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O-LevelAdditional MathematicsTrigonometry4037/22 · Oct/Nov 2012 · Q1112 Marks

Solve 4sinx + 9cosx = 0 for 0° < x < 360°.

  1. (a)Solve 4sinx + 9cosx = 0 for 0° < x < 360°.[3]
  2. (b)Solve cosecy – 1 = 12 siny for 0° < y < 360°.[5]
  3. (c)Solve 3sec(z/3) = 5 for 0 < z < 6π radians.[4]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2012). The mark or mark type is shown in brackets.

  1. [B1] tan x = -2.25
  2. [B1] 114
  3. [B1] 294
  4. [B1] Uses cosec y = 1/sin y
  5. [M1] Forms quadratic in sin y : 12sin²y + sin y – 1 [= 0]
  6. [M1] (4sin y-1)(2sin y + 1)[= 0]
  7. [A1] 14.5 and 199.5
  8. [A1] 165.5 and 340.5
  9. [B1] cos(z/3) = 3/5
  10. [M1] z/3 = 0.927
  11. [A1] z = 2.78 to 2.79 inc
  12. [A1] z = 16.1

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About this question

Topic
Trigonometry, O-Level Additional Mathematics (syllabus 4037). Structured question, 12 marks.
Source
O-Level Additional Mathematics, Oct/Nov 2012 Paper 2 Variant 2, question 11.

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