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Rates and compound measures Cambridge IGCSE Mathematics revision

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In plain words

A rate compares two different kinds of thing: kilometres per hour, dollars per kilogram, people per square kilometre. "Per" means "divided by", and that tells you what to do.

Three things to know

  1. Speed = distance ÷ time. Density = mass ÷ volume. Pressure = force ÷ area.
  2. Average speed is the total distance divided by the total time, not the average of the speeds.
  3. To change km/h into m/s, divide by 3.6. To change money, multiply by the exchange rate (or divide to go back).

Worked example

A car travels 150 km in 2 hours 30 minutes. Find its average speed.

  1. Write the time as a decimal: 2 h 30 min = 2.5 h.
  2. Speed = distance ÷ time = 150 ÷ 2.5.
  3. = 60 km/h.

Tips and tricks

  • 2 hours 30 minutes is 2.5 hours, not 2.30. Divide the minutes by 60.
  • The units tell you the formula: km/h is kilometres divided by hours.
5 questions, about 2 minutes.

It lands in your notebook with its questions as flashcards.

Rates and compound measures: 5 questions and answers

These are the quiz’s questions. Do the quiz first, then come back here for the ones that got you.

  1. A train travels 120 km in 1.5 hours. What is its average speed?
    • 60 km/h
    • 80 km/h (the answer)
    • 90 km/h
    • 180 km/h

    120 ÷ 1.5.

  2. How far do you travel in 2 minutes at 5 m/s?
    • 10 m
    • 100 m
    • 600 m (the answer)
    • 2.5 m

    2 minutes is 120 seconds; 5 × 120.

  3. What is 36 km/h in metres per second?
    • 10 m/s (the answer)
    • 36 m/s
    • 100 m/s
    • 129.6 m/s

    36 ÷ 3.6.

  4. A block has a mass of 200 g and a volume of 50 cm³. What is its density?
    • 0.25 g/cm³
    • 4 g/cm³ (the answer)
    • 150 g/cm³
    • 10 000 g/cm³

    200 ÷ 50.

  5. How long does it take to travel 45 km at 30 km/h?
    • 40 minutes
    • 1 hour 15 minutes
    • 1 hour 30 minutes (the answer)
    • 1 hour 50 minutes

    45 ÷ 30 = 1.5 hours.

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