A-LevelMathematicsFunctions9709/31 · May/June 2023 · Q24 Marks

Sketch the graph of y = |2x + 3|.

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Mark scheme

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

[B1] Show a recognizable sketch graph of y = |2x+3|. (Ignore any attempt to sketch y = 3x + 8). Straight lines. Vertex in approximately correct position on x axis. Symmetry.
[M1] Find x-coordinate of intersection with y = 3x + 8 OR Solve the linear inequality 3x +8>−(2x+3) OR Solve the quadratic inequality (3x+8)² >(2x+3)².
[A1] Obtain critical value x = -11/5 (or equivalent -2.2). Ignore -5 if seen if from quadratic method.
[A1] State final answer x > -11/5 only (x > -2.2) Do not condone ≥ for >.

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Topic: Functions, A-Level Mathematics (syllabus 9709). Structured question, 4 marks.
Source: A-Level Mathematics, May/June 2023 Paper 3 Variant 1, question 2.

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