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WMA12/01 Jan 2024, Question 7: Arithmetic Progressions in Problems

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

The question, in short

Wheat output is 300 tonnes in year 1 and predicted 4000 tonnes in year 12. Using linear model A and percentage-increase model B, find year 4, year 2, and the difference in 12-year totals.

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

Part (a) · 3 marks

With model A (equal yearly increase), find the year 4 wheat amount to the nearest 10 tonnes.

  1. 1Arithmetic sequence: u₁₂ = a + 11d
  2. 24000 = 300 + 11d, so d = 3700/11 ≈ 336.36
  3. 3u₄ = 300 + 3d = 300 + 1009.09 = 1309.09…
  4. 4≈ 1310 tonnes

Answer1310 tonnes

Part (b) · 3 marks

With model B (equal yearly percentage increase), find the year 2 wheat amount to the nearest 10 tonnes.

  1. 1Geometric sequence: u₁₂ = ar¹¹
  2. 24000 = 300r¹¹, so r¹¹ = 40/3
  3. 3r = (40/3)^(1/11) ≈ 1.2655
  4. 4u₂ = 300r ≈ 379.65 ≈ 380 tonnes

Answer380 tonnes

Part (c) · 3 marks

Find the difference between the year 1 to year 12 total amounts under models A and B, nearest 10 tonnes.

  1. 1Model A total: S₁₂ = 12/2 × (300 + 4000) = 25800
  2. 2Model B total: S₁₂ = 300(r¹² − 1)/(r − 1) with r ≈ 1.26551
  3. 3≈ 17935.2
  4. 4Difference = 25800 − 17935.2 = 7864.8 ≈ 7860 tonnes

Answer7860 tonnes (7870 also accepted)

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Also searched as: WMA12 January 2024 · WMA12/01 · wma12 jan24 · IAS Maths Pure Mathematics 2 January 2024 · question 7.
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