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WMA12/01 Oct 2021, Question 5: Arithmetic Progressions in Problems

Pearson Edexcel International AS Level Mathematics · Pure Mathematics 2 (WMA12) · Calculator · 6 marks

The question, in short

Silver output falls by a constant 15 tonnes each year from 480 tonnes in year 1; work with this arithmetic sequence to find a later year's output, a stopping year equation, and that year.

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

Part (a) · 2 marks

Calculate how many tonnes of silver are taken from the mine in year 14.

  1. 1a = 480, d = −15
  2. 2u₁₄ = 480 + 13 × (−15)
  3. 3= 285 tonnes

Answer285 tonnes

Part (b) · 3 marks

Using the 7770 tonne total at the end of year N, derive the quadratic N² − 65N + 1036 = 0.

  1. 1(N/2)[2 × 480 + (N − 1)(−15)] = 7770
  2. 2(N/2)(975 − 15N) = 7770
  3. 3975N − 15N² = 15540
  4. 415N² − 975N + 15540 = 0
  5. 5N² − 65N + 1036 = 0

AnswerShown: (N/2)(975 − 15N) = 7770 ⇒ N² − 65N + 1036 = 0

Part (c) · 1 mark

From the quadratic, give the number of years N.

  1. 1(N − 28)(N − 37) = 0
  2. 2N = 37 would need negative amounts in later years, so N = 28

AnswerN = 28

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