Advanced problem solving with loci and constructions

12 questions

1. The ___ of points equidistant from another point can be represented by a circle.
2. 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?
3. 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?
4. 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).
5. 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 ___.
6. 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?
7. A ___ is an angle measured in degrees from North in the clockwise direction and written with three figures.
8. 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.
9. 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 ___.
10. 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?
11. A ship, S, needs to pass through a point that is midway between two buoys. What bearing should the ship sail on?
12. 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.

License: OGL