Primary 5 Mathematics Rate Quiz

Answer Key: Primary 5 Mathematics Quiz - Rate

Total Marks: 50

Section A: Multiple Choice Questions (10 marks)

1. B) 30

• Marks: 2
• Working: Rate = Total pages ÷ Total time = 120 pages ÷ 4 minutes = 30 pages per minute.
• Explanation: Rate is the amount of one quantity per unit of another quantity. Here, we find pages per minute by dividing the total pages by the total minutes.
• Common mistake: Students may multiply 120 × 4 = 480 (option D), confusing rate with total.

2. C) 80

• Marks: 2
• Working: Average speed = Total distance ÷ Total time = 240 km ÷ 3 hours = 80 km/h.
• Explanation: Speed is a rate that tells us how far something travels in one unit of time (usually one hour). We divide distance by time.
• Common mistake: Students may divide time by distance (3 ÷ 240 = 0.0125) or multiply (240 × 3 = 720).

3. C) 40

• Marks: 2
• Working: Total water = Rate × Time = 5 litres/minute × 8 minutes = 40 litres.
• Explanation: When we know the rate (amount per minute) and the time, we multiply to find the total amount.
• Common mistake: Students may add (5 + 8 = 13) or divide (8 ÷ 5 = 1.6).

4. D) 60

• Marks: 2
• Working: Rate = Total toys ÷ Total time = 360 toys ÷ 6 hours = 60 toys per hour.
• Explanation: To find the number of toys produced in one hour, we divide the total by the number of hours.
• Common mistake: Students may divide 6 ÷ 360 = 0.0167, confusing the order of division.

5. C) 60

• Marks: 2
• Working: Distance = Speed × Time = 15 km/h × 4 hours = 60 km.
• Explanation: Distance travelled is found by multiplying speed (rate) by time.
• Common mistake: Students may divide (15 ÷ 4 = 3.75) or add (15 + 4 = 19).

Section B: Short Answer Questions (20 marks)

6. 0.125 kg per loaf (or 1/8 kg per loaf)

• Marks: 2 (1 mark for correct method, 1 mark for correct answer)
• Working: Rate = 3 kg ÷ 24 loaves = 0.125 kg per loaf.
• Explanation: To find the amount of flour per loaf, divide the total flour by the number of loaves.
• Common mistake: Students may divide 24 ÷ 3 = 8, getting "8 loaves per kg" instead of "kg per loaf."

7. 8 km per litre

• Marks: 2
• Working: Rate = 96 km ÷ 12 litres = 8 km per litre.
• Explanation: To find how many km the car travels per litre of petrol, divide distance by petrol used.
• Common mistake: Students may divide 12 ÷ 96 = 0.125, getting litres per km instead of km per litre.

8. 30 boxes per minute

• Marks: 2
• Working: Rate = 150 boxes ÷ 5 minutes = 30 boxes per minute.
• Explanation: Divide the total boxes by the total minutes to find the rate per minute.
• Common mistake: Students may multiply 150 × 5 = 750.

9. 9 minutes

• Marks: 2
• Working: Time = Total water ÷ Rate = 18 litres ÷ 2 litres/minute = 9 minutes.
• Explanation: To find time, divide the total amount by the rate.
• Common mistake: Students may multiply 18 × 2 = 36.

10. 270 km

• Marks: 2
• Working: Distance = Speed × Time = 90 km/h × 3 hours = 270 km.
• Explanation: Multiply speed by time to find total distance.
• Common mistake: Students may divide 90 ÷ 3 = 30.

11. 420 bottles

• Marks: 2
• Working: Rate = 240 bottles ÷ 4 hours = 60 bottles per hour. Then, 60 bottles/hour × 7 hours = 420 bottles.
• Explanation: First find the rate per hour, then multiply by the new time.
• Common mistake: Students may do 240 ÷ 4 × 7 but forget the order of operations or skip finding the rate first.

12. $120

• Marks: 2
• Working: Total earnings = Rate × Time = $15/hour × 8 hours =$120.
• Explanation: Multiply the hourly rate by the number of hours worked.
• Common mistake: Students may add 15 + 8 = 23.

