◈ Oracle PrepSign Up Free
O-LevelAdditional MathematicsTrigonometry4037/21 · Oct/Nov 2010 · Q1111 Marks

Solve the equation

  1. (i)5 sin x – 3 cos x = 0, for 0° ≤ x ≤ 360°,[3]
  2. (ii)2 cos² y – sin y – 1 = 0, for 0° ≤ y ≤ 360°,[5]
  3. (iii)3 sec z = 10, for 0 < z ≤ 6 radians.[3]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2010). The mark or mark type is shown in brackets.

  1. [B1] (i) tan x = 0.6
  2. [B1] (i) 31(.0) or 30.96(...)
  3. [B1√] (i) 211 (= 31 + 180)
  4. [M1] (ii) Use cos² y = 1 – sin² y
  5. [A1] (ii) 2sin² y + sin y – 1 = 0
  6. [M1] (ii) Solve 3 term quadratic for sin y
  7. [A1] (ii) 30 and 150
  8. [B1] (ii) 270
  9. [B1] (iii) cos z = 0.3
  10. [B1] (iii) 1.27
  11. [B1√] (iii) 5.02 or 5.01 (= 2π – 1.27)

Write your answer and get it marked

On Oracle Prep you can write or photograph your own answer and have it marked by AI against this mark scheme, with feedback on what you missed.

Sign up free →

About this question

Topic
Trigonometry, O-Level Additional Mathematics (syllabus 4037). Structured question, 11 marks.
Source
O-Level Additional Mathematics, Oct/Nov 2010 Paper 2 Variant 1, question 11.

Questions and mark schemes are from past examination papers and remain the copyright of the exam board. How Oracle Prep builds its content

Related Additional Mathematics questions

TrigonometryMay/June 20116m

Prove that 1/(1 - sinx) - 1/(1 + sinx) = 2 tanx secx.

TrigonometryMay/June 20127m

Given that 15cos²θ + 2sin²θ = 7, show that tan²θ = 8/5.

TrigonometryMay/June 20124m

Show that cot A + (sin A) / (1 + cos A) = cosec A.

Simultaneous equationsMay/June 20125m

In a competition the contestants search for hidden targets which are classed as difficult, medium or easy. In the fir…

Factors of polynomialsMay/June 20127m

It is given that x – 2 is a factor of f(x) = x³ + kx² – 8x – 8.

SeriesMay/June 20126m

(1 – 2x)⁷,

← Browse all past-paper questions

© 2026 Oracle Prep