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A-LevelMathematicsIntegration9709/22 · Feb/Mar 2025 · Q23 Marks

A curve passes through the point with coordinates (½π, 5) and is such that dy/dx = 4 sec²(½x). Find the equation of the curve.

  1. A curve passes through the point with coordinates (½π, 5) and is such that dy/dx = 4 sec²(½x). Find the equation of the curve.[3]

Mark scheme

Marking points from the official mark scheme (Feb/Mar 2025). The mark or mark type is shown in brackets.

  1. [*M1] Integrate to obtain the form y = k tan ½ x No need for c yet.
  2. [DM1] Substitute x = ½π and y=5 to determine value of c
  3. [A1] Obtain y = 8 tan ½ x – 3

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About this question

Topic
Integration, A-Level Mathematics (syllabus 9709). Structured question, 3 marks.
Source
A-Level Mathematics, Feb/Mar 2025 Paper 2 Variant 2, question 2.

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