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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

Year 11

Higher

Advanced problem solving with vectors

I can use my knowledge of vectors to solve problems.

Download all resources

Share activities with pupils

These resources will be removed by end of Summer Term 2025.

Switch to our new teaching resources now - designed by teachers and leading subject experts, and tested in classrooms.

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Lesson details

Key learning points

Drawing a diagram can make things clearer.
Adding to an existing diagram can make things clearer.
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).

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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

A E D B

is a trapezium.

Correct answer:

\vec{A E} = 2 \vec{B D}

\vec{E A} = 2 \vec{B D}

2 \vec{A E} = \vec{B D}

Correct answer:

\vec{A B} \neq k \vec{E D}

\vec{A B} = \vec{E D}

Q3.

Select the correct statements to show that

A B E F

is a parallelogram.

\vec{A F} = \vec{E B}

Correct answer:

\vec{A F} = \vec{B E}

\vec{F A} = \vec{B E}

Correct answer:

\vec{A B} = \vec{F E}

\vec{A B} = \vec{E F}

Q4.

A B C D

is a kite. The midpoints of each side are shown.

\vec{W X} = k (a - b)

where

k =

Correct Answer: 2

Q5.

A B C D

is a kite.

W, X, Y, Z

are midpoints of the lines they lie on. Find

\vec{W Z}

- c - b

- 2 c - 2 b

Correct answer:

2 b + 2 c

c + b

Q6.

A B C D

is a kite.

W, X, Y, Z

are midpoints of the lines they lie on. Find

\vec{Z X}

- c - 2 b + a

c + 2 b - a

Correct answer:

- 2 c - 4 b + 2 a

2 c + 4 b - 2 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

a = (\binom{2}{3})

and

b = (\binom{- 1}{2})

, find

4 a - 2 b

(\binom{8}{8})

(\binom{8}{4})

(\binom{6}{4})

Correct answer:

(\binom{10}{8})

(\binom{10}{6})

Q3.

Given that

(\binom{x}{8})

is parallel to

(\binom{15}{12})

, then

x =

Correct Answer: 10

Q4.

a (\binom{3}{- 2}) + 4 (\binom{3}{b}) = (\binom{3}{14})

. The value of

b

Correct Answer: 2

Q5.

Given that

a (\binom{2}{1}) + b (\binom{4}{4}) = (\binom{16}{14})

, find the value of

a + b

a + b =

Correct Answer: 5

Q6.

a = (\binom{2}{- 3})

and

b = (\binom{- 2}{y})

. Given that

3 a - 2 b

is parallel to

(\binom{30}{- 51})

, the value of

y

is .

Correct Answer: 4

Advanced problem solving with vectors

Advanced problem solving with vectors

These resources will be removed by end of Summer Term 2025.

Slide deck

Lesson details

Key learning points

Keywords

Common misconception

How to plan a lesson using our resources

Licence

Lesson video

Worksheet

Starter quiz

6 Questions

Exit quiz

6 Questions