1. Calculate $ (5 + 47)^2 $. Calculate the sum inside the parentheses first: $$ 5 + 47 = 52 $$ Now square the result: $$ 52^2 = 52 \times 52 = 2704 $$ Answer: $2704$ 2. Write $48.9855$ correct to two decimal places. Look at the third decimal place (which is 5) to decide rounding. Since it is 5 or more, round the second decimal place up: $$ 48.98 \to 48.99 $$ Answer: $48.99$ 3. Given numbers: $120$, $121$, $123$, $124$, $125$. (a) Square number: check which number is a perfect square. $121 = 11^2$ so answer is $121$. (b) Common factor of $375$ and $500$: Find factors: $375 = 3 \times 5^3$ $500 = 2^2 \times 5^3$ Common factors include $5^3 = 125$. So answer: $125$ (c) Multiple of $41$ from the list: Check multiples of $41$: $41 \times 3 = 123$ So answer: $123$ 4. Convert $0.6$ km to meters. 1 km = 1000 m, so: $$ 0.6 \times 1000 = 600 \text{ meters} $$ Answer: $600$ m 5. Write missing numbers in sequences: (a) $48.2; 45.5; 42.8; 40.1; ... ; 34.7$ Find the difference between terms: $45.5 - 48.2 = -2.7$ $42.8 - 45.5 = -2.7$ $40.1 - 42.8 = -2.7$ So next term: $$40.1 - 2.7 = 37.4$$ (b) $1; 9; 25; 49; ... ; 121$ These are squares of odd numbers: $1^2=1$, $3^2=9$, $5^2=25$, $7^2=49$, next is $9^2=81$, last is $11^2=121$ Answer: $81$ 6. Calculate change from $50$ after buying items: Tea bags = $14.95$ Cooking oil = $18.50$ Total cost: $$14.95 + 18.50 = 33.45$$ Change: $$50 - 33.45 = 16.55$$ Answer: $16.55$ 7. Lower bound of time $t$ for $15.8$ seconds correct to 1 decimal place Lower bound is the smallest value $t$ can have before rounding up: For 1 decimal place: $$ 15.8 - 0.05 = 15.75 $$ Answer: $15.75$ seconds 8. Use $>,<$ or $=$ to compare: (a) $3.12$ ? $3.1222$ Since $3.12 = 3.1200$, $3.1200 < 3.1222$, so: $$3.12 < 3.1222$$ (b) $-4.5$ ? $-5.4$ Since $-4.5 > -5.4$, so: $$-4.5 > -5.4$$ (c) $13$ ? $3$ Clearly, $$13 > 3$$ 9. Family arrives at $17:20$ after $7$ hours $45$ minutes journey. Find start time by subtracting journey time: $17:20 - 7:45$ Subtract hours: $17:20 - 7:00 = 10:20$ Subtract minutes: $10:20 - 0:45 = 9:35$ Answer: $9:35$ 10. Mrs Kazonga invests $4200$ at $5\%$ compound interest for 2 years. Formula: $$A = P(1 + r)^n$$ $$= 4200 \times (1 + 0.05)^2 = 4200 \times 1.1025 = 4629$$ Answer: $4629$ 11. Temp difference between $5 ^\circ C$ and $-4 ^\circ C$: $$5 - (-4) = 5 + 4 = 9$$ Answer: $9$ °C 12. Percentage increase from $62750$ to $85420$: Increase: $$85420 - 62750 = 22670$$ Percentage increase: $$\frac{22670}{62750} \times 100 = 36.14\%$$ Answer: $36.14$ 13. Masses are: Baking powder: $100$ kg Flour: $2$ kg Sugar: $4$ kg Butter: $4$ kg (a) Total mass: $$100 + 2 + 4 + 4 = 110$$ kg (b) Fraction of flour: $$\frac{2}{110} = \frac{1}{55}$$ 14. Simplify: (a) $y^5$ No change needed. (b) $8f - 2e + 10f - 12e = (8f + 10f) + (-2e - 12e) = 18f - 14e$ (c) Multiply out $4w^2(5w - 4w^3y)$: $$4w^2 \times 5w = 20w^3$$ $$4w^2 \times (-4w^3 y) = -16w^{5}y$$ Answer: (a) $y^5$ (b) $18f - 14e$ (c) $20w^{3} - 16w^{5}y$ 15. Solve $(x - 7)(2x - 1) = 0$ Zero product property: $x - 7 = 0 \Rightarrow x = 7$ $2x - 1 = 0 \Rightarrow x = \frac{1}{2}$ 16. Find $8^{-1}$ as a fraction: By definition: $$8^{-1} = \frac{1}{8}$$ Answer: $\frac{1}{8}$ 17. Measure angle ABC: Since no measure given, cannot provide numerical answer. 18. Given graph details: (a) Coordinates of point Q: From the graph, Q at $(2,4)$ (b) y-intercept of line p: where $x=0$, from graph $y=6$ (c) Gradient of line p: $$ m = \frac{\Delta y}{\Delta x} = \frac{6 - 4}{0 - 2} = \frac{2}{-2} = -1 $$ 19. Mathematical names of diagrams provided: Not visible, cannot answer. 20. Order of rotation: Not visible, cannot answer. 21. Volume of cuboid with dimensions $5 cm, 12 cm, h cm$ (height missing, assume 7 cm): Volume formula: $$ V = l \times w \times h = 5 \times 12 \times 7 = 420$$ cm$^3$ 22. Bearing of P from Q is $280^\circ$. Bearing of Q from P is given by: $$ (280 - 180) = 100^\circ $$ or $$ (280 + 180) - 360 = 100^\circ $$ Answer: $100^\circ$ 23. Given $p=-2$, $r=6$: (a) $p + r = -2 + 6 = 4$ (b) $3p = 3 \times (-2) = -6$ 24. Constructing perpendicular bisector of line MN: construction instructions provided, not numerical. 25. Heights frequency: Heights and frequency: 165: 4 166: 2 167: 1 168: 2 169: 2 170: 5 171: 1 (b) Probability of height exactly 166 cm: Total players count: $$4 + 2 + 1 + 2 + 2 + 5 + 1 = 17$$ Probability: $$ \frac{2}{17} $$ Probability height at least 165 cm = 1 (since all are 165 or above) 26. Pie chart with angles 100°, 150°, and x. Sum angles are $360^$: $$ x = 360 - (100+150) = 110^ $$ Fraction of people using wood: Wood angle = 150° Fraction: $$ \frac{150}{360} = \frac{5}{12} $$ 270 people use gas (100°), find total: $$ \text{Total} = \frac{270 \times 360}{100} = 972 $$ Electricity users angle = 110° Number using electricity: $$ \frac{110}{360} \times 972 = 297 $$ 27. Calculate angle SGP in triangle with sides 5 cm, 8 cm, and unknown opposite side. Assuming SGP is angle at G opposite side 5 cm: Use Law of Cosines: $$ SG = 5, GP = 8, SP = ? $$ If given other side lengths needed for calculation, use Law of Cosines: $$ \cos(\angle SGP) = \frac{SG^2 + GP^2 - SP^2}{2 \times SG \times GP} $$ Without length SP, cannot compute angle numerically.