Lemmara logoLemmaraWorked solution

WMA11/01 Jun 2021, Question 5: Quadratic Inequalities

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

The question, in short

Given P_A = 53 − 0.4(t − 8)² and P_B = −1.6t + 44.2 for t ≥ 0, with a graph of both models, work out values and compare the two share value models over 15 years.

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

Part (a) · 2 marks

Work out how far apart the two companies' share values are at the moment monitoring started.

  1. 1At t = 0: P_A = 53 − 0.4 × 64 = 27.4
  2. 2At t = 0: P_B = 44.2
  3. 3Difference = 44.2 − 27.4 = 16.8, so £16.8 million

Answer£16.8 million

Part (b) · 1 mark

Give the largest share value company A reaches within the 15-year window.

  1. 1(t − 8)² ≥ 0, so P_A is greatest when t = 8
  2. 2Maximum P_A = 53, so £53 million

Answer£53 million

Part (c) · 4 marks

Using algebra with clear working, determine the time intervals when company A's share value exceeds company B's.

  1. 1Set equal: 53 − 0.4(t − 8)² = −1.6t + 44.2
  2. 253 − 0.4t² + 6.4t − 25.6 = −1.6t + 44.2
  3. 30.4t² − 8t + 16.8 = 0, so t² − 20t + 42 = 0
  4. 4t = 10 ± √58, giving t = 2.38 or t = 17.6 (outside the period)
  5. 5P_A > P_B between the roots, so 2.38 < t ≤ 15

Answer2.38 < t ≤ 15 (t > 10 − √58)

Part (d) · 1 mark

Give a reason the company A formula is unsuitable for predicting the share value at t = 20.

  1. 1P_A(20) = 53 − 0.4 × 12² = 53 − 57.6 = −4.6
  2. 2A share value cannot be negative, so the model fails at t = 20 (it was only fitted for 15 years)

AnswerAt t = 20, P_A = 53 − 0.4(12)² = −4.6, a negative share value, which is impossible (also the model was only for 15 years)

Stuck on a step? Read the free lesson: Quadratic Inequalities

Practise more quadratic inequalities 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 quadratic inequalities

Also searched as: WMA11 June 2021 · WMA11/01 · wma11 jun21 · IAS Maths Pure Mathematics 1 June 2021 · question 5.
Lemmara is an independent study tool, not affiliated with or endorsed by Pearson Edexcel. The worked solutions are Lemmara’s own.