1. (a) Problem: A box contains 80 plant seeds. Ben takes $\frac{1}{8}$, Clara takes $\frac{1}{4}$. Find: (i) fraction taken, (ii) number left. Step 1: Calculate fraction taken: $\frac{1}{8} + \frac{1}{4} = \frac{1}{8} + \frac{2}{8} = \frac{3}{8}$. Step 2: Calculate seeds taken: $80 \times \frac{3}{8} = 30$. Step 3: Calculate seeds left: $80 - 30 = 50$. (b) Simplify $\frac{18x^2 y^2}{24x^3 y^3}$ for $x=2$, $y=5$. Step 1: Simplify expression: $\frac{18}{24} \cdot \frac{x^2}{x^3} \cdot \frac{y^2}{y^3} = \frac{3}{4} \cdot \frac{1}{x} \cdot \frac{1}{y} = \frac{3}{4xy}$. Step 2: Substitute values: $\frac{3}{4 \times 2 \times 5} = \frac{3}{40} = 0.075$. (c) Simplify expressions: (i) $-7x + 8y - 2x - 3y$ Step 1: Combine like terms: $(-7x - 2x) + (8y - 3y) = -9x + 5y$. (ii) $2(3a - b) - 7(-2a + b)$ Step 1: Expand: $6a - 2b + 14a -7b = (6a+14a) + (-2b - 7b) = 20a - 9b$. (d) (i) Given shape: top length $2x$, height $3y$, bottom length $4y$, right vertical $6x$. Step 1: Assume shape is composite rectangles. Area = sum of areas. Step 2: Area of rectangle 1 (top): $2x \times 3y = 6xy$. Step 3: Area of rectangle 2 (bottom): length $4y$, height $6x - 3y$ (assuming) Area = $4y \times (6x - 3y) = 24xy - 12y^2$. Step 4: Total area = $6xy + 24xy - 12y^2 = 30xy - 12y^2$. (ii) Find value of $-x^2 +4y$ at $x=4$, $y=-3$. Step 1: Calculate: $-(4)^2 + 4(-3) = -16 - 12 = -28$. 4. (a) Coconut vendor sells 120 coconuts/day, 6 days/week, for 40 weeks. Step 1: Total coconuts = $120 \times 6 \times 40 = 28800$. Step 2: Express in standard form: $2.88 \times 10^4$. Step 3: Calculate $0.00182 \times 0.00013$. Step 4: Multiply: $0.00182 \times 0.00013 = 2.366 \times 10^{-7}$ (in standard form). (b) Cell phone cost: $40$ per month plus $35$ activation fee. Step 1: Expression for $m$ months: $40m + 35$. Step 2: For $m=10$: $40 \times 10 + 35 = 435$. (c) (i) Solve $\frac{5}{x} + 3x = \frac{23}{6}$. Step 1: Multiply both sides by $6x$: $6 \times 5 + 6x \times 3x = 6x \times \frac{23}{6}$ gives $30 + 18x^2 = 23x$. Step 2: Rearrange: $18x^2 - 23x + 30 = 0$. Step 3: Solve quadratic using discriminant: $\Delta = (-23)^2 - 4 \times 18 \times 30 = 529 - 2160 = -1631 < 0$ no real solution. (ii) Fourteen less than eight times a number equals three more than four times the number. Step 1: Let number be $x$: $8x - 14 = 4x + 3$. Step 2: $8x - 4x = 3 + 14 \Rightarrow 4x = 17 \Rightarrow x = \frac{17}{4} = 4.25$. (d) Angela's garden fence problem: Step 1: Calculate perimeter: sum of all sides = $15 + 11 + 7 + 21 = 54$ m. Step 2: Fence cost per 2m = 15, so cost per m = $\frac{15}{2} = 7.5$. Step 3: Total cost = $54 \times 7.5 = 405$. Step 4: Budget $500$ meets cost since $405 \leq 500$. Final answers: 1.(a)(i) $\frac{3}{8}$; (ii) $50$ seeds left (b) $\frac{3}{40} = 0.075$ (c)(i) $-9x + 5y$; (ii) $20a - 9b$ (d)(i) Area = $30xy - 12y^2$; (ii) $-28$ 4.(a) Total coconuts = $2.88 \times 10^4$; product $= 2.366 \times 10^{-7}$ (b) Cost expression = $40m + 35$; for $m=10$ cost = $435$ (c)(i) No real solution; (ii) Number $= 4.25$ (d) Cost $= 405$, budget sufficient.