Mathematics (Core)Exam code: 0580
Compound Measures
Number
Matching units before calculating
- Both quantities must be in units that match the answer required
- Convert first, then divide, since converting afterwards invites a second error
- A speed wanted in m/s needs the distance in metres and the time in seconds
- A rate given per hour becomes a rate per minute by dividing by 60, and the reverse by multiplying
Exam tip
Change both units, not just one
Changing 5 m/s into km/h, or kilograms per hour into grams per second, changes two units at once. The method mark needs both changes, as in 5 × 60 × 60 ÷ 1000, not just one of them. The right digits with the wrong place value, such as 180 or 1.8 for 18, still keep one mark. Write the whole calculation, then check the size.
Worked example
Changing km/h to m/s and back
A cyclist rides at 27 km/h. Write this speed in metres per second. A runner's speed is 4.5 m/s. Write this speed in km/h.
Solution:
- 27 km/h means 27 km travelled in 1 hour
- 27 km is 27 000 m, and 1 hour is 60 × 60 = 3600 seconds
- 27 000 ÷ 3600 = 7.5 m/s
- 4.5 m/s means 4.5 m travelled every second
- In 3600 seconds that is 4.5 × 3600 = 16 200 m
- 16 200 m is 16.2 km, so the speed is 16.2 km/h
- Check: 7.5 × 3.6 = 27 and 16.2 ÷ 3.6 = 4.5, and each m/s value is the smaller number