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Topic 16 Practice Paper: Trigonometry — question paper

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QQ/IGCSE-MATHS/T16

IGCSE · Cambridge IGCSE Mathematics (Extended (Core + Extended))

Topic 16 Practice Paper

Trigonometry

Duration: 40 minutes
Total: 30 marks
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Class:
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Date:

READ THESE INSTRUCTIONS FIRST

  • Answer all questions.
  • Section A contains ten multiple-choice questions. Choose one answer, A, B, C or D, for each.
  • Section B contains structured questions. Write your answers in the spaces provided.
  • The number of marks is given in brackets [ ] at the end of each question or part question.
  • The total mark for this paper is 30.

Original practice material written against the Cambridge IGCSE Mathematics syllabus. It is not an official Cambridge examination paper. Topic 16: Pythagoras’ theorem, SOHCAHTOA in right-angled triangles, angles of elevation and depression, exact trigonometric values, trigonometric graphs and equations, the sine and cosine rules, ½ab sin C, and 3-D problems.

For Examiner’s Use
Section A/ 10
Section B/ 20
Total/ 30

Section A: Multiple-choice questions[10 marks]

Choose one answer for each question. Every correct answer scores one mark.

  1. 1

    A right-angled triangle has shorter sides 9 cm and 40 cm. The hypotenuse is

    1. A49 cm
    2. B41 cm
    3. C32 cm
    4. D39 cm
    ( )
  2. 2

    The exact value of sin 60° is

    1. A½
    2. B√2⁄2
    3. C√3⁄3
    4. D√3⁄2
    ( )
  3. 3

    If tan θ = 0.75, then θ is closest to

    1. A36.9°
    2. B41.6°
    3. C48.4°
    4. D53.1°
    ( )
  4. 4

    One solution of sin x = sin 40° is x = 40°. The other solution between 0° and 360° is

    1. A50°
    2. B130°
    3. C140°
    4. D220°
    ( )
  5. 5

    A kite string is 25 m long and makes an angle of 62° with the ground. The kite’s height is closest to

    1. A11.7 m
    2. B22.1 m
    3. C28.3 m
    4. D47.0 m
    ( )
  6. 6

    In triangle ABC, angle A = 52°, side a = x, angle B = 37° and side b = 8 cm. Using the sine rule, x is closest to

    1. A6.1 cm
    2. B8.9 cm
    3. C10.5 cm
    4. D12.8 cm
    ( )
  7. 7

    Two sides of a triangle are 5 cm and 7 cm with 80° between them. The third side is closest to

    1. A8.6 cm
    2. B9.3 cm
    3. C7.9 cm
    4. D12.1 cm
    ( )
  8. 8

    The area of a triangle with sides 6 cm and 9 cm enclosing an angle of 40° is closest to

    1. A17.4 cm²
    2. B20.7 cm²
    3. C27.0 cm²
    4. D34.7 cm²
    ( )
  9. 9

    A cuboid measures 2 cm by 5 cm by 14 cm. Its space diagonal is

    1. A14.9 cm
    2. B15 cm
    3. C19 cm
    4. D21 cm
    ( )
  10. 10

    From a window 30 m above the ground, the angle of depression of a car is 35°. The car’s horizontal distance from the building is closest to (Extended)

    1. A21.0 m
    2. B24.6 m
    3. C36.6 m
    4. D42.8 m
    ( )

Section B: Structured questions[20 marks]

Answer all questions in the spaces provided. Show all your working.

  1. 11

    An isosceles triangle has two equal sides of 10 cm and a base of 12 cm.

    1. (a)

      Find the height of the triangle.

      [2]
    2. (b)

      Find the area of the triangle.

      [2]
    3. (c)

      Find the perimeter of the triangle.

      [1]
  2. 12

    A 5 m ladder leans against a vertical wall and reaches 4.6 m up the wall.

    1. (a)

      Find the angle the ladder makes with the ground, to 1 decimal place.

      [3]
    2. (b)

      Find the distance from the foot of the ladder to the wall, to 3 significant figures.

      [2]
  3. 13

    Exact values and trigonometric equations. (Extended)

    1. (a)

      Evaluate (sin 30°)² + (cos 30°)².

      [1]
    2. (b)

      Solve tan x = √3 for 0° ⩽ x ⩽ 360°.

      [2]
    3. (c)

      Solve sin x = −½ for 0° ⩽ x ⩽ 360°.

      [2]
  4. 14

    A triangle has sides 7 cm and 10 cm with an angle of 68° between them. (Extended)

    1. (a)

      Find the third side, to 3 significant figures.

      [3]
    2. (b)

      Find the area of this triangle, giving your answer to 3 significant figures.

      [2]

— End of paper —