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WMA11/01 Jun 2023, Question 4: Fractional Indices

Pearson Edexcel International AS Level Mathematics · Pure Mathematics 1 (WMA11) · Calculator · 7 marks

The question, in short

Rewrite y = (5x² + √(x³)) / ∛(8x) as y = Axᵖ + Bx^q, finding constants A, B, p and q, then differentiate.

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

Part (a) · 4 marks

Express the given fraction in the form Axᵖ + Bx^q and state the constants A, B, p and q.

  1. 1√(x³) = x^(3/2) and ∛(8x) = 2x^(1/3)
  2. 2y = 5x²/(2x^(1/3)) + x^(3/2)/(2x^(1/3))
  3. 3Subtract indices: 2 − 1/3 = 5/3 and 3/2 − 1/3 = 7/6
  4. 4y = (5/2)x^(5/3) + (1/2)x^(7/6)

Answery = (5/2)x^(5/3) + (1/2)x^(7/6)

Part (b) · 3 marks

Using the result from part a, find dy/dx with each coefficient in simplest form.

  1. 1Differentiate (5/2)x^(5/3): (5/2)(5/3)x^(2/3) = (25/6)x^(2/3)
  2. 2Differentiate (1/2)x^(7/6): (1/2)(7/6)x^(1/6) = (7/12)x^(1/6)
  3. 3dy/dx = (25/6)x^(2/3) + (7/12)x^(1/6)

Answerdy/dx = (25/6)x^(2/3) + (7/12)x^(1/6)

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