1. **Question:** How many edges does a cuboid have? Choices: A. 6, B. 12, C. 8, D. 14. Step 1. Recall that a cuboid has 12 edges. **Answer:** B. 12 2. **Question:** Which of the following is NOT a basic arithmetic operator? A. Square root, B. Multiplication, C. Addition, D. Division. Step 1. Basic arithmetic operators are addition, subtraction, multiplication, division. Step 2. Square root is a mathematical operation but not a basic arithmetic operator. **Answer:** A. Square root 3. **Question:** Identify the incorrect statements: A. The square root of 4 is -2 and +2 B. When two positive numbers are multiplied the result is positive C. When two negative numbers are added together the result is positive D. Division of a negative and a positive number gives a negative result Step 1. The square root of 4 is +2 by definition; -2 is also a root but the principal root is +2. So statement A is incorrect. Step 2. Multiplying two positive numbers yields positive (True). Step 3. Adding two negative numbers results in a negative number (statement C is incorrect). Step 4. Division of negative by positive is negative (True). **Answer:** C. When two negative numbers are added together the result is positive 4. **Question:** Find sum of 27, -74, 84, -19. Step 1. Calculate: $$27 + (-74) + 84 + (-19) = (27 - 74) + (84 - 19) = -47 + 65 = 18$$ **Answer:** A. 18 5. **Question:** To make an estimate for work, the necessary data include drawings, specifications, and __________. Step 1. Options: Materials, Rates, Labours, Transportation. Step 2. Estimation requires knowing the rates (prices or costs). **Answer:** B. Rates 6. **Question:** Which is NOT a type of fraction? Step 1. Mixed numbers, improper fractions, and proper fractions are types. Step 2. Numerical fraction is not a standard category. **Answer:** D. Numerical fraction 7. **Question:** Which number is approximated to four decimal places? Options: 2154, 21.54, 2154.0012, 215.01 Step 1. Four decimal places means four digits after the decimal point. Step 2. 2154.0012 has exactly four digits after decimal. **Answer:** C. 2154.0012 8. **Question:** The map title gives information about: Options: What map shows, Position of north, Physical features, Human features. Step 1. The title gives information about what the map shows. **Answer:** A. What map shows 9. **Question:** Types of angles except? Options: Obtuse angle, Acute angle, Right angle, Corner angle Step 1. Corner angle is not a standard angle type. **Answer:** D. Corner angle 10. **Question:** What to add to $$6 + 0.6 + 0.06 + 0.006 = 6.666$$ to get 7? Step 1. Calculate the sum: $$6 + 0.6 + 0.06 + 0.006 = 6.666$$ Step 2. Required addition: $$7 - 6.666 = 0.334$$ **Answer:** B. 0.334 11. **Question:** Time reduced by 15% from 50 minutes. Find new time. Step 1. Calculate reduction: $$15\% \times 50 = 0.15 \times 50 = 7.5\text{ minutes}$$ Step 2. New time: $$50 - 7.5 = 42.5\text{ minutes}$$ **Answer:** 42.5 minutes 12. **Question:** Mass of 1200 pens, each 15 grams, convert to kilograms. Step 1. Total mass in grams: $$1200 \times 15 = 18000\text{ grams}$$ Step 2. Convert grams to kilograms: $$18000 \div 1000 = 18\text{ kilograms}$$ **Answer:** 18 kilograms 13. **Question:** Cut 