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WMA11/01 Oct 2022, Question 1: Differentiating Polynomials

Pearson Edexcel International AS Level Mathematics · Pure Mathematics 1 (WMA11) · Calculator · 6 marks

The question, in short

Differentiate a cubic-plus-reciprocal curve for x > 0, then find the tangent at R(2, 13/2) and give it as 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) · 3 marks

Find dy/dx of y = x³/4 − x² + 17/x in its simplest form.

  1. 1y = (1/4)x³ − x² + 17x⁻¹
  2. 2dy/dx = (3/4)x² − 2x − 17x⁻²

Answerdy/dx = (3/4)x² − 2x − 17x⁻²

Part (b) · 3 marks

Find the tangent to C at R(2, 13/2), writing it as ax + by + c = 0 with integers a, b, c.

  1. 1At x = 2: dy/dx = (3/4)(4) − 4 − 17/4 = −21/4
  2. 2y − 13/2 = −21/4 (x − 2)
  3. 34y − 26 = −21x + 42
  4. 421x + 4y − 68 = 0

Answer21x + 4y − 68 = 0

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