Measuring lengths, angles, and scale drawings
Edexcel 1MA1 examines this on Foundation papers (1F and 2F) routinely, and occasionally on 1H. It is examined in two ways: physical measurement on a printed diagram and conversion using a scale.
Measuring a line segment
Use a ruler aligned to one endpoint, reading off the length to the nearest mm. Always state units.
Measuring an angle
Place a protractor with its centre on the vertex of the angle and the 0° baseline along one arm. Read off the size from the appropriate scale (inner or outer scale, depending on direction).
Scale drawings
A scale of 1:n means 1 unit on the drawing represents n units in real life.
- Scale 1:50 → 1 cm on paper = 50 cm in real life.
- Scale 1:25 000 → 1 cm on paper = 25 000 cm = 250 m in real life.
- Scale 1:100 000 → 1 cm = 1 km.
To go from drawing → real: multiply by the scale. To go from real → drawing: divide by the scale.
Map scales (common UK exam values)
- OS 1:25 000 (Explorer): 4 cm = 1 km.
- OS 1:50 000 (Landranger): 2 cm = 1 km.
Bearings
Measured clockwise from north, given as 3 digits (e.g. 045°, not 45°). Always include three digits.
Common Edexcel mark-scheme phrasing
- B1 for a measurement within ±2 mm or ±2°.
- M1 for setting up the scale conversion correctly.
- A1 for the converted real-world distance.
⚠Common mistakes— Common errors
- Reading the wrong scale on the protractor (inner vs outer).
- Forgetting the 3-digit bearing convention (writing 45° instead of 045°).
- Multiplying when you should divide (or vice versa) on a scale conversion.
- Mixing units mid-calculation (e.g. cm and m on the same line).
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