Vectors and bearings

AQA GCSE Maths

8 ready-made resources for teaching Vectors and bearings, written for AQA GCSE Maths. Slides, worksheets, mark schemes, homework, an assessment and retrieval quizzes, all with SEN-friendly scaffolding built in as standard. Below is what the topic requires and where students usually go wrong, free to read whether or not you sign up.

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What is in this bundle

Assessment mark schemeWord, editable
End-of-topic assessmentWord, editable
HomeworkWord, editable
Retrieval-practice quizzesWord, editable
SlidesPowerPoint, editable
Starter & exit ticketWord, editable
Tiered worksheetWord, editable
Worksheet mark schemeWord, editable

Foundation tier

Understand and use column vector and letter (a, b) notation.
Add and subtract vectors.
Multiply a vector by a scalar.
Find the resultant of two or more vectors.
Use three-figure bearings to describe a direction.
Solve simple bearing problems using angle facts.

Higher tier, in addition

Use vectors to solve geometric problems, including showing that points are collinear or that two lines are parallel.
Express a vector in terms of other given vectors within a geometric diagram, such as one involving midpoints.
Solve bearing problems that combine bearings with trigonometry or scale diagrams.

Where students go wrong

Adding vectors as if they were plain coordinates, without regard for direction.
Making a sign error when subtracting one vector from another.
Measuring a bearing from the wrong reference direction, or in the wrong rotational direction (bearings are measured clockwise from north).
Giving a bearing that is not in three-figure form, for example writing 45° instead of 045°.
Stopping at "the vectors are equal" in a proof without stating what that implies, such as that the lines are parallel or that points are collinear.

How it gets asked in the exam

"Write down the vector...", "Find AB in terms of a and b", "Work out the bearing of A from B", "Show that ... are collinear".

Key vocabulary

Vector, scalar, magnitude, resultant, column vector, bearing, collinear, parallel.

Assumed prior knowledge

Coordinates and translation vectors.
Right-angled trigonometry.
Angle facts, including angles on parallel lines.

How Speca scaffolds this topic

Use a consistent arrow-and-label convention in every vector diagram, the vector always drawn as an arrow with its letter placed above it, so magnitude and direction are always visually reinforced together.
Anchor every bearings question with a compass rose showing north marked and a clockwise arrow, reinforcing the two details students most often get backwards: starting from north, and turning clockwise.
Teach a fixed vector route-tracing routine for geometric proof questions: trace the path from the start letter to the end letter, writing down each vector passed along the way, using + for travelling in the vector's own direction and − for travelling against it.

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