Length: 10 mm = 1 cm; 100 cm = 1 m; 1000 m = 1 km. Mass: 1000 g = 1 kg; 1000 kg = 1 tonne. Capacity: 1000 ml = 1 litre.
Compound units: speed (m/s, km/h), density (g/cm³), pressure. Convert 72 km/h to m/s: 72 \times \frac{1000}{3600} = 20 m/s.
Time: 60 s = 1 min; 60 min = 1 h. Convert decimal hours carefully: 2.5 h = 2 h 30 min.
Scale and maps
A scale 1 : 50 000 means 1 cm on the map is 50 000 cm = 500 m in real life.
Scale drawings: choose a scale, measure with a ruler and protractor, and convert lengths back.
A ratio scale has no units; a "1 cm to 5 m" scale needs conversion.
Area scales by the square of the length scale. At 1 : 20 000, 1 cm represents 200 m and 1 cm² represents 40 000 m².
Scale 1 : 50 000
Bearings
A bearing is an angle measured clockwise from north, written with three figures (e.g. 045°, 270°).
Add 180° and subtract 360° if the result is 360° or more. Thus 070° reverses to 250°, and 180° reverses to 000°.
Bearing of Q from P
Compound measures
Speed = distance ÷ time; density = mass ÷ volume; pressure = force ÷ area.
Use the formula triangle or rearrange: d = s \times t.
Constructions
Use a ruler, protractor and compasses: construct triangles (SSS, SAS, ASA), the perpendicular bisector of a line, the angle bisector, and a perpendicular from a point to a line. Leave construction arcs visible.
Plans and elevations
A plan is the view from above; front and side elevations show the corresponding vertical views.
For a 6 cm by 4 cm by 2 cm cuboid, the plan is 6 × 4 cm, front elevation 6 × 2 cm and side elevation 4 × 2 cm. Use a common scale.
Plan, front and side views
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