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A-LevelMathematicsFunctions9709/21 · Oct/Nov 2021 · Q26 Marks

Sketch, on the same diagram, the graphs of y = 3x and y = |x − 3|.

  1. (a)Sketch, on the same diagram, the graphs of y = 3x and y = |x − 3|.[2]
  2. (b)Find the coordinates of the point where the two graphs intersect.[3]
  3. (c)Deduce the solution of the inequality 3x < |x-3|.[1]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2021). The mark or mark type is shown in brackets.

  1. [B1] Draw V-shaped graph with vertex on positive x-axis
  2. [B1] Draw straight line through origin with positive gradient greater than gradient of first graph, together with a V shaped graph
  3. [M1] Solve linear equation with signs of 3x and x different or solve non-modulus equation (3x)² = (x-3)²
  4. [A1] Obtain x = 3/2
  5. [A1] Obtain y = 9/2
  6. [B1 FT] State x < 3/2

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About this question

Topic
Functions, A-Level Mathematics (syllabus 9709). Structured question, 6 marks.
Source
A-Level Mathematics, Oct/Nov 2021 Paper 2 Variant 1, question 2.

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