IGCSE Mathematics: Rates Practice Questions
A rate compares two quantities with different units, such as kilometres per hour or grams per cubic centimetre. To convert between compound units, convert each part separately.
Topic 1.12 of Cambridge IGCSE Mathematics 0580 supplies the compound units used in Physics as well as Maths. Converting km per hour into metres per second is the conversion that appears most, and it needs two steps rather than one. The questions below cover it and the best buy comparison.
What you need to know for Rates
- RateA comparison of two quantities measured in different units, written as one unit per another, such as km/h or g/cm3.
- SpeedSpeed = distance divided by time. Rearranged, distance = speed x time and time = distance divided by speed.
- DensityDensity = mass divided by volume, usually in g/cm3 or kg/m3.
- Converting km/h to m/sMultiply by 1000 to convert kilometres to metres, then divide by 3600 to convert hours to seconds. Together, divide by 3.6.
- Unit rateDivide to find the cost or amount for one unit. This is what makes two different package sizes directly comparable.
- Best buyCompare the cost per unit, or the amount per ringgit. Whichever measure you use, apply it to both options.
IGCSE Mathematics Rates questions and answers
4 exam-style questions written to the 0580 syllabus. Try each one on paper first, then open the worked answer to check your method against the marks.
A cyclist covers 150 km in 2.5 hours. Calculate her average speed.
Show the worked answer
- Use speed = distance divided by time.
- The time is already in decimal hours, so no conversion is needed.
- Speed = 150 divided by 2.5.
- Speed = 60 km/h.
Convert a speed of 72 km/h into metres per second.
Show the worked answer
- Convert kilometres to metres: 72 km = 72 x 1000 = 72000 metres travelled in one hour.
- Convert hours to seconds: one hour = 60 x 60 = 3600 seconds.
- Speed = 72000 divided by 3600.
- Speed = 20 m/s. As a shortcut, dividing km/h by 3.6 converts directly to m/s.
A block has a mass of 480 g and a volume of 60 cm3. Calculate its density.
Show the worked answer
- Use density = mass divided by volume.
- Both quantities are already in matching units, grams and cubic centimetres.
- Density = 480 divided by 60.
- Density = 8 g/cm3. The unit follows directly from the calculation: grams divided by cubic centimetres.
Rice is sold in a 3 kg bag for RM12.60 and a 5 kg bag for RM20.50. Determine which is better value, showing your working.
Show the worked answer
- Find the cost per kilogram for each option so they can be compared directly.
- 3 kg bag: 12.60 divided by 3 = RM4.20 per kg.
- 5 kg bag: 20.50 divided by 5 = RM4.10 per kg.
- RM4.10 is less than RM4.20, so the 5 kg bag is better value. It saves 10 sen on every kilogram bought.
Common mistakes in this topic
- Converting only one part of a compound unit.
- Dividing the wrong way round in a rate calculation.
- Comparing total prices instead of unit rates in a best buy question.
- Leaving time in hours and minutes when a decimal is needed.
- Omitting the compound unit from the final answer.
Exam tips
- Check the unit of your answer. If it reads the wrong way round, the division is inverted.
- For km/h to m/s, divide by 3.6. For m/s to km/h, multiply by 3.6.
- In best buy questions, state the unit rate for both options and then compare them in words.
- Convert time to decimal hours before any speed calculation.
- Write the formula first. It is usually worth a method mark on its own.
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Rates FAQs
How do I convert km/h to m/s?
Multiply by 1000 to change kilometres into metres, then divide by 3600 to change hours into seconds. Combined, this means dividing by 3.6. So 72 km/h becomes 20 m/s. To go the other way, multiply by 3.6.
How do I compare value for money?
Work out the cost per unit for each option by dividing the price by the quantity, then compare those figures. Alternatively work out the quantity per ringgit. Whichever measure you choose, apply it to both options and state the comparison in words.
What is a compound unit?
A unit made from two others, such as kilometres per hour, grams per cubic centimetre or ringgit per kilogram. The word per means divided by, so the unit itself tells you which quantity to divide by which.
How do I remember the speed formula?
Speed equals distance divided by time, which matches the unit: kilometres per hour is kilometres divided by hours. Rearranging gives distance equals speed multiplied by time, and time equals distance divided by speed.
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Written to the published Cambridge IGCSE Mathematics (0580) syllabus. Check your school entry code and syllabus year, because Core and Extended candidates are assessed on different content. Last reviewed 2026-08-12.