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This topic represents vectors as column vectors and with diagrams, adds and subtracts them, multiplies by a scalar, and uses vector geometry to prove points are collinear. It's examined right across GCSE and iGCSE Maths. Work through it free on eClassroom, with clear worked examples and instantly-marked questions that build your confidence for the exam.
How you do it
Add vectors by following one then the other, and subtract by reversing direction. A multiple of a vector is parallel to it. To find a path across a shape, write it as a route through vectors you already know, then simplify.
Before you start
It draws heavily on coordinates and column notation. It appears at Higher tier. It then feeds into vector geometry at A-Level.
What you learn
A vector has both size and direction. We write it as a column vector (top number = movement right, bottom = movement up). To add or subtract column vectors, work on the top numbers and bottom numbers separately. Multiplying a vector by a number (a scalar) multiplies both components, making it longer or shorter in the same (or opposite) direction. Vectors let you describe positions and prove results. The course works through column vectors: adding and subtracting, scalar multiples and magnitude and vectors in geometry. Every section has instant-feedback practice questions matched to Edexcel iGCSE 4MA1 and the other major GCSE boards, and the course finishes with full exam-style questions you mark yourself.
Related Topics
Vectors is part of the Geometry strand of our free GCSE maths courses, studied in Higher tier. It runs to 3 concepts, each followed by a check, with 2 worked examples along the way. Related topics students usually take next include Volume & Surface Area, Angles, Area & Perimeter, Circle Theorems and Circles. You can drill this strand further on the Geometry revision engine, with your accuracy saved to your skill tree.
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