01 — Explanation
How does a scale drawing relate paper to reality?
A scale drawing represents a real object using a fixed ratio, so every length on paper is proportional to a real-world length. A scale of means on paper represents () in real life:
Worked example. A map has scale . A road measures on the map. Find its true length in kilometres.
Exam tip
a scale ratio compares like-for-like units. Always finish by converting into whatever unit the question actually asks for — don't stop at "" if kilometres were requested. Work in centimetres throughout the scale calculation, then convert only at the very last step, to avoid rounding errors creeping in early.
Worked example. A garden is to be drawn using a scale of to . The real garden is a rectangle by . Find the dimensions of the scale drawing.
The scale drawing should measure — always use a ruler for every straight edge in the finished drawing, since freehand lines lose accuracy marks even if the maths is correct.
02 — Explanation
How do I read and give a three-figure bearing?
A bearing gives a direction as an angle measured from north, clockwise, always written with three digits — , , .
North (000°)
│
Bearing 315° │ Bearing 045°
\ │ /
West (270°) ──┼─────┼─────── East (090°)
/ │ \
Bearing 225° │ Bearing 135°
│
South (180°)The compass directions north, east, south and west correspond to the fixed bearings , , and . A phrase like "point is due east of point " is simply another way of saying the bearing of from is — exam questions often switch between compass words and bearing numbers, so both descriptions must be treated as identical information.
03 — Explanation
How do I find the back bearing?
The bearing of from is always different from the bearing of from , since the north line drawn at is parallel to the north line drawn at , and alternate angles between these parallel north lines link the two bearings:
Worked example. The bearing of a campsite from a car park is . Find the bearing of from .
Since , add : .
Common mistake
writing instead of . Bearings always need three figures, padded with leading zeros where necessary — this applies to the final answer even when every number used to reach it was written correctly along the way.
Worked example. A ship sails from port on a bearing of to reach point . Find the bearing would appear on, if viewed from .
Since , subtract : . The bearing of from is .