Vectors (AQA GCSE Maths: Foundation): Exam Questions

Here are two column vectors.

$\mathbf{a}=\left(\begin{array}{c}4\\ 1\end{array}\right)$     $\mathbf{b}=\left(\begin{array}{c}2\\ -3\end{array}\right)$

On the grid below, draw and label the vector $\mathbf{a}+2\mathbf{b}$.

$ABCD$ is a parallelogram.

$\overrightarrow{AB}=\mathbf{p}$ and $\overrightarrow{AD}=\mathbf{q}$.

$M$ is the midpoint of the line $BD$.

Find the vector $\overrightarrow{AM}$ in terms of $\mathbf{p}$ and $\mathbf{q}$.

$\mathbf{a}=\left(\begin{array}{c}-5\\ 2\end{array}\right)\mathbf{b}=\left(\begin{array}{c}-3\\ 4\end{array}\right)$

Work out $3\mathbf{a}-\mathbf{b}$ as a column vector.

The vector $\mathbf{a}$and the vector $\mathbf{b}$ are shown on the grid.

On the grid, draw and label vector $-2\mathbf{a}$

Work out $\mathbf{a}+2\mathbf{b}$ as a column vector.

Vectors $\mathbf{a}$ and $4\mathbf{b}$ are drawn on the grid.

Write vector $\mathbf{a}$ as a column vector.

Find vector $\mathbf{b}$ as a column vector.

Vector $\mathbf{a}=\left(\begin{array}{c}2\\ 1\end{array}\right)$ , vector $\mathbf{b}=\left(\begin{array}{c}-2\\ 1\end{array}\right)$.

On each grid below, draw a vector to represent

Emma says that if she draws vector $\mathbf{a}$ and vector $\mathbf{b}$ they will be the same.

Explain why this is incorrect.

Here are two column vectors.

$\mathbf{a}=\left(\begin{array}{c}3\\ -1\end{array}\right)$     $\mathbf{b}=\left(\begin{array}{c}1\\ 0.5\end{array}\right)$

On the grid below, draw and label the vector $2\mathbf{a}-4\mathbf{b}$.

The shape in the diagram shows the vectors $\mathbf{p}$, $\mathbf{q}$ and $\mathbf{r}$.

$M$ is the midpoint of the line $AF$.

 Find $\overrightarrow{AM}$ in terms of $\mathbf{p}$, $\mathbf{q}$ and $\mathbf{r}$.

$\mathbf{a}=\left(\begin{array}{c}-6\\ 4\end{array}\right)\mathbf{b}=\left(\begin{array}{c}-2\\ -3\end{array}\right)$

Work out $-2\mathbf{a}-4\mathbf{b}$ as a column vector.

$\mathbf{a}=\left(\begin{array}{c}-3\\ 2\end{array}\right)$ and $\mathbf{b}=\left(\begin{array}{c}1\\ -5\end{array}\right)$

Work out $\mathbf{a}–3\mathbf{b}$
Circle your answer.

Vector $\mathbf{a}=\left(\begin{array}{c}3\\ -1\end{array}\right)$ and vector $\mathbf{b}=\left(\begin{array}{c}1\\ 3\end{array}\right)$

Gavin starts to draw a diagram to show that $\mathbf{a}+2\mathbf{b}=\left(\begin{array}{c}5\\ 5\end{array}\right)$

Complete Gavin’s diagram.

$\mathbf{a}=\left(\begin{array}{c}6\\ -2\end{array}\right)$ and $\mathbf{b}=\left(\begin{array}{c}10\\ -5\end{array}\right)$

Work out $2\mathbf{a}-\mathbf{b}$ as a column vector.

Given that $3\mathbf{a}+k\mathbf{b}=\left(\begin{array}{c}-2\\ 4\end{array}\right)$

Work out the value of $k$