Lemmara logoLemmaraWorked solution

WMA11/01 Jan 2020, Question 10: Sketching Cubics and Reciprocal Curves

Pearson Edexcel International AS Level Mathematics · Pure Mathematics 1 (WMA11) · Calculator · 8 marks

The question, in short

Given cubic f(x) = (4x − 3)(x − 5)², draw its curve with axis intercepts, solve related equations, and work with the shifted curve g(x) = f(x + 1).

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

Part (a) · 3 marks

Draw the graph of y = f(x), marking where it meets the x-axis and y-axis, including any touching point.

  1. 1The x³ coefficient is 4 > 0, so it is a positive cubic
  2. 2Roots: 4x − 3 = 0 gives x = 3/4 (crosses); (x − 5)² gives a repeated root at x = 5 (touches)
  3. 3At x = 0: y = (−3)(25) = −75

AnswerPositive cubic: rises from bottom left, crosses the y-axis at (0, −75), crosses the x-axis at (3/4, 0), reaches a maximum, then comes down to touch the x-axis at (5, 0) (a minimum) and rises again

Part (bi) · 1 mark

Solve f((1/4)x) = 0 to find the x values.

  1. 1f(¼x) = 0 when ¼x = 3/4 or ¼x = 5
  2. 2So x = 3 or x = 20

Answerx = 3, x = 20

Part (bii) · 1 mark

Determine the constant p so that y = f(x) + p goes through the origin.

  1. 1The curve meets the y-axis at (0, −75)
  2. 2Shifting up by 75 makes it pass through the origin, so p = 75

Answerp = 75

Part (ci) · 2 marks

Express g(x) = f(x + 1) in simplest form, factorised if preferred.

  1. 1g(x) = f(x + 1) = (4(x + 1) − 3)((x + 1) − 5)²
  2. 2= (4x + 1)(x − 4)²

Answerg(x) = (4x + 1)(x − 4)²

Part (cii) · 1 mark

Use your g(x) to find where curve C₂ meets the y-axis.

  1. 1Set x = 0 in g(x): (1)(−4)²
  2. 2= 16, so the y-intercept is 16

Answer16 (the point (0, 16))

Stuck on a step? Read the free lesson: Sketching Cubics and Reciprocal Curves

Practise more sketching cubics and reciprocal curves questions

Real XMA01 past-paper questions, marked on your working like the exam, with a worked solution for every part.

Practise free on Lemmara

More past-paper questions on sketching cubics and reciprocal curves

Also searched as: WMA11 January 2020 · WMA11/01 · wma11 jan20 · IAS Maths Pure Mathematics 1 January 2020 · question 10.
Lemmara is an independent study tool, not affiliated with or endorsed by Pearson Edexcel. The worked solutions are Lemmara’s own.