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GCSE/Mathematics/WJEC

G15Measure line segments and angles; interpret maps and scale drawings

Notes

Measurement, maps and scale

WJEC Foundation and Intermediate test practical measuring and scale-reading skills.

Measuring line segments

  • Use a ruler in mm where possible; one decimal place in cm is sufficient.
  • Measure between marks/points carefully.
  • WJEC tolerance: ±2 mm on a printed paper; ±1° on angles.

Measuring angles

  • Use a protractor with the centre on the vertex and the zero line along one arm.
  • Read the inner or outer scale according to the direction.
  • Acute, obtuse, reflex, right — classify before reading. If you see an obtuse angle but read 45°, you read the wrong scale.

Scale notation

  • 1 : 50 means 1 unit on the drawing represents 50 of the same unit in real life.
  • 1 cm : 5 m means 1 cm on the drawing = 5 m in reality. Equivalent ratio: 1 : 500 (since 5 m = 500 cm).

Converting drawing → real

Multiply by the scale factor.

  • Drawing 6 cm at 1 : 200 → 6 × 200 = 1200 cm = 12 m in real life.

Converting real → drawing

Divide by the scale factor.

  • 8 m at 1 : 200 → 800 ÷ 200 = 4 cm on the drawing.

Bearings

Bearings are angles measured CLOCKWISE from north. Always 3 digits: 045°, 130°, 270°.

Map reading

  • Compute distance: measure on the map, multiply by scale.
  • Compute bearing: align north, measure clockwise from N to the line.

Scale drawings — practical exam pattern

WJEC asks candidates to draw an accurate scale plan from given measurements.

  • Choose a scale that fits the page.
  • Construct using ruler + protractor + compasses.
  • Annotate with all real measurements and the scale used.

WJEC exam tip

When asked for a real-world distance from a printed map, write the SCALE EQUATION first ("1 cm represents 25 m") then your measurement, then the multiplication. The scale statement is a B1 mark in its own right.

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Practice questions

Try each before peeking at the worked solution.

  1. Question 14 marks

    Measure and interpret a scale

    WJEC Unit 2 (Calculator) — Foundation

    A scale drawing of a garden uses scale 1 : 200. On the drawing, the lawn measures 6 cm by 4 cm.

    (a) Find the real dimensions of the lawn. (2 marks)
    (b) Find the real area of the lawn. (2 marks)

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  2. Question 26 marks

    Bearing and distance on a map

    WJEC Unit 2 (Calculator) — Intermediate

    A map has scale 1 : 25 000. Town A is at grid reference (0, 0) and town B is 8 cm to the east and 6 cm to the north on the map.

    (a) Find the actual straight-line distance from A to B in km. (3 marks)
    (b) Find the bearing of B from A, to the nearest degree. (3 marks)

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  3. Question 34 marks

    Construct a scale drawing

    WJEC Unit 2 (Calculator) — Intermediate

    A field is a triangle with sides 60 m, 80 m and 100 m. Using a scale of 1 : 1000 (so 1 cm represents 10 m):

    (a) State the lengths to draw on paper for each side. (2 marks)
    (b) Describe the angle at the vertex between the 60 m and 80 m sides. (2 marks)

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Flashcards

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

7-card SR deck for WJEC GCSE Mathematics (leaves batch 5) topic G15

7 cards · spaced repetition (SM-2)