Advanced problem solving with loci and constructions | Maths

Starter quiz

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

'locus' ✓
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?

A

B ✓

C

D
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?

A

B ✓

C
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).

A

B

C ✓
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 ______.

'a' ✓
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?

A

B ✓

C

D

E ✓

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

'bearing' ✓
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.

'45' ✓
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 ______.

'E' ✓
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 $_{2}$

perpendicular bisector of B $_{1}$ B $_{2}$ ✓

perpendicular bisector of SB $_{2}$

Circle centred on S

2 circles centres on B $_1$ and B $_2$
A ship, S, needs to pass through a point that is midway between two buoys. What bearing should the ship sail on?

020°

120°

240° ✓

300°
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.

'256' ✓

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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.

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.