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O-LevelAdditional MathematicsDifferentiation and integration4037/22 · Oct/Nov 2019 · Q25 Marks

Given that y = 2 sin 3x + cos 3x, show that d²y/dx² + dy/dx + 3y = k sin 3x, where k is a constant to be determined.

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2019). The mark or mark type is shown in brackets.

  1. B1 dy/dx = 6 cos 3x
  2. B1 -3 sin 3x
  3. B1 d²y/dx² = -18sin3x-9cos3x FT Correct derivative of their dy/dx
  4. M1 Insert and collect like terms Must insert for y, their dy/dx and d²y/dx² correctly resulting in 6 terms.
  5. A1 k = -15 Allow -15sin3x seen nfww

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About this question

Topic
Differentiation and integration, O-Level Additional Mathematics (syllabus 4037). Structured question, 5 marks.
Source
O-Level Additional Mathematics, Oct/Nov 2019 Paper 2 Variant 2, question 2.

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