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WMA12/01 Oct 2019, Question 7: Sigma Notation

Pearson Edexcel International AS Level Mathematics · Pure Mathematics 2 (WMA12) · Calculator · 7 marks

The question, in short

Given logₐ b = k, express three logarithmic quantities in simplest form in terms of k.

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

Part (i) · 2 marks

Find logₐ(√a / b) in simplest form using k.

  1. 1logₐ(√a / b) = logₐ a^(1/2) − logₐ b
  2. 2= (1/2)logₐ a − logₐ b
  3. 3= 1/2 − k

Answer1/2 − k

Part (ii) · 2 marks

Find logₐ(a²b) ÷ logₐ(b³) in simplest form using k.

  1. 1logₐ(a²b) = 2logₐ a + logₐ b = 2 + k
  2. 2logₐ(b³) = 3logₐ b = 3k
  3. 3Ratio = (2 + k)/(3k)

Answer(2 + k)/(3k)

Part (iii) · 3 marks

Find the sum from n=1 to 50 of (k + logₐ bⁿ) in terms of k.

  1. 1logₐ bⁿ = n logₐ b = nk, so each term is k + nk
  2. 2Sum = 50k + (k + 2k + … + 50k)
  3. 3k + 2k + … + 50k is an AP: (50/2)(2k + 49k) = 1275k
  4. 4Total = 50k + 1275k = 1325k

Answer1325k

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Also searched as: WMA12 October 2019 · WMA12/01 · wma12 oct19 · IAS Maths Pure Mathematics 2 October 2019 · question 7.
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