Sheet № 42 · Foundation + Higher · AQA · Edexcel · OCR
Scale Drawings and Maps –
Scale drawings and map questions test your understanding of ratio in a practical, real-world context — and they appear frequently on GCSE Maths papers for AQA, Edexcel and OCR. Whether you are reading a map, interpreting an architect's floor plan, or producing your own scale drawing, the skills involved are the same: converting between a
§Key definitions
Step 1:
Real distance in cm = 7.4 × 50,000 = 370,000 cm.
Step 2:
Convert to metres: 370,000 ÷ 100 = 3,700 m.
Step 3:
Convert to km: 3,700 ÷ 1,000 = 3.7 km.
Method:
You cannot simply multiply the drawing area by 200. You must square the scale factor for area.
§Formulas to memorise
1 : 50,000 — this means 1 cm on the map represents 50,000 cm (or 500 m) in real life.
1 : 25 — this means 1 cm on the drawing represents 25 cm in real life.
1 cm represents 5 km — a written scale.
Real area = drawing area × 200² = π × 40,000 = 125,663.7 cm² = 12.57 m².
Worked example
See example below.
A map has a scale of 1 : 50,000. Two towns are 7.4 cm apart on the map. What is the actual distance between them in kilometres?
⚠ Common mistakes
- ✗Forgetting to convert units after scaling. If 1 cm = 50,000 cm in real life, remember to then convert that answer into metres or kilometres.
- ✗Dividing instead of multiplying (or vice versa). Drawing to real life → multiply. Real life to drawing → divide.
- ✗Using the scale factor for area without squaring it. If lengths are scaled by factor k, areas are scaled by k², and volumes by k³.
- ✗Measuring inaccurately. When a question says "measure the distance on the diagram", use a ruler carefully — even 1 mm off can affect the answer.
- ✗Using the wrong units. If the question gives real life in metres but the scale is in cm, you must convert before dividing.
✦ Exam tips
- →Always state the scale if you are asked to produce a scale drawing. Write it clearly on your diagram.
- →Show unit conversions in your working. Examiners want to see you converting cm to m or km — it earns method marks.
- →For map questions, learn the shortcut: on a 1 : 25,000 map, 4 cm = 1 km. On a 1 : 50,000 map, 2 cm = 1 km. These save time.
- →Bearings and scale drawings often appear together. You may need to measure both a distance and an angle.
- →Use a sharp pencil and ruler for scale drawing questions — accuracy marks require precision.