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Chapter 12 Practice Paper: Trigonometry — question paper

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QQ/S3EM/CH12

Secondary 3 · Elementary Mathematics (G2 / G3)

Chapter 12 Practice Paper

Trigonometry

Duration: 40 minutes
Total: 30 marks
Name:
Class:
Register No.:
Date:

READ THESE INSTRUCTIONS FIRST

  • Write your name, class and register number in the spaces at the top of this page.
  • Answer all questions.
  • Show all necessary working. Omission of essential working will result in loss of marks.
  • Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless a different level of accuracy is specified in the question.
  • Geometrical instruments and an approved calculator may be used.
  • The number of marks is given in brackets [ ] at the end of each question or part question.
  • The total number of marks for each paper is shown on its cover.

Original practice material written for the MOE Elementary Mathematics syllabus. It is not an official MOE or school examination paper. Chapter 12 (G4 Trigonometry: Pythagoras, trig ratios, area formula, sine and cosine rules, elevation/depression and bearings).

For Examiner’s Use
Section A/ 30
Total/ 30

Section A: Structured questions[30 marks]

Answer all questions in the spaces provided. Show all necessary working — omission of essential working will result in loss of marks. Give non-exact numerical answers correct to 3 significant figures, and angles correct to 1 decimal place.

  1. 1

    This question tests Pythagoras’ theorem.

    1. (a)

      The two shorter sides of a right-angled triangle measure 5 cm and 12 cm. Calculate the length of the longest side.

      [2]
    2. (b)

      Determine whether a triangle with sides 6, 8 and 11 is right-angled.

      [1]
  2. 2

    In a right triangle, an angle of 38° has an adjacent side of 9 cm.

    1. (a)

      Find the length of the opposite side.

      [2]
    2. (b)

      Find the length of the hypotenuse.

      [2]
  3. 3

    This question is about the area formula ½ab sin C.

    1. (a)

      Triangle XYZ has XY = 6 cm, XZ = 10 cm and angle YXZ = 72°. Calculate the area of triangle XYZ.

      [2]
    2. (b)

      A triangle has area 40 cm² with two sides 8 cm and 15 cm. Find the included angle.

      [2]
  4. 4

    In triangle ABC, A = 38°, B = 63° and a = 9.5 cm.

    1. (a)

      Find angle C.

      [1]
    2. (b)

      Find side b.

      [3]
  5. 5

    In triangle ABC, b = 11 cm, c = 14 cm and A = 75°.

    1. (a)

      Find side a.

      [3]
    2. (b)

      Explain why the cosine rule, rather than the sine rule, is needed here.

      [1]
  6. 6

    A hiker walks 12 km on a bearing of 040°, then 15 km on a bearing of 125°.

    1. (a)

      Show that the angle between the two legs of the walk is 95°.

      [2]
    2. (b)

      Find the hiker’s distance from the starting point.

      [3]
  7. 7

    A cuboid has edges AB = 9 cm, BC = 5 cm and CG = 6 cm, with G vertically above C.

    1. (a)

      Find the length of the base diagonal AC.

      [2]
    2. (b)

      Find the space diagonal AG.

      [2]
    3. (c)

      Find the angle between AG and the base plane, correct to 1 decimal place.

      [2]

— End of paper —