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GCSE/Mathematics/AQA

G15Measure line segments and angles; interpret maps and scale drawings

Notes

Measuring line segments, angles; reading maps and scale drawings

This topic combines practical skills (using a ruler and protractor) with map and scale interpretation.

Measuring with a ruler

  • Always align the 0 mark with one endpoint, not the edge of the ruler.
  • Read to the nearest mm unless otherwise specified.
  • Hold ruler firmly to avoid slipping.

Measuring angles with a protractor

  • Place protractor centre on the vertex.
  • Align baseline with one ray.
  • Read the angle on the inner or outer scale (whichever passes through 0° on your aligned ray).
  • Common error: reading 130° as 50° (wrong scale).

Bearings

A bearing is a 3-figure direction: clockwise from north.

  • N = 000° (or 360°).
  • E = 090°.
  • S = 180°.
  • W = 270°.

Always state bearings as 3 digits: 045°, not 45°.

Maps and scale drawings

A scale describes the ratio between map distance and real distance, e.g. 1 : 25 000. (Topic G15 ↔ R2 overlap.)

Worked example: on a 1 : 50 000 map, the distance between two churches measures 7 cm. Real distance?

  • 7 × 50 000 = 350 000 cm = 3.5 km.

Bearings problems

Worked example: from A, you walk 4 km on a bearing of 060°. State the position relative to A.

  • 060° means 60° clockwise from north.
  • Draw a line at 60° (clockwise from north arrow at A) and mark 4 km along it.

Three-figure bearing computation

To find a return bearing: add or subtract 180°. If the bearing from A to B is 120°, the bearing from B to A is 300°.

Common mistakes

  1. Wrong protractor scale — pick the one matching your aligned 0°.
  2. Bearings without 3 digits — write 045°, not 45°.
  3. Measuring from end of ruler instead of the 0 mark.
  4. Reading clockwise from south instead of from north.
  5. Forgetting unit conversion in scale problems.

Try thisQuick check

A bearing of 075° from A. The reverse (B to A)?

  • 075° + 180° = 255°.

AI-generated · claude-opus-4-7 · v3-deep-geometry

Practice questions

Try each before peeking at the worked solution.

  1. Question 12 marks

    Convert direction to bearing

    (F1) A point is due east of a port. State the bearing from the port.

    [Foundation tier]

    Ask AI about this

    AI-generated · claude-opus-4-7 · v3-deep-geometry

  2. Question 22 marks

    Reverse bearing

    (F2) The bearing from A to B is 060°. State the bearing from B to A.

    [Foundation tier]

    Ask AI about this

    AI-generated · claude-opus-4-7 · v3-deep-geometry

  3. Question 32 marks

    Reverse bearing > 180°

    (F/H3) The bearing from P to Q is 220°. State the bearing from Q to P.

    [Crossover tier]

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    AI-generated · claude-opus-4-7 · v3-deep-geometry

  4. Question 42 marks

    Map scale

    (F4) A map has scale 1 : 50 000. Two places are 8 cm apart on the map. State the actual distance in km.

    [Foundation tier]

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    AI-generated · claude-opus-4-7 · v3-deep-geometry

  5. Question 52 marks

    Scale drawing real distance

    (F/H5) Scale 1 cm : 5 m. A driveway measures 7 cm on the plan. Find its real length.

    [Crossover tier]

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    AI-generated · claude-opus-4-7 · v3-deep-geometry

  6. Question 63 marks

    Bearings on diagram

    (H6) Ship sails 5 km on bearing 070°, then 4 km on bearing 160°. Sketch the path; calculate the angle between the two legs at the turning point.

    [Higher tier]

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    AI-generated · claude-opus-4-7 · v3-deep-geometry

  7. Question 74 marks

    Distance on map and time

    (H7) Map scale 1 : 25 000. Two villages are 12 cm apart on the map. A walker walks at 4 km/h. How long, in hours and minutes, does the journey take?

    [Higher tier]

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    AI-generated · claude-opus-4-7 · v3-deep-geometry

Flashcards

G15 — Measure line segments and angles; interpret maps and scale drawings

12-card SR deck for AQA GCSE Maths topic G15

12 cards · spaced repetition (SM-2)