GRADE 12 MATHEMATICAL LITERACY
Maps, Plans & Other Representations of the
Physical World
A learner-friendly revision guide with visual examples from EASY → MEDIUM → HARD
Scale 1 : 50 000
1 cm on the map represents 50 000 cm in reality.
Example bar scale
0 1 2 3 4 5
Topics covered
5.1 Scale
5.2 Maps
5.3 Plans
5.4 Models
How to use this guide: Learn the rule → study the worked example → try the challenge yourself → check the answer.
Key exam skills: unit conversions, scale calculations, map interpretation, directions, bearings, grid references,
area, perimeter and scale models.
Grade 12 Mathematical Literacy • Maps, Plans & Models Page 1
, 5.1 SCALE
A scale compares a measurement on a map, plan or model with the real measurement. In a ratio scale such as
1 : 50 000, 1 unit on the representation equals 50 000 of the same units in reality.
Scale 1 : 50 000
1 cm on the map represents 50 000 cm in reality.
Example bar scale
0 1 2 3 4 5
Golden rule: Keep the units the same before using the scale. Remember: 1 km = 1 000 m = 100 000 cm.
Easy Example
A map has a scale of 1 : 10 000. A road measures 3 cm on the map. What is the real distance?
Actual distance = 3 × 10 000 = 30 000 cm.
30 000 cm ÷ 100 000 = 0.3 km.
Answer: 0.3 km (300 m)
Medium Example
A map has a scale of 1 : 50 000. Two towns are 7.2 cm apart. Find the actual distance in kilometres.
Actual distance = 7.2 × 50 000 = 360 000 cm.
Convert: 360 000 ÷ 100 000 = 3.6 km.
Answer: 3.6 km
Hard Example
A hiking trail is actually 12.5 km long. On a map with scale 1 : 25 000, how long should the trail be on the map?
Convert 12.5 km to cm: 12.5 × 100 000 = 1 250 000 cm.
Map distance = 1 250 000 ÷ 25 000 = 50 cm.
Answer: 50 cm
Challenge: Find the scale
A drawing shows a road as 8 cm long. The real road is 4 km long. Find the scale.
Convert 4 km to cm: 4 × 100 000 = 400 000 cm.
Scale = 8 : 400 000.
Divide both sides by 8: 1 : 50 000.
Answer: 1 : 50 000
Grade 12 Mathematical Literacy • Maps, Plans & Models Page 2
Maps, Plans & Other Representations of the
Physical World
A learner-friendly revision guide with visual examples from EASY → MEDIUM → HARD
Scale 1 : 50 000
1 cm on the map represents 50 000 cm in reality.
Example bar scale
0 1 2 3 4 5
Topics covered
5.1 Scale
5.2 Maps
5.3 Plans
5.4 Models
How to use this guide: Learn the rule → study the worked example → try the challenge yourself → check the answer.
Key exam skills: unit conversions, scale calculations, map interpretation, directions, bearings, grid references,
area, perimeter and scale models.
Grade 12 Mathematical Literacy • Maps, Plans & Models Page 1
, 5.1 SCALE
A scale compares a measurement on a map, plan or model with the real measurement. In a ratio scale such as
1 : 50 000, 1 unit on the representation equals 50 000 of the same units in reality.
Scale 1 : 50 000
1 cm on the map represents 50 000 cm in reality.
Example bar scale
0 1 2 3 4 5
Golden rule: Keep the units the same before using the scale. Remember: 1 km = 1 000 m = 100 000 cm.
Easy Example
A map has a scale of 1 : 10 000. A road measures 3 cm on the map. What is the real distance?
Actual distance = 3 × 10 000 = 30 000 cm.
30 000 cm ÷ 100 000 = 0.3 km.
Answer: 0.3 km (300 m)
Medium Example
A map has a scale of 1 : 50 000. Two towns are 7.2 cm apart. Find the actual distance in kilometres.
Actual distance = 7.2 × 50 000 = 360 000 cm.
Convert: 360 000 ÷ 100 000 = 3.6 km.
Answer: 3.6 km
Hard Example
A hiking trail is actually 12.5 km long. On a map with scale 1 : 25 000, how long should the trail be on the map?
Convert 12.5 km to cm: 12.5 × 100 000 = 1 250 000 cm.
Map distance = 1 250 000 ÷ 25 000 = 50 cm.
Answer: 50 cm
Challenge: Find the scale
A drawing shows a road as 8 cm long. The real road is 4 km long. Find the scale.
Convert 4 km to cm: 4 × 100 000 = 400 000 cm.
Scale = 8 : 400 000.
Divide both sides by 8: 1 : 50 000.
Answer: 1 : 50 000
Grade 12 Mathematical Literacy • Maps, Plans & Models Page 2
