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Year 11
Higher

Advanced problem solving with vectors

I can use my knowledge of vectors to solve problems.

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New
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Year 11
Higher

Advanced problem solving with vectors

I can use my knowledge of vectors to solve problems.

Download all resources
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Share activities with pupils
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These resources will be removed by end of Summer Term 2025.

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Lesson details

Key learning points

  1. Drawing a diagram can make things clearer.
  2. Adding to an existing diagram can make things clearer.
  3. It can be helpful to start with what you know or can deduce.

Keywords

  • Vector - A vector can be used to describe a translation.

  • Displacement - Displacement is the distance from the starting point when measured in a straight line.

  • Resultant vector - A resultant vector is the single vector that produces the same effect as a combination of other vectors.

Common misconception

When calculating the resultant vector, pupils can incorrectly sum vectors due to opposite directions or proportions of vectors.

Encourage pupils to write a clear vector pathway, sometimes using highlighters can help visualise this pathway.


To help you plan your year 11 maths lesson on: Advanced problem solving with vectors, download all teaching resources for free and adapt to suit your pupils' needs...

Give pupils the opportunity to calculate a resultant column vector using scalars and summing other vectors. They replace two known values with x and y, thus creating a problem solving question which they could give to a peer to solve. For a greater challenge, replace a third value with z.
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Licence

This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Lesson video

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Starter quiz

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6 Questions

Q1.
Three points that lie along the ___________ are said to be collinear.
same curve
same pair of parallel lines
Correct answer: same straight line
Q2.
Select the correct statements to show that $$AEDB$$ is a trapezium.
An image in a quiz
Correct answer: $$\overrightarrow{AE}=2\overrightarrow{BD}$$
$$\overrightarrow{EA}=2\overrightarrow{BD}$$
$$2\overrightarrow{AE}=\overrightarrow{BD}$$
Correct answer: $$\overrightarrow{AB}\neq k\overrightarrow{ED}$$
$$\overrightarrow{AB}=\overrightarrow{ED}$$
Q3.
Select the correct statements to show that $$ABEF$$ is a parallelogram.
An image in a quiz
$$\overrightarrow{AF}=\overrightarrow{EB}$$
Correct answer: $$\overrightarrow{AF}=\overrightarrow{BE}$$
$$\overrightarrow{FA}=\overrightarrow{BE}$$
Correct answer: $$\overrightarrow{AB}=\overrightarrow{FE}$$
$$\overrightarrow{AB}=\overrightarrow{EF}$$
Q4.
$$ABCD$$ is a kite. The midpoints of each side are shown. $$\overrightarrow{WX} = k(\mathbf a - \mathbf b)$$ where $$k=$$ .
An image in a quiz
Correct Answer: 2
Q5.
$$ABCD$$ is a kite. $$W,X,Y,Z$$ are midpoints of the lines they lie on. Find $$\overrightarrow{WZ}$$.
An image in a quiz
$$- \mathbf c - \mathbf b$$
$$-2 \mathbf c -2 \mathbf b$$
Correct answer: $$2\mathbf b + 2\mathbf c$$
$$\mathbf c + \mathbf b$$
Q6.
$$ABCD$$ is a kite. $$W,X,Y,Z$$ are midpoints of the lines they lie on. Find $$\overrightarrow{ZX}$$.
An image in a quiz
$$- \mathbf c - 2\mathbf b + \mathbf a$$
$$ \mathbf c + 2\mathbf b - \mathbf a$$
Correct answer: $$-2 \mathbf c -4 \mathbf b + 2\mathbf a$$
$$ 2\mathbf c + 4\mathbf b - 2\mathbf a$$

Exit quiz

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6 Questions

Q1.
A vector is the single vector that produces the same effect as a combination of other vectors.
Correct Answer: resultant
Q2.
Given $$\mathbf a = {2 \choose 3}$$ and $$\mathbf b = {-1 \choose 2}$$, find $$4\mathbf a - 2 \mathbf b$$
$$8 \choose8$$
$$8 \choose4$$
$$6 \choose4$$
Correct answer: $$10 \choose8$$
$$10 \choose6$$
Q3.
Given that $$ x\choose 8$$ is parallel to $$ 15 \choose 12$$, then $$x =$$
Correct Answer: 10
Q4.
$$ a {3\choose -2} + 4{ 3 \choose b} = {3\choose 14}$$. The value of $$b$$ is
Correct Answer: 2
Q5.
Given that $$a {2\choose 1} + b{ 4 \choose4}= {16 \choose 14}$$, find the value of $$a + b$$. $$a+b=$$ .
Correct Answer: 5
Q6.
$$\mathbf a = {2\choose -3}$$ and $$\mathbf b = {-2 \choose y}$$. Given that $$3 \mathbf a - 2 \mathbf b$$ is parallel to $$30 \choose -51$$, the value of $$y$$ is .
Correct Answer: 4