13. 72 litres

• Marks: 2
• Working: Total water = Rate × Time = 6 litres/minute × 12 minutes = 72 litres.
• Explanation: Multiply the rate by the time to find the total amount of water.
• Common mistake: Students may divide 12 ÷ 6 = 2.

Section C: Problem Sums (20 marks)

14. 60 km/h

• Marks: 2 (1 mark for correct method, 1 mark for correct answer)
• Working: Average speed = 180 km ÷ 3 hours = 60 km/h.
• Explanation: Speed is a rate that tells distance per unit time. Divide total distance by total time.
• Common mistake: Students may write 180 ÷ 3 = 60 but forget the units (km/h).

15. 600 pencils per hour

• Marks: 2
• Working: Rate = 3600 pencils ÷ 6 hours = 600 pencils per hour.
• Explanation: Divide the total number of pencils by the total hours to find the rate per hour.
• Common mistake: Students may divide 6 ÷ 3600 = 0.00167.

16. 288 pages

• Marks: 3 (1 mark for finding rate, 1 mark for correct multiplication, 1 mark for correct answer)
• Working:
  • Step 1: Find rate per minute: 180 pages ÷ 5 minutes = 36 pages per minute.
  • Step 2: Find pages in 8 minutes: 36 pages/minute × 8 minutes = 288 pages.
• Explanation: First find the unit rate (pages per minute), then multiply by the new time.
• Common mistake: Students may do 180 ÷ 5 × 8 but make an arithmetic error.

17. 14 litres

• Marks: 3 (1 mark for correct method, 1 mark for correct working, 1 mark for correct answer)
• Working:
  • Method 1 (Unitary): 1 litre → 14 km. To travel 196 km: 196 km ÷ 14 km/litre = 14 litres.
  • Method 2 (Proportion): 1/14 = x/196, so x = 196/14 = 14 litres.
• Explanation: Find how many groups of 14 km are in 196 km. Each group needs 1 litre.
• Common mistake: Students may multiply 196 × 14 = 2744.

18. 160 litres

• Marks: 3 (1 mark for finding water already in tank, 1 mark for correct method, 1 mark for correct answer)
• Working:
  • Step 1: Water already in tank = Rate × Time = 8 litres/minute × 15 minutes = 120 litres.
  • Step 2: Total capacity = Water in tank + Water needed = 120 litres + 40 litres = 160 litres.
• Explanation: First find how much water has been added in 15 minutes, then add the amount still needed.
• Common mistake: Students may forget to add the 40 litres needed and just give 120 litres.

19. 7 kg

• Marks: 3 (1 mark for finding sugar per cake, 1 mark for correct method, 1 mark for correct answer)
• Working:
  • Step 1: Sugar per cake = 5 kg ÷ 40 cakes = 0.125 kg per cake.
  • Step 2: Sugar for 56 cakes = 0.125 kg/cake × 56 cakes = 7 kg.
• Explanation: Find the unit rate (sugar per cake), then multiply by the new number of cakes.
• Alternative method: 40 cakes → 5 kg. 1 cake → 5/40 = 1/8 kg. 56 cakes → 56/8 = 7 kg.
• Common mistake: Students may do 5 ÷ 40 × 56 but make a calculation error.

20. 3 hours

• Marks: 4 (1 mark for finding distance, 1 mark for correct method for return time, 1 mark for correct working, 1 mark for correct answer)
• Working:
  • Step 1: Distance from Town A to Town B = Speed × Time = 60 km/h × 4 hours = 240 km.
  • Step 2: Time for return journey = Distance ÷ Speed = 240 km ÷ 80 km/h = 3 hours.
• Explanation: The distance is the same for both journeys. First find the distance using the outbound speed and time. Then use the return speed to find the return time.
• Common mistake: Students may average the speeds (60 + 80) ÷ 2 = 70 km/h and use that, which is incorrect because the time spent at each speed is different.
• Marking note: Award 1 mark for finding the distance (240 km). Award 1 mark for the correct method for return time. Award 1 mark for correct working. Award 1 mark for the correct final answer (3 hours).