Lemmara logoLemmaraWorked solution

WMA12/01 Jan 2021, Question 10: Arithmetic Progressions in Problems

Pearson Edexcel International AS Level Mathematics · Pure Mathematics 2 (WMA12) · Calculator · 11 marks

The question, in short

Compare two 12-week Sunday running plans from 15 km to 37 km, one linear and one percentage-based, then find the largest whole Wednesday distance x keeping the 12-week total within 360 km.

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

Part (a) · 3 marks

For plan A, with equal Sunday increases, work out the distance run on Sunday of week 5.

  1. 115 + 11d = 37
  2. 2d = 22/11 = 2
  3. 3u₅ = 15 + 4 × 2 = 23 km

Answer23 km

Part (b) · 3 marks

For plan B, with equal percentage Sunday increases, work out the week 5 Sunday distance to one decimal place in km.

  1. 115r¹¹ = 37, so r¹¹ = 37/15
  2. 2r = (37/15)^(1/11) = 1.08554…
  3. 3u₅ = 15 × 1.08554…⁴ = 20.829…
  4. 4Week 5 Sunday run = 20.8 km

Answer20.8 km

Part (ci) · 3 marks

Using plan A Sunday distances plus a fixed x km each Wednesday, find the greatest integer x with total at most 360 km.

  1. 1Plan A Sundays: S₁₂ = 12/2 × (15 + 37) = 312 km
  2. 2Wednesdays: 12x km
  3. 3312 + 12x ≤ 360, so x ≤ 4
  4. 4Maximum x = 4

Answerx = 4

Part (cii) · 2 marks

Using plan B Sunday distances plus a fixed x km each Wednesday, find the greatest integer x with total at most 360 km.

  1. 1Plan B Sundays: S₁₂ = 15(1.08554…¹² − 1)/(1.08554… − 1) = 294.185… km
  2. 2294.185… + 12x ≤ 360, so x ≤ 5.48…
  3. 3x is an integer, so maximum x = 5

Answerx = 5

Stuck on a step? Read the free lesson: Arithmetic Progressions in Problems

Practise more arithmetic progressions in problems 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 arithmetic progressions in problems

Also searched as: WMA12 January 2021 · WMA12/01 · wma12 jan21 · IAS Maths Pure Mathematics 2 January 2021 · question 10.
Lemmara is an independent study tool, not affiliated with or endorsed by Pearson Edexcel. The worked solutions are Lemmara’s own.