Revision notes, worked examples and methods for units, rates and scale.
Notes and quizzes ready · 50 questions · Revision video ready.
Foundation shows shared notes and questions. Higher includes the shared content and labelled Higher extensions. Changing tier starts the notes and a new quiz set.
Revise the key ideas
Converting units and using scales
Convert length using 10 mm = 1 cm, 100 cm = 1 m and 1000 m = 1 km. Convert mass using 1000 g = 1 kg and 1000 kg = 1 tonne.
For area, square the length conversion: 1 m2 = 10 000 cm2. For volume, cube it: 1 m3 = 1 000 000 cm3.
Capacity conversions include 1 litre = 1000 ml and 1 ml = 1 cm3. Therefore 1 litre = 1000 cm3.
Time uses 60 seconds per minute and 60 minutes per hour. 1 h 30 min = 1.5 h, not 1.30 h.
A map scale 1 : 50 000 means 1 cm represents 50 000 cm = 500 m. A 6 cm map distance represents 3 km. Measure in matching units before applying the scale.
Worked example: A drawing uses scale 1 : 20. A real length of 2.4 m is 240 cm, so the drawn length is 240 ÷ 20 = 12 cm.
Compound measures
Average speed = distancetime, distance = speed × time, and time = distancespeed. Use consistent units. Converting kilometres per hour to metres per second
Worked example: 150 km in 2.5 h gives an average speed of 60 km/h. This does not mean the speed was 60 km/h throughout.
To convert km/h to m/s, divide by 3.6: 72 km/h = 72 0003600 = 20 m/s. Reverse by multiplying by 3.6.
Density = massvolume. A 540 g object with volume 200 cm3 has density 2.7 g/cm3. Rearrange to mass = density × volume.
Pressure = forcearea. 120 N spread over 0.03 m2 gives 4000 N/m2, or 4000 Pa. The same force on a smaller area gives greater pressure.
Rates of pay and unit prices compare amount per unit. £18 for 12 kg costs £1.50/kg; £14 for 8 kg costs £1.75/kg, so the first is cheaper per kilogram.
Multi-stage calculations
Worked example: A journey covers 60 km in 1 h and 120 km in 3 h. Overall average speed = 1804 = 45 km/h. It is not the arithmetic mean of 60 and 40 km/h because the time intervals differ.
For exchange rates, identify the direction: if £1 buys €1.20, £50 buys €60, while €60 converts to £60 ÷ 1.20 = £50. Include any stated fees separately.
Check units by cancelling them: (g/cm3) × cm3 gives g. Dimensional checks can reveal an inverted formula.
Test yourself
50 questions · Sets of 10 from the selected tier. For fractions, use / when typing; for powers, use superscripts or ^. Follow each question's answer format. These quick checks support revision; practise full written solutions and proofs too.
Watch M25 · Units, rates and scale
Revise units, rates and scale with this narrated video. Use the player controls to pause, seek, adjust the volume or mute. Turn English captions on or off using the captions menu.
Mr Kidman's Classroom
