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Year 11
Foundation

Problem solving with loci and constructions

I can use my knowledge of loci and constructions to solve problems.

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New
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Year 11
Foundation

Problem solving with loci and constructions

I can use my knowledge of loci and constructions to solve problems.

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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. Your knowledge of loci can be applied to your knowledge of bearings
  2. Your knowledge of loci can be used to help solve area problems

Keywords

  • Locus/loci - A locus is a set of points that satisfy a given set of conditions. Multiple sets of points are referred to as loci.

  • Bearing - A bearing is an angle measured in degrees from North in the clockwise direction and written with three figures. E.g. an angle of 82° is written as 082°.

  • Area - The area is the size of the surface and states the number of unit squares needed to completely cover that surface.

Common misconception

Pupils may not consider that, in some contexts (e.g. a corded lawnmower), the shape of the locus will include sectors of different radii, if a shape/object is creating a barrier.

Have pupils consider the impact of going around the corner of a shape.


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

This lesson involves bearings, so you may want to check your pupils recall of bearings before delivering this lesson.
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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.
The locus of points __________ from another point can be represented by a circle.
bisecting
Correct answer: equidistant
parallel
perpendicular
Q2.
A goat is tied to a railing by a 1 metre long rope. There is a barn near the railing. Which of these shows the locus of points the goat can walk to?
An image in a quiz
Correct answer: A
B
C
D
Q3.
A motion sensor (S) can film any object up to 5 metres away. It can only detect in locations that it can see in a straight line. Which construction shows the locus of locations the sensor can detect?
An image in a quiz
A
B
Correct answer: C
Q4.
This map shows two rocks, P and S, out at sea. Any ship must stay 10 metres or more away from each rock. Which locus shows points that are all 10 metres away from rock P? (A, C have radii of 10 m).
An image in a quiz
Correct answer: A
B
C
Q5.
Laura’s grandma wants to move to a house that is within 7 km of Laura’s house at P, but more than 3 km from the river. Laura's grandma should move to region .
An image in a quiz
Correct Answer: c, C
Q6.
Two mobile phone masts (X and Y) can broadcast their signal to a maximum of 24 km. The further away from the mast, the weaker the signal is. Which points will receive a signal from both masts?
An image in a quiz
A
Correct answer: D
E
F
Correct answer: G

Exit quiz

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6 Questions

Q1.
A bearing is an angle measured in degrees from __________ in the clockwise direction and written with three figures.
East
Correct answer: North
South
West
Q2.
A boat (B) leaves a port (P) on a bearing of 047° at a speed of 20 km/h. The boat has been travelling for hours.
An image in a quiz
Correct Answer: 4
Q3.
Three sensors are set up for security. Sensor 1 has a range 15 m, sensor 2 has a range 12 m and sensor 3 has a range 20 m. Sensors 2 and 3 are activated. The intruder is likely to be in region .
An image in a quiz
Correct Answer: D, d
Q4.
A ship, S, needs to pass through a point that is midway between two buoys. Alex and Sam both do some constructions to find the correct point to pass through. Whose construction is correct?
An image in a quiz
An image in a quiz
Correct Answer: An image in a quiz
An image in a quiz
Q5.
A ship, S, needs to pass through a point that is midway between two buoys. What bearing should the ship sail on?
An image in a quiz
20°
020°
Correct answer: 160°
240°
Q6.
A goat is tethered to a horizontal pole by a rope with a ring attached. The pole is 5 metres long and the rope is 3 metres long. What is the area of region that the goat can graze?
An image in a quiz
3(12π + 5) m²
6(6π + 5) m²
3(3π + 5) m²
Correct answer: 3(3π + 10) m²