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WMA12/01 Jun 2019, Question 7: Arithmetic Progressions in Problems

Pearson Edexcel International AS Level Mathematics · Pure Mathematics 2 (WMA12) · Calculator · 9 marks

The question, in short

Kim's year 1 salary is £16 200 and year 10 salary is £31 500. Using two salary models, find year 2 salaries and compare total earnings over years 1 to 10.

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

Part (a) · 3 marks

With model A, salary rises by a fixed amount yearly. Find Kim's year 2 annual salary.

  1. 131 500 = 16 200 + 9d
  2. 29d = 15 300, so d = 1700
  3. 3Year 2 salary = 16 200 + 1700 = £17 900

Answer£17 900

Part (b) · 3 marks

With model B, salary rises by a fixed percentage yearly. Find year 2 salary to the nearest £10.

  1. 131 500 = 16 200r⁹
  2. 2r⁹ = 31 500/16 200 = 35/18
  3. 3r = (35/18)^(1/9) = 1.07668...
  4. 4Year 2 salary = 16 200 × 1.07668... = 17 442.3
  5. 5To the nearest £10: £17 440

Answer£17 440

Part (c) · 3 marks

Using both models, find the difference in total earnings from year 1 to year 10 inclusive, to the nearest £10.

  1. 1Model A total: S₁₀ = (10/2)(16 200 + 31 500) = 238 500
  2. 2Model B total: S₁₀ = 16 200(r¹⁰ − 1)/(r − 1) with r = (35/18)^(1/9), = 231 019.2...
  3. 3Difference = 238 500 − 231 019.2 = 7480.8
  4. 4To the nearest £10: £7480

Answer£7480

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Also searched as: WMA12 June 2019 · WMA12/01 · wma12 jun19 · IAS Maths Pure Mathematics 2 June 2019 · question 7.
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