)(ii) $1.3524$ 1. (b) The 450 ml carton is the better buy because it has a lower cost per ml. 1. (c)(i) Interest for first year is 768. 1. (c)(ii) Amount owed at second year start is 6000. 1. (c)(iii) Interest for second year is 480.