New

Year 11

Higher

Advanced problem solving with loci and constructions

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

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New

Year 11

Higher

Advanced problem solving with loci and constructions

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

Download all resources

Share activities with pupils

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Lesson details

Key learning points

Your knowledge of loci can be applied to your knowledge of bearings
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 give an angle rather than a bearing.

Remind pupils that a bearing is an angle, measured clockwise from North and given as three figures.

This lesson involves non-right angle trigonometry, so you may want to check your pupils recall the sine rule and cosine rule before delivering this lesson.

Teacher tip

Equipment

Protractor, pair of compasses, ruler, pencil

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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Worksheet

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Starter quiz

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6 Questions

Q1.

The of points equidistant from another point can be represented by a circle.

Correct Answer: locus

Q2.

A goat is tied to a railing by a 2 metre long rope. There is a barn near the railing. Which of these shows the locus of points the goat can walk to?

Correct answer: B

Q3.

A security camera (S) can film any object up to 5 metres away. It can only film in locations that it can see in a straight line. Which construction shows the locus of locations the camera can film?

Correct answer: B

Q4.

This map shows two rocks, P and S, out at sea. Any ship must stay 10 metres of more away from each rock. Which locus shows that are 10 metres away from rock S? (A, C have radii of 10 m).

Correct answer: C

Q5.

Sam’s family want to move to a house that is further than 7 km from a factory at P, but also still at most 3 km from the river. Sam's family should move to region .

Correct Answer: a, A

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 not receive a signal from either mast?

Correct answer: B

Correct answer: E

Exit quiz

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6 Questions

Q1.

A is an angle measured in degrees from North in the clockwise direction and written with three figures.

Correct Answer: bearing

Q2.

A boat (B) leaves a port (P) on a bearing of 051° at a speed of 20 km/h. The boat has been travelling for 3 hours and minutes.

Correct Answer: 45

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. All 3 sensors are activated. The intruder is likely to be in region .

Correct Answer: E, e

Q4.

A ship, S, needs to pass through a point that is midway between two buoys. Which construction can be used to determine the point that the ship must pass through?

angle bisector of angle B$$_{1}$$SB$$_{2}$$

Correct answer: perpendicular bisector of B$$_{1}$$B$$_{2}$$

perpendicular bisector of SB$$_{2}$$

Circle centred on S

2 circles centres on B$$_1$$ and B$$_2$$

Q5.

A ship, S, needs to pass through a point that is midway between two buoys. What bearing should the ship sail on?

020°

120°

Correct answer: 240°

300°

Q6.

A rear windscreen wiper cleans only part of the glass. The wiper blade is 24 cm long and pivots 160° from the horizontal. The area of the window that is cleaned by the blade is π cm².

Correct Answer: 256