Core Mathematics

1The bearing of due south-west is

2A man walks 5 km on bearing 090° and then 12 km on bearing 180°. Find the bearing of his final position from the start (tan⁻¹ 2.4 ≈ 67.4°).

3A ship sails 5 km due east then 12 km due north. How far is it from the start?

4What is the bearing of due west?

5If a = (2, 3) and b = (−1, 4), find a + 2b.

6If the bearing of P from Q is 130°, the bearing of Q from P is

7The bearing of north-west is

8A plane flies 300 km on a bearing of 150°. How far south of its start is it? (cos 30° ≈ 0.866)

9If a = (3, 4) and b = (1, −2), find a + b.

10P is 6 km east and 8 km north of Q. The bearing of Q from P is about (tan⁻¹ 0.75 ≈ 36.9°)