1. Simplify $4^{5a+3b} + 3(2a-b)$. Step 1: Recognize $4^{5a+3b}$ is an exponential term that cannot be simplified further without values for $a$ and $b$. Step 2: Expand the second part: $3(2a-b) = 6a - 3b$. Final expression: $$4^{5a+3b} + 6a - 3b$$ 2. The distance on the map between towns is 15 cm, scale is 1 cm = 20 km. Calculate actual distance: $$15 \times 20 = 300$$ km. 3. Convert XLVI + XV to Hindu Arabic numerals. XLVI = 40 + 6 = 46 XV = 10 + 5 = 15 Sum: $$46 + 15 = 61$$ 4. Volume of cuboid with length=5 cm, width=4 cm, height=4 cm. Volume formula: $$V = l \times w \times h$$ Compute: $$5 \times 4 \times 4 = 80$$ cm³. 5. Measure angle marked X with adjacent angles 76° and 67°. If angle X is supplementary to sum of 76° and 67°, then $$X = 180° - (76° + 67°) = 180° - 143° = 37°$$ 6a. Draw bar graph and tally table for Abraham's subjects and marks: Kis(70), Eng(90), Maths(85), Sci(75), Socs(80), CRE(95), Music(80). 6b. Subjects with same marks: Socs(80) and Music(80). 6c. Total marks: $$70 + 90 + 85 + 75 + 80 + 95 + 80 = 575$$ 7. Area of shaded triangle with base=30 cm and height=12 cm. Formula: $$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$$ Compute: $$\frac{1}{2} \times 30 \times 12 = 180$$ cm². 8. Convert 23 kg 356 g to grams. $$23\text{ kg} = 23000\text{ g}$$ Total grams: $$23000 + 356 = 23356$$ g. 9. Add fractions: $\frac{3}{2} + 5 \frac{3}{4}$. Convert mixed number: $$5 \frac{3}{4} = \frac{23}{4}$$ Rewrite $\frac{3}{2}$ as $\frac{6}{4}$ Sum: $$\frac{6}{4} + \frac{23}{4} = \frac{29}{4} = 7 \frac{1}{4}$$ 10. Perimeter of Andrew's plot with length=75 m and width=68 m. Perimeter formula: $$P = 2(l + w) = 2(75 + 68) = 2 \times 143 = 286$$ m. 11. Work out: $0.083 + 12.3 + 4.8$. Sum: $$0.083 + 12.3 = 12.383$$ $$12.383 + 4.8 = 17.183$$ 12. Find the value of X given adjacent angles 76° and 67°. Assuming X is the angle between them: $$X = 180° - 76° - 67° = 37°$$ 13. Subtract lengths: $$15 \text{ km } 118 \text{ m } 5 \text{ cm} - 7 \text{ km } 200 \text{ m } 15 \text{ cm}$$ Convert: 15 km 118 m 5 cm = 15 km 118 m 5 cm Subtract 7 km 200 m 15 cm Borrow meters and centimeters: Meters: 118 m - 200 m (borrow 1 km=1000 m), meters = 1118 m - 200 m = 918 m Centimeters: 5 cm -15 cm (borrow 1 m=100 cm), centimeters = 105 cm - 15 cm = 90 cm Kilometers: 15 km - 7 km - 1 km (borrowed) = 7 km Result: 7 km 918 m 90 cm 14. Subtract 500 g from 3 1/4 kg. Convert 3 1/4 kg to grams: $$3.25 \text{ kg} = 3250 \text{ g}$$ Subtract: $$3250 - 500 = 2750 \text{ g}$$ Or back to kg: $$2.75 \text{ kg}$$ 15. Solve for $m$: $3(2m + 2) = 48$. Step 1: Expand left side: $$6m + 6 = 48$$ Step 2: Subtract 6: $$6m = 42$$ Step 3: Divide by 6: $$m = 7$$ 16. Josjam’s plot perimeter = 74 m, width = 14 m, find length. Formula: $$P = 2(l + w)$$ Solve for $l$: $$74 = 2(l + 14)$$ $$37 = l + 14$$ $$l = 23$$ m 17. Multiply $14 \times 5 \frac{2}{7}$. Convert mixed number: $$5 \frac{2}{7} = \frac{37}{7}$$ Multiply: $$14 \times \frac{37}{7} = 2 \times 37 = 74$$ 18. In right-angled triangle ABC, with $\angle ACB = 90°$, $AB = 8$ cm, $AC = 5$ cm. Find length $BC$ using Pythagoras theorem: $$BC = \sqrt{AB^2 - AC^2} = \sqrt{8^2 - 5^2} = \sqrt{64 - 25} = \sqrt{39} \approx 6.24$$ cm.