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Chapter 7 Practice Paper: Ratio, Rate and Speed — mark scheme

QuizQuipPractice Series
QQ/S1MATH/CH7

Secondary 1 · Lower Secondary Mathematics (G2 / G3)

Mark scheme

Ratio, Rate and Speed

Chapter 7 Practice Paper · Maximum mark: 30

Notes for markers

  • Award one mark for each point marked [1], up to the marks shown for the part.
  • Accept answers worded differently that show the same understanding.
  • Units are required where the answer line shows one. ecf: allow an error carried forward.

Section A: Multiple-choice questions[10 marks]

QuestionAnswer
1BDivide both parts by the HCF 15: 45 ÷ 15 : 60 ÷ 15 = 3 : 4.1
2DThere are 11 equal parts, each worth $8. The shares are 5 × 8 = $40 and 6 × 8 = $48.1
3A12 is 3 times 4, so the missing number is 3 times 7: 21.1
4CRate = 250 ÷ 5 = 50 words per minute.1
5BDistance = speed × time = 65 × 4 = 260 km.1
6AThere are 12 parts, each worth $12. The largest share is 5 × 12 = $60.1
7DActual length = 8 × 25 000 = 200 000 cm = 2 000 m = 2 km.1
8CTime = distance ÷ speed = 90 ÷ 60 = 1.5 hours (1 h 30 min).1
9A4 m = 400 cm, and 8 : 400 = 1 : 50. Both lengths must be in the same unit first.1
10DAverage speed = 126 ÷ 1.5 = 84 km/h.1

Section B: Structured questions[20 marks]

QuestionAnswer and marking pointsMarks
1(a)

Divide all parts by the HCF 6: 3 : 4 : 5 [1]

1
1(b)

There are 9 parts, each worth 126 ÷ 9 = $14. The shares are 4 × 14 = $56 and 5 × 14 = $70.

  • Finds one part = $14 [1]
  • Shares $56 and $70 [1]
2
1(c)

The difference is 5 - 3 = 2 parts, and 2 parts = 12, so one part = 6. Total parts = 8, giving 8 × 6 = 48 marbles.

  • Links the difference of 12 to 2 parts [1]
  • Total 48 marbles [1]

Answers that assume the total is a multiple found by guessing a unit part must still verify 3 : 5 with a difference of 12.

2
Total for Question 15
2(a)

675 ÷ 3 = 225 bottles per minute

  • 225 bottles per minute [1]
  • Correct division shown [1]
2
2(b)

225 × 7 = 1 575 bottles [1]

1
2(c)

Time = 330 ÷ 24 = 13.75 minutes = 13 minutes 45 seconds.

  • 330 ÷ 24 = 13.75 min seen [1]
  • 0.75 min converted to 45 s, answer 13 min 45 s [1]
2
Total for Question 25
3(a)

3 h 15 min = 3.25 h, so the average speed is 260 ÷ 3.25 = 80 km/h.

  • Converts 3 h 15 min to 3.25 h [1]
  • Uses speed = distance ÷ time [1]
  • 80 km/h [1]
3
3(b)

Time = 150 ÷ 60 = 2.5 h = 2 hours 30 minutes.

  • 2.5 h [1]
  • Converted to 2 h 30 min [1]
2
Total for Question 35
4(a)

Actual distance = 5 × 40 000 = 200 000 cm = 2 km.

  • 200 000 cm (or 2 000 m) seen [1]
  • 2 km [1]
2
4(b)

1.2 km = 120 000 cm, so the map distance is 120 000 ÷ 40 000 = 3 cm.

  • Converts 1.2 km to 120 000 cm [1]
  • 3 cm [1]
2
4(c)

It compares two lengths in the same unit (cm to cm), so the units cancel — it works for any unit as long as both measurements use the same one.

  • States that both lengths are measured in the same unit so the units cancel [1]
1
Total for Question 45

— End of mark scheme —