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Bearings

FoundationHigherAQAEdexcelOCR

Get to grips with bearings using these Foundation and Higher GCSE Maths practice questions. The worksheet focuses on measuring and calculating with bearings, and the accompanying mark scheme breaks down each solution clearly. Suitable for AQA, Edexcel and OCR. Download the questions and answers for free. Bearings are measured clockwise from north and written with three figures.

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These worksheets and mark schemes are original, written for Virtus Academy and checked against the current AQA, Edexcel and OCR specifications. Every worksheet comes with a full mark scheme.

Foundation

WorksheetFoundation · PDFMark SchemeFoundation · PDF

Higher

WorksheetHigher · PDFMark SchemeHigher · PDF

Topic overview

A bearing describes a direction as an angle measured clockwise from north. It is always written with three figures, so an angle of \(45^\circ\) is written as \(045^\circ\).

The three-figure convention matters and is worth a mark. Writing \(45^\circ\) rather than \(045^\circ\) is treated as an incomplete answer even though the value is correct.

Back bearings reverse the direction. Add \(180^\circ\) to the original bearing, or subtract \(180^\circ\) if the result would exceed \(360^\circ\). Drawing a north line at the second point makes the reasoning much clearer.

Revision notes

Measuring a bearing

Draw a north line at the starting point, then measure clockwise from north to the direction of travel.

Always measure clockwise, and always from north — anticlockwise measurements are the most common error.

The three-figure rule

Bearings are written with three digits, using leading zeros where needed.

So \(7^\circ\) becomes \(007^\circ\) and \(60^\circ\) becomes \(060^\circ\). This is a convention that questions expect.

Back bearings

The bearing of A from B is the reverse of the bearing of B from A.

Add \(180^\circ\) if the original is less than \(180^\circ\), or subtract \(180^\circ\) if it is more. So a bearing of \(070^\circ\) has a back bearing of \(250^\circ\).

Key points

  • A bearing is measured clockwise from north.
  • Bearings always use three figures.
  • Use leading zeros, such as \(045^\circ\).
  • Draw a north line at the point you measure from.
  • Add \(180^\circ\) for a back bearing under \(180^\circ\).
  • Subtract \(180^\circ\) if the bearing is over \(180^\circ\).

Worked examples

Example 1

Write \(38^\circ\) as a bearing.

Working

\[\text{Bearings use three figures}\]add a leading zero
\[038^\circ\]write the bearing correctly

Example 2

The bearing of B from A is \(065^\circ\). Find the bearing of A from B.

Working

\[065 + 180\]the original is less than 180, so add
\[= 245^\circ\]state the back bearing

Example 3

The bearing of Q from P is \(210^\circ\). Find the bearing of P from Q.

Working

\[210 - 180\]the original is more than 180, so subtract
\[= 030^\circ\]write with three figures

Common mistakes

  • Measuring anticlockwise.

    Bearings are always measured clockwise from north.

  • Writing fewer than three figures.

    45° must be written 045°. The leading zero is required.

  • Adding 180 when the bearing is already over 180.

    That would exceed 360, so subtract instead.

  • Measuring from the wrong point.

    The bearing of B from A is measured at A, with the north line drawn there.

Exam tips

  • Draw a north line at the point you are measuring from.
  • Always measure clockwise.
  • Write every bearing with three figures.
  • Sketch the situation before calculating a back bearing.

Key terms

Bearing
A direction measured clockwise from north, in three figures.
Back bearing
The bearing in the reverse direction.
North line
The reference line from which bearings are measured.
Clockwise
In the direction the hands of a clock move.

Related topics

Written and reviewed against the current AQA, Edexcel and OCR specifications. Spotted an error? Let us know.