A-LevelMathematicsFunctions9709/32 · Oct/Nov 2023 · Q15 Marks

1 (a) Sketch the graph of y = |4x − 2|. (b) Solve the inequality 1 + 3x < |4x − 2|.

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Mark scheme

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

B1 Show a recognizable sketch graph of y = |4x-2|. Roughly symmetrical. Should extend into the second quadrant. Ignore y=4x-2 below the axis if intention is clear e.g. dashed or the required lines are clearly bolder. Some indication of scale on both axes – accept dashes. Must go beyond (0, 2) and (1, 2). Ignore any attempt to sketch y=1+3x.
B1 Obtain critical value x=3
M1 Solve the linear equation 1+3x=2-4x
A1 Obtain critical value 1/7
A1 Obtain final answer x<1/7 [or] x>3

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Topic: Functions, A-Level Mathematics (syllabus 9709). Structured question, 5 marks.
Source: A-Level Mathematics, Oct/Nov 2023 Paper 3 Variant 2, question 1.

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