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Chapter 7 Practice Paper: Trigonometric Functions, Identities and Graphs — question paper

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QQ/S3AM/CH7

Secondary 3 · Additional Mathematics (G3)

Chapter 7 Practice Paper

Trigonometric Functions, Identities and Graphs

Duration: 40 minutes
Total: 30 marks
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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.
  • 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 Additional Mathematics syllabus. It is not an official MOE or school examination paper. Chapter 7 (G1 Trigonometric functions, identities and equations — Sec 3 portion).

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, or 1 decimal place for angles in degrees, unless told otherwise.

  1. 1

    Do not use a calculator in this question.

    1. (a)

      State the exact value of each of sin 45° and tan 30°.

      values =[2]
    2. (b)

      Convert 40° into radians, leaving your answer as a multiple of π.

      radians =[1]
    3. (c)

      Find the exact value of cos 210°.

      [2]
  2. 2

    The curve y = a sin(x°) + c, where a is a positive constant, has a maximum point at (90°, 6), a minimum point at (270°, −2) and a second maximum at (450°, 6).

    1. (a)

      Write down the period of the curve.

      period =[1]
    2. (b)

      Find the values of a and c.

      [3]
    3. (c)

      Solve the equation a sin x° + c = 3.2 for 0° ≤ x ≤ 360°, using your values of a and c, giving your answers correct to 1 decimal place.

      [2]
  3. 3

    It is given that the angle A is such that cos A ≠ 0.

    1. (a)

      Express 5 − 5 sin²A as a single trigonometric term.

      term =[1]
    2. (b)

      Prove the identity (sin A + cos A)² + (sin A − cos A)² = 2.

      [3]
    3. (c)

      Given instead that sin A = 1/3 and A is obtuse, find the exact value of cos A.

      [2]
  4. 4

    Solve the following equations for 0° ≤ x ≤ 360°.

    1. (a)

      sin x = −0.6, giving your answers correct to 1 decimal place.

      [3]
    2. (b)

      2 sin²x = 1 + cos x.

      [3]
  5. 5

    Answer this question in radians. Throughout this question, 0 ≤ x ≤ 2π.

    1. (a)

      Solve the equation tan x = 1/√3, giving your answers in exact form.

      [2]
    2. (b)

      Solve the equation cos 2x = −1/2.

      [4]
    3. (c)

      State the number of roots of the equation tan x = 5 in the interval 0 ≤ x ≤ 2π.

      [1]

— End of paper —