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O-LevelAdditional MathematicsFunctions4037/12 · May/June 2025 · Q13 Marks

The diagram shows the graph of y = |f(x)|, where f is a cubic polynomial. Find expressions for the two possible functions f(x). Write each expression in fully factorised form.

  1. Find expressions for the two possible functions f(x). Write each expression in fully factorised form.[3]

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Mark scheme

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

  1. [B1] ± with 3 factors or expanded out cubic
  2. [B1] 1/2 in a product with 3 factors
  3. [B1] (x+2)(2x+1)(x-3) and no extra terms or 2(x+2)(x+0.5)(x-3) and no extra terms

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About this question

Topic
Functions, O-Level Additional Mathematics (syllabus 4037). Structured question, 3 marks.
Source
O-Level Additional Mathematics, May/June 2025 Paper 1 Variant 2, question 1.

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