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4MA1/2HR Jun 2023, Question 12: Recognising and Sketching Graph Shapes

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2HR (Higher) · Calculator · 3 marks

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The question, in short

Six sketched graphs A to F are shown; identify which letter matches each of three given equations.

Summarised in our own words. Use the official paper for the exact wording and the diagram.

Part (a) · 1 mark

Choose the letter of the graph matching y = 10/x².

  1. 110/x² is never negative, so the graph stays above the x-axis.
  2. 2x² is the same for x and −x, so the graph is symmetric about the y-axis.
  3. 3y gets very large near x = 0 and close to 0 for large x.
  4. 4D

AnswerD

Part (b) · 1 mark

Choose the letter of the graph matching y = x − 3 + 3x² − x³.

  1. 1Simplify y = x − 3 + 3x² − x³ to y = −x³ + 3x² + x − 3
  2. 2This is a cubic function with negative leading coefficient, so it tends to -∞ as x increases
  3. 3It has turning points and crosses the x-axis in three places
  4. 4Graph C matches this shape

AnswerC

Part (c) · 1 mark

Choose the letter of the graph matching y = −3/x.

  1. 1Identify the graph of y = −3/x
  2. 2This is a reciprocal graph in quadrants II and IV, with asymptotes at axes
  3. 3Graph B shows this hyperbolic shape symmetric about the origin

AnswerB

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