Scale drawings and maps · Foundation
도입됨| English | 의미 |
|---|---|
| scale/skeɪl/ | 비율 |
The written scale compares centimetres with centimetres, not centimetres with kilometres.
- A map at 1:25,000 shows a 4 cm route.
- This lesson studies scale 比例尺: The ratio of a drawing length to its corresponding real length.
The method
- In a scale 1:n, one drawing unit represents n of the same real unit.
- Multiply a drawing length by n to obtain the real length; divide a real length by n to draw it.
- Then convert the unit.
- Measure only when the diagram explicitly supplies an accurate scale.
At scale 1:25,000, what does 4 cm on the map represent?
난이도 1/5 · 100 코인 + 오늘 첫 완료 시 소액 보너스
The scale multiplies the drawing length by 25,000 in the SAME unit: 4×25,000=100,000 cm, which then converts to 1 km. Skipping the unit conversion inflates the answer a hundred-thousand-fold.
A worked case
At 1:25,000, 4 cm represents 100,000 cm=1000 m=1 km. A real 1.5 km path is 150,000 cm, so it measures 150,000/25,000=6 cm on the map. A room 6 m by 4 m drawn at 1:100 becomes 6 cm by 4 cm because each metre is 100 cm. Its drawing diagonal is √(6²+4²)≈7.21 cm and the real diagonal is about 7.21 m. Enlarging the printed map changes its numerical scale: doubling drawing lengths halves the scale denominator. A scale bar printed with the map enlarges with it.
Scale drawings and maps
In a scale 1:n, one drawing unit represents n of the same real unit
Classify the worked-case statements, then explain the units or invariant that justifies each decision.
At 1:25000, find the real length in km for 4 cm.
난이도 2/5 · 140 코인 + 오늘 첫 완료 시 소액 보너스
4×25000/100000=1 km.
Where it goes wrong
- A ratio compares matching units.
- Never measure a diagram marked not to scale.
- A photocopied numerical scale can become invalid even though its scale bar still works.
Not true: A scale of 1:25000 means 1 cm represents 25000 km. The scale has no units, so 1 cm represents 25 000 cm, which is 250 m.
Find the drawing length in cm of a 1.5 km route at that scale.
난이도 2/5 · 140 코인 + 오늘 첫 완료 시 소액 보너스
1.5 km=150000 cm; divide by 25000.
A scale of 1:25000 means 1 cm represents 25000 km.
난이도 1/5 · 100 코인 + 오늘 첫 완료 시 소액 보너스
The scale has no units, so 1 cm represents 25 000 cm, which is 250 m.
Applying it
- AQA R2 includes maps, scale factors and geometric problems.
- Label drawing and real dimensions separately; reverse the calculation to verify the scale.
- Use an exact ratio until the context asks for rounding.
Find the drawing width in cm of a 4 m room at 1:100.
난이도 2/5 · 140 코인 + 오늘 첫 완료 시 소액 보너스
4 m=400 cm; 400/100=4 cm.
Match each scale task to its operation.
난이도 2/5 · 140 코인 + 오늘 첫 완료 시 소액 보너스
Scale is a ratio of matching units; direction of conversion matters, and only a bar scale survives enlargement.
In your course
- AQA GCSE Mathematics (8300), Foundation tier, specification section 3.3.
- Paper 1 is non-calculator: keep fractions, surds and π exact and show each step. On calculator papers, still write the expression before its value.
- Scale: The ratio of a drawing length to its corresponding real length.
- In a scale 1:n, one drawing unit represents n of the same real unit.
- Watch for: A ratio compares matching units.