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O-LevelAdditional MathematicsTrigonometry4037/12 · Oct/Nov 2024 · Q17 Marks

The curve y = acos bx+c, where a, b and c are integers, passes through the points (-π/6,-2) and (π/2, 1). The curve has a period of 2π/3.

  1. (a)Find the values of a, b and c.[4]
  2. (b)Find the least value of y on the curve for 0 ≤ x ≤ π/2, and state the value of x at which this occurs.[3]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2024). The mark or mark type is shown in brackets.

  1. [B1] b = 3
  2. [M1] Use of y = a cosbx + c, with their b and either set of given coordinates
  3. [A1] c = -2
  4. [A1] a = 5
  5. [B1] Minimum when cos bx = −1 soi
  6. [B1] x = π / 3
  7. [B1] y = -7

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About this question

Topic
Trigonometry, O-Level Additional Mathematics (syllabus 4037). Structured question, 7 marks.
Source
O-Level Additional Mathematics, Oct/Nov 2024 Paper 1 Variant 2, question 1.

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