Vectors GCSE revision and worksheets

Vectors are one of the most difficult topics in the new GCSE Maths 9-1 and they will only appear in the higher tier paper. If you are aiming for a higher level in your GCSE Maths then understanding vectors is going to be important. Vector questions are often worth a lot of marks and require a good understanding of algebra and often ratio and fraction rules. If you are looking to revise vectors or you want to access GCSE Maths vector resources then take a look below.

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What you need to know

What you need to know:

A vector is a quantity which has both magnitude (size) and direction, compared to normal numbers (1, 2, 3, …) which have a size, i.e. we can see how big they are, but no direction. There are 3 different ways to express a vector:

  • Boldface notation, \mathbf{a} (or if you’re writing this by hand, its often expressed with an underline: \underline{x});
  • Arrow notation, \vec{AB}, which denotes a vector that goes from point A to point B;
  • Column notation, \begin{pmatrix}5 \\ -3\end{pmatrix}, which denotes a vector that goes 5 in the x-direction and -3 in the y-direction.

Often (but not always) we use the boldface notation \mathbf{a} to represent the vector \vec{OA}, i.e. the vector which would take you from the origin to the point A.

You should be able to add and subtract vectors (in all forms), as well as multiply them by scalars (numbers). Furthermore, you should understand how this corresponds to a diagram, for example adding \mathbf{a} to \mathbf{b} would represent travelling along the \mathbf{a} vector and then the \mathbf{b} vector in a diagram.

In the higher course, you are also required to use vectors to “construct mathematical arguments and proofs”, which sounds more complex than it is. It usually amounts to finding the vector quantity of a point that is some fraction of the way along a line in a vector diagram, or proving that two vectors are parallel (which requires you to show that one is a multiple of the other).

Vectors Revision and Worksheets

Vectors
Level 6-7
Vectors 2
Level 6-7
Vectors 3
Level 6-7
Vectors 4
Level 6-7
Vectors 5
Level 6-7
Vectors 6
Level 6-7
Column Vectors
Level 6-7

Whether you are a GCSE Maths tutor in London or a Harrogate Maths tutor, you will find the vector resources on this page useful. From parallel vector questions to proof and perpendicular vectors, there are many different types of questions that can be used to stretch higher ability students in this topic. Browse our vector worksheets and revision tests and see what you want to incorporate into your resource bank.

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