# Exam-style Questions: Trigonometry

1. In the diagram A and B are the midpoints of OC and OD respectively. a) Write down in terms of a and b.

(1 mark)

b) (i) Write down in terms of a.

(1 mark)

(ii) Use a vector method to prove that CD is parallel to AB.

(3 marks)

(iii) What other conclusions can you make about AB and CD?

(1 mark)

E is the midpoint of CD.

c) Use a vector method to prove that OAEB is a parallelogram.

(2 marks)

(Marks available: 8)

Answer outline and marking scheme for question: 1

a) 2a

(1 mark)

b) (i) b - a

(1 mark)

(ii) 2b - 2a

(3 marks)

(iii) CD is twice as long as AB.

(2 marks)

c) AE = AC + ½ CD = b

(1 mark)

(Marks available: 8)

2. The diagram shows the positions of points A, B, C and D.

A is due North of C. The straight line BCD is perpendicular to AC.

A is 12.4 kilometres from B and 8.5 kilometres from C.

a) Calculate the distance BC.

(3 marks)

b) The bearing of D from A is 138°.

Calculate the distance DC.

(3 marks)

(Marks available: 6)

Answer outline and marking scheme for question: 2

a) 8.9 to 8.94

(3 marks)

b) 7.7 to 7.75

(3 marks)

(Marks available: 6)

3. a) The diagram shows a kite ABCD with measurements in metres.

BD bisects AC at right angles.

Calculate the size of angle ABC.

(4 marks)

b) PQRS is similar to ABCD.

PR is of length 1m.

Calculate the length of the side PS.

(2 marks)

(Marks available: 6)

Answer outline and marking scheme for question: 3

a) 83.6° to 84°

(4 marks)

b) 1.125

(2 marks)

(Marks available: 6)

4. O is the centre of a circle through A, B, C and D.

Angle DOC is 110° and angle OCB is 65°.

a) (i) Find angle DBC.

(1 mark)

(ii) Fnd angle DCO.

(1 mark)

(iii) Find angle DAB.

(1 mark)

b) (i) Find angle PXZ.

(1 mark)

(ii) Find angle OTY.

(2 marks)

(Marks available: 6)

Answer outline and marking scheme for question: 4

a) (i) 55

(1 mark)

(ii) 35

(1 mark)

(iii) 80

(1 mark)

b) (i) 54°

(1 mark)

(ii) 22°

(2 marks)

(Marks available: 6) 