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O-LevelAdditional MathematicsDifferentiation and integration4037/22 · Oct/Nov 2023 · Q810 Marks

A curve has equation y = xsin 2x.

  1. (a)Find dy/dx.[2]
  2. (b)Find the equation of the tangent to the curve at x = π/4.[3]
  3. (c)Use your answer to part (a) to find the exact value of ∫₀^(π/8) 2x cos 2x dx.[5]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2023). The mark or mark type is shown in brackets.

  1. [B1] Derivative of sin2x: 2cos2x soi
  2. [B1] Product rule: x × 2cos2x + [1]sin 2x isw
  3. [B1] y = π/4 soi, isw
  4. [B1] dep on correct derivative for gradient of tangent: 1 soi
  5. [B1] dep on correct derivative for y = x or y - x = 0 or x - y = 0
  6. [M3] M2 for xsin2x + k cos 2x where k > 0 or k = -1/2; nfww
  7. [M1] for ∫2xcos2xdx = xsin2x - ∫sin2xdx or -cos2x/2 + ∫2xcos2xdx = xsin2x
  8. [A1] (π/8)sin(π/4) + 1/2 cos(π/4) - 1/2 cos(0)
  9. [A1] (π√2 + 4√2 - 8) / 16

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About this question

Topic
Differentiation and integration, O-Level Additional Mathematics (syllabus 4037). Structured question, 10 marks.
Source
O-Level Additional Mathematics, Oct/Nov 2023 Paper 2 Variant 2, question 8.

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