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WMA11/01 Jan 2023, Question 1: Differentiating Polynomials

Pearson Edexcel International AS Level Mathematics · Pure Mathematics 1 (WMA11) · Calculator · 5 marks

The question, in short

Differentiate y = 2 + 10x^(1/2) − 2x^(3/2) for x > 0, then use the derivative to find the tangent gradient at x = 2 exactly.

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

Part (a) · 3 marks

Find dy/dx of the given curve, giving the derivative in its simplest form.

  1. 12 → 0
  2. 210x^(1/2) → 10 × ½ x^(−1/2) = 5x^(−1/2)
  3. 3−2x^(3/2) → −2 × (3/2)x^(1/2) = −3x^(1/2)
  4. 4dy/dx = 5x^(−1/2) − 3x^(1/2)

Answerdy/dx = 5x^(−1/2) − 3x^(1/2)

Part (b) · 2 marks

Using your derivative, calculate the exact gradient of the tangent to C at x = 2, simplified, without calculator methods.

  1. 1At x = 2: dy/dx = 5/√2 − 3√2
  2. 25/√2 = (5/2)√2
  3. 3(5/2)√2 − 3√2 = −½√2

Answer−½√2

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Also searched as: WMA11 January 2023 · WMA11/01 · wma11 jan23 · IAS Maths Pure Mathematics 1 January 2023 · question 1.
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