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A-LevelMathematicsDifferentiation9709/22 · Oct/Nov 2017 · Q36 Marks

The equation of a curve is y = tan ½x + 3 sin ½x. The curve has a stationary point M in the interval π < x < 2π. Find the coordinates of M, giving each coordinate correct to 3 significant figures.

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2017). The mark or mark type is shown in brackets.

  1. [M1] Differentiate to obtain form k₁ sec² ½x + k₂ cos ½x
  2. [A1] Obtain ½ sec² ½x + ½ cos ½x
  3. [*M1] Equate first derivative to zero and produce cos³½ x = k₃
  4. [DM1] Use correct process to find one value of x
  5. [A1] Obtain x = 4.67
  6. [A1] Obtain y = 1.12

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About this question

Topic
Differentiation, A-Level Mathematics (syllabus 9709). Structured question, 6 marks.
Source
A-Level Mathematics, Oct/Nov 2017 Paper 2 Variant 2, question 3.

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