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New
New
Year 11
Higher

Advanced problem solving with vectors

I can use my knowledge of vectors to solve problems.

icon-background-square
New
New
Year 11
Higher

Advanced problem solving with vectors

I can use my knowledge of vectors to solve problems.

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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.

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

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: AE=2BD
EA=2BD
2AE=BD
Correct answer: ABkED
AB=ED
Q3.
Select the correct statements to show that ABEF is a parallelogram.
An image in a quiz
AF=EB
Correct answer: AF=BE
FA=BE
Correct answer: AB=FE
AB=EF
Q4.
ABCD is a kite. The midpoints of each side are shown. WX=k(ab) 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 WZ.
An image in a quiz
cb
2c2b
Correct answer: 2b+2c
c+b
Q6.
ABCD is a kite. W,X,Y,Z are midpoints of the lines they lie on. Find ZX.
An image in a quiz
c2b+a
c+2ba
Correct answer: 2c4b+2a
2c+4b2a

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=(23) and b=(12), find 4a2b
(88)
(84)
(64)
Correct answer: (108)
(106)
Q3.
Given that (x8) is parallel to (1512), then x=
Correct Answer: 10
Q4.
a(32)+4(3b)=(314). The value of b is
Correct Answer: 2
Q5.
Given that a(21)+b(44)=(1614), find the value of a+b. a+b= .
Correct Answer: 5
Q6.
a=(23) and b=(2y). Given that 3a2b is parallel to (3051), the value of y is .
Correct Answer: 4
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