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WMA11/01 Jun 2021, Question 1: Differentiating Polynomials

Pearson Edexcel International AS Level Mathematics · Pure Mathematics 1 (WMA11) · Calculator · 8 marks

The question, in short

Differentiate y = x²/3 + 4/√x + 8/(3x) − 5 for x > 0, then use point P(4, 3) on C to find the normal's equation in the form ax + by + c = 0 with integer coefficients.

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

Part (a) · 4 marks

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

  1. 1y = (1/3)x² + 4x^(−1/2) + (8/3)x⁻¹ − 5
  2. 2Differentiate each term: (2/3)x, 4 × (−1/2)x^(−3/2), (8/3) × (−1)x⁻², and 0
  3. 3dy/dx = (2/3)x − 2x^(−3/2) − (8/3)x⁻²

Answerdy/dx = (2/3)x − 2x^(−3/2) − (8/3)x⁻²

Part (b) · 4 marks

Using P(4, 3) on C, find the normal line's equation at P as ax + by + c = 0 with integers a, b, c.

  1. 1At x = 4: dy/dx = 8/3 − 2 × 1/8 − (8/3) × 1/16 = 8/3 − 1/4 − 1/6 = 9/4
  2. 2Gradient of normal = −4/9
  3. 3y − 3 = −(4/9)(x − 4)
  4. 49y − 27 = −4x + 16
  5. 54x + 9y − 43 = 0

Answer4x + 9y − 43 = 0

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