Chapter 1 Practice Paper: Further Trigonometry — Identities and Equations — question paper (print)

Back to Chapter 1

Mark scheme PDF

QuizQuipPractice Series

QQ/S4AM/CH1

Secondary 4 · Additional Mathematics (G3)

Chapter 1 Practice Paper

Further Trigonometry — Identities and Equations

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.
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 1 (G1 Trigonometric functions, identities and equations — Sec 4 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
Answer this question without a calculator.
1. (a)
  Show, using the compound-angle formulae, that cos 105° = (√2 − √6)/4.
  [3]
2. (b)
  Write down the exact value of cos 15°.
  cos 15° =[1]
3. (c)
  Show that tan 15° = 2 − √3.
  [2]
2
It is given that 2 sin θ − 5 cos θ can be written as R sin(θ − α), where R > 0 and 0° < α < 90°.
1. (a)
  State the value of R and the value of α, giving α correct to 1 decimal place.
  [4]
2. (b)
  State the maximum and minimum values of 2 sin θ − 5 cos θ.
  max, min =[2]
3. (c)
  Write down the smallest positive value of θ at which the maximum occurs.
  θ =[1]
3
A is an acute angle.
1. (a)
  Show that (sin A + cos A)² = 1 + sin 2A.
  [3]
2. (b)
  Given that cos 2A = 1/3, find the exact value of cos A.
  [3]
4
Find all the angles x between 0° and 360° for which sin 2x = 0.6, giving your answers correct to 1 decimal place.
1. Show all steps of your working, from the principal value to the full solution set.
  [6]
5
Solve the equation cos 2θ = cos θ for 0° ≤ θ ≤ 360°.
1. Solve the equation, showing the substitution and factorising clearly.
  [5]

— End of paper —