Vectors GCSE revision and worksheets

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).