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A-LevelMathematicsFunctions9709/12 · Oct/Nov 2009 · Q46 Marks

The function f is defined by f : x → 5 – 3 sin 2x for 0 ≤ x ≤ π.

  1. (i)Find the range of f.[2]
  2. (ii)Sketch the graph of y = f(x).[3]
  3. (iii)State, with a reason, whether f has an inverse.[1]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2009). The mark or mark type is shown in brackets.

  1. [1] 2 (B1 for 2, B1 for 8. Must be stated, not on graph.)
  2. [1] 8 (B1 for 2, B1 for 8. Must be stated, not on graph.)
  3. [1] 1 complete oscillation
  4. [1] 1st quadrant, not touching x-axis.
  5. [1] Needs to be "down" first and curves. nb If no labels, assume 0 to π.
  6. [1] No inverse – not 1 : 1. (co. Independent of graph.)

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About this question

Topic
Functions, A-Level Mathematics (syllabus 9709). Structured question, 6 marks.
Source
A-Level Mathematics, Oct/Nov 2009 Paper 1 Variant 2, question 4.

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