273 cm into 3 pieces in ratio 3:7:11. Step 1. Sum of ratio parts: $$3 + 7 + 11 = 21$$ Step 2. Lengths: $$\text{Piece 1} = \frac{3}{21} \times 273 = 39 \text{ cm}$$ $$\text{Piece 2} = \frac{7}{21} \times 273 = 91 \text{ cm}$$ $$\text{Piece 3} = \frac{11}{21} \times 273 = 143 \text{ cm}$$ Step 3. Verify sum: $$39 + 91 + 143 = 273$$ **Answer:** 39 cm, 91 cm, and 143 cm 14. **Question:** 3 people take 4 hours. How long will 5 people take? Step 1. The rate of work is inversely proportional: $$\text{Time} \times \text{People} = \text{constant}$$ Step 2. Calculate total work: $$3 \times 4 = 12 \text{ person-hours}$$ Step 3. Time for 5 people: $$\frac{12}{5} = 2.4 \text{ hours} = 2 \text{ hours and } 24 \text{ minutes}$$ **Answer:** 2.4 hours 15. **Question:** Cross sectional area of pipe is 320 mm². Find diameter. Step 1. Area formula: $$A = \pi r^2$$ Step 2. Solve for radius: $$r = \sqrt{\frac{A}{\pi}} = \sqrt{\frac{320}{3.1416}} \approx \sqrt{101.86} \approx 10.09\text{ mm}$$ Step 3. Diameter: $$d = 2r = 2 \times 10.09 = 20.18 \text{ mm}$$ **Answer:** Approximately 20.18 mm 16. **Question:** Surface area of open cylinder; diameter 3.5 cm, height 45 cm, answer in m². Step 1. Radius: $$r = \frac{3.5}{2} = 1.75 \text{ cm}$$ Step 2. Surface area of open cylinder (curved surface + base): $$A = \pi r^2 + 2 \pi r h$$ Step 3. Calculate: $$\pi r^2 = 3.1416 \times 1.75^2 = 3.1416 \times 3.0625 = 9.621 \text{ cm}^2$$ $$2 \pi r h = 2 \times 3.1416 \times 1.75 \times 45 = 2 \times 3.1416 \times 78.75 = 494.34 \text{ cm}^2$$ Step 4. Total area: $$9.621 + 494.34 = 503.96 \text{ cm}^2$$ Step 5. Convert to m²: $$503.96 \text{ cm}^2 = 503.96 \times 10^{-4} = 0.0504 \text{ m}^2$$ **Answer:** Approximately 0.0504 m² 17. **Question:** A traveler left Voi to Kitale, 520 km, at 11:00 p.m. Travels 3 hours at 60 km/h, rests 30 mins, arrives at 9:38 a.m. Find: (i) Average speed for whole journey (ii) Average speed for second part Step 1. Distance first part: $$60 \text{ km/h} \times 3 \text{ h} = 180 \text{ km}$$ Step 2. Remaining distance: $$520 - 180 = 340 \text{ km}$$ Step 3. Total time from 11:00 p.m. to 9:38 a.m.: From 11:00 p.m. to midnight = 1 hour Midnight to 9:38 a.m. = 9 hours 38 minutes = 9.633 hours Total = 1 + 9.633 = 10.633 hours Step 4. Subtract rest time 0.5 hours: Effective travel time = 10.633 - 0.5 = 10.133 hours Step 5. Average speed whole journey: $$\frac{\text{Total distance}}{\text{Total time}} = \frac{520}{10.133} \approx 51.3 \text{ km/h}$$ Step 6. Time second part: $$\text{Total travel time} - \text{first part time} = 10.133 - 3 = 7.133 \text{ hours}$$ Step 7. Average speed second part: $$\frac{340}{7.133} \approx 47.65 \text{ km/h}$$ **Answers:** (i) 51.3 km/h (ii) 47.65 km/h 18. **Question:** John is twice as old as son (S), daughter is 5 years younger than son, wife is 6 years younger than John. Daughter is 25 years old. Find ages. Step 1. Let son's age be $S$. John's age = $2S$ Daughter's age = $S - 5$ Wife's age = $2S - 6$ Step 2. Daughter's age = 25, so: $$S - 5 = 25 \implies S = 30$$ Step 3. John's age: $$2S = 2 \times 30 = 60$$ Step 4. Wife's age: $$60 - 6 = 54$$ **Answer:** Son = 30 years, John = 60 years, Daughter = 25 years, Wife = 54 years