Scale factors and scale drawings

WJEC includes a scale-drawing or map question on most Unit 2 papers. The Welsh context (OS maps of Snowdonia, plans of Senedd buildings, ferry timetable distances) is common.

Scale notation

A scale of 1 : 50 means 1 unit on the drawing equals 50 units in real life. Same units on both sides.

So 1 cm on a 1 : 50 plan = 50 cm in reality. Or 1 cm on a 1 : 25 000 OS map = 25 000 cm = 250 m in reality.

Converting map distance ↔ real distance

• Drawing → Real: multiply by the scale factor.
• Real → Drawing: divide by the scale factor.

Example: an OS map has scale 1 : 50 000. Two villages are 7 cm apart on the map.

Real distance = 7 × 50 000 cm = 350 000 cm = 3500 m = 3.5 km.

Scale factors of enlargement

When a shape is enlarged by scale factor k:

• All lengths × k.
• All areas × k^2.
• All volumes × k^3.

Example: a triangle with area 12 cm^2 is enlarged with k = 3. New area = 12 × 9 = 108 cm^2.

If 0 < k < 1, the shape gets smaller. If k is negative, the shape is rotated 180° about the centre.

Drawing to scale (constructions)

WJEC asks students to "draw an accurate scale diagram of…" worth 3–4 marks. Marks:

• M1 — correct scale chosen and applied.
• M1 — correct angles using protractor.
• A1 — accurate within tolerance.

WJEC exam tip

Always state your chosen scale at the top of a diagram (e.g. "1 cm represents 100 m"). Marks are dropped when the scale isn't stated, even if the drawing is correct.