Chapter 8 Practice Paper: Trigonometric Ratios — question paper (print)

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QQ/S2MATH/CH8

Secondary 2 · Lower Secondary Mathematics (G2 / G3)

Chapter 8 Practice Paper

Trigonometric Ratios

Duration: 40 minutes

Total: 30 marks

Name:

Class:

Date:

READ THESE INSTRUCTIONS FIRST

Write your name, class and register number in the spaces at the top of this page.
Answer all questions.
Section A: write the letter (A, B, C or D) of the correct answer in the brackets provided.
Section B: write your answers in the spaces provided.
Show all working. Marks may be awarded for correct working even if the final answer is wrong.
Give units with your answers where appropriate.
The number of marks is given in brackets [ ] at the end of each question or part question.

Original practice material written for the MOE Lower Secondary Mathematics syllabus. It is not an official MOE or school examination paper. Chapter 8.

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

Section A: Multiple-choice questions[10 marks]

Answer all questions. For each question, write the letter (A, B, C or D) of the correct answer in the brackets provided.

1
In a right triangle, the side opposite the right angle is
1. Athe hypotenuse
2. Bthe opposite side of a marked angle
3. Cthe adjacent side
4. Da leg
( )
2
The tangent of an angle compares
1. Aadjacent ÷ opposite
2. Bopposite ÷ hypotenuse
3. Copposite ÷ adjacent
4. Dhypotenuse ÷ adjacent
( )
3
sin 30° equals
1. A1
2. B0.5
3. C0
4. D2
( )
4
A right triangle has an opposite side of 5 and a hypotenuse of 10. The angle is
1. A60°
2. B45°
3. C90°
4. D30°
( )
5
An angle of 45° has an adjacent side of 8. The opposite side is
1. A8
2. B5.7
3. C11.3
4. D1
( )
6
A right triangle has hypotenuse 20 and an angle of 25°. The adjacent side is closest to
1. A8.5
2. B23.8
3. C18.1
4. D9.4
( )
7
The opposite side of an angle is 7 and the hypotenuse is 25. The angle equals
1. Atan⁻¹(7/25)
2. Bsin⁻¹(7/25)
3. Ccos⁻¹(7/25)
4. D25 ÷ 7
( )
8
tan θ evaluates to 0.75. The angle θ is closest to
1. A53.1°
2. B45°
3. C30°
4. D36.9°
( )
9
A 12 m ladder leans at 65° to the ground. How high does it reach?
1. A5.1 m
2. B13.2 m
3. C10.9 m
4. D6.4 m
( )
10
As an acute angle grows from 0° towards 90°, its cosine
1. Adecreases from 1 to 0
2. Bincreases from 0 to 1
3. Cstays at 1
4. Dbecomes negative
( )

Section B: Structured questions[20 marks]

Answer all questions in the spaces provided. Show your working clearly. Give angles correct to 1 decimal place and lengths correct to 2 decimal places.

1
A right triangle has, relative to angle θ, an opposite side of 8, an adjacent side of 15 and a hypotenuse of 17.
1. (a)
  State the value of sin θ.
  sin θ =[1]
2. (b)
  State the value of cos θ.
  cos θ =[1]
3. (c)
  State the value of tan θ.
  tan θ =[1]
4. (d)
  Verify that the three sides satisfy Pythagoras’ theorem.
  [2]
2
A right triangle has a hypotenuse of 14, and an angle of 32° at one end.
1. (a)
  Which ratio finds the side opposite the 32° angle from the hypotenuse?
  ratio =[1]
2. (b)
  Work out the length of the opposite side (2 d.p.).
  [2]
3. (c)
  Work out the adjacent side as well (2 d.p.).
  [2]
3
A zipline drops 40 m in height over a horizontal distance of 75 m.
1. (a)
  Write the tangent of the cable’s angle with the horizontal as a fraction.
  tan θ =[1]
2. (b)
  Find the cable’s angle with the horizontal, correct to 1 decimal place.
  [2]
3. (c)
  Find the exact length of the cable.
  [2]
4
A ladder of length 7.5 m rests against a vertical wall, making 72° with the ground.
1. (a)
  Compute the height reached on the wall, to 2 decimal places.
  [2]
2. (b)
  How far from the wall is the foot of the ladder? Correct to 2 decimal places.
  distance =[1]
3. (c)
  A window sill sits 7.2 m up the wall. Does the ladder reach above the sill? Justify with your answer to part (a).
  [2]

— End of paper —