Measurement, plans and scale drawings

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Units and conversions

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

Slides

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Practice questions

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1.How many millimetres are in 1 cm?
Easy
- A10
- B100
- C1000
- D1
2.How many metres are in 1 km?
Easy
- A10
- B100
- C1000
- D10 000
3.Convert 3.5 km to metres.
Easy
- A350 m
- B3500 m
- C35 000 m
- D0.35 m
4.Convert 2500 g to kg.
Easy
- A0.25 kg
- B2.5 kg
- C25 kg
- D250 kg
5.What is 2.5 hours in hours and minutes?
Easy
- A2 h 5 min
- B2 h 30 min
- C2 h 50 min
- D2 h 25 min
6.On a map with scale 1 : 50 000, 3 cm represents:
Easy
- A150 m
- B1.5 km
- C15 km
- D150 km
7.A scale is 1 cm to 5 m. A room is 40 m long. How long is the drawing?
Easy
- A8 cm
- B20 cm
- C200 cm
- D0.8 cm
8.What is the bearing of east?
Easy
- A000°
- B090°
- C180°
- D270°

More questions

9.What is the bearing of south-west?
Easy
- A135°
- B225°
- C315°
- D045°
10.A person walks 12 km in 3 hours. What is the average speed?
Easy
- A36 km/h
- B4 km/h
- C0.25 km/h
- D15 km/h
11.What is the density of a block with mass 200 g and volume 50 cm³?
Easy
- A4 g/cm³
- B0.25 g/cm³
- C10 000 g/cm³
- D150 g/cm³
12.The bearing of A from B is 070°. What is the bearing of B from A?
Medium
- A110°
- B250°
- C290°
- D070°
13.The bearing of P from Q is 230°. What is the bearing of Q from P?
Medium
- A050°
- B130°
- C410°
- D310°
14.Convert 72 km/h to m/s.
Medium
- A20 m/s
- B72 m/s
- C259 m/s
- D7.2 m/s
15.Convert 15 m/s to km/h.
Medium
- A54 km/h
- B4.2 km/h
- C900 km/h
- D15 km/h
16.A force of 200 N acts on an area of 0.5 m². What is the pressure?
Medium
- A100 N/m²
- B400 N/m²
- C200.5 N/m²
- D40 N/m²
17.A car travels at 60 km/h for 45 minutes. How far does it go?
Medium
- A45 km
- B80 km
- C27 km
- D36 km
18.What is the volume of an object with density 8 g/cm³ and mass 96 g?
Medium
- A12 cm³
- B768 cm³
- C0.08 cm³
- D104 cm³
19.The scale of a model is 1 : 20. A real length of 3 m becomes:
Medium
- A6 cm
- B15 cm
- C60 cm
- D150 cm
20.A map has scale 1 : 20 000. A field has area 8 cm² on the map. What is its real area in hectares? (1 ha = 10 000 m²)
Medium
- A32
- B3.2
- C320
- D16
21.A cyclist travels 10 km at 20 km/h then 10 km at 10 km/h, without stopping. What is the average speed to 1 decimal place?
Medium
- A15 km/h
- B13.3 km/h
- C12 km/h
- D14 km/h
22.A ship sails 12 km on a bearing of 060°. How far east has it gone (1 d.p.)?
Medium
- A10.4 km
- B6.0 km
- C12 km
- D13.9 km
23.Two cities are 5 cm apart on a map of scale 1 : 2 000 000. What is the real distance?
Medium
- A10 km
- B100 km
- C1000 km
- D10 000 km
24.What is 1 litre in cm³?
Easy
- A10
- B100
- C1000
- D10 000
25.What is 1 m in cm?
Easy
- A10
- B100
- C1000
- D0.01
26.To construct the perpendicular bisector of a segment using compass arcs from its endpoints, you should:
Medium
- Ause the same radius, greater than half the segment length
- Buse only a protractor
- Cguess the midpoint
- Derase your arcs
27.When constructing, construction arcs should:
Medium
- Abe left visible
- Bbe rubbed out
- Cbe coloured
- Dbe drawn freehand
28.A triangle is constructed with sides 5, 6 and 7 cm. Which method is used?
Medium
- ASSS with compasses
- BSAS with protractor
- CASA
- DRHS
29.A bearing is measured clockwise from north.
Easy
True or false?
30.A bearing of 090° points east.
Easy
True or false?
31.Speed equals time divided by distance.
Easy
True or false?
32.1 litre is 1000 cm³.
Easy
True or false?
33.A scale of 1 : 100 means 1 cm on the drawing is 1 m in real life.
Medium
True or false?
34.Which are correct conversions?
Medium
- A1 km = 1000 m
- B1 litre = 1000 ml
- C1 m = 10 cm
- D1 kg = 1000 g
- E1 hour = 100 minutes
35.Which equal 45 minutes?
Medium
- A0.75 h
- B0.45 h
- C\frac{3}{4} h
- D45 s
- E2700 s
36.A car travels 90 km in 1 hour 15 minutes. Calculate its average speed in km/h.
Medium

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