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4MA1/1H Jun 2023, Question 11: Gradient of a Curve at a Point

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1H (Higher) · Calculator · 6 marks

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The question, in short

For the curve y = 4x³ + x² − 20x, differentiate it and then find the x coordinates of points where the gradient equals 4, showing algebraic working.

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

Part (a) · 2 marks

Differentiate y = 4x³ + x² − 20x to obtain dy/dx.

  1. 1Differentiate 4x³: 3 × 4x² = 12x²
  2. 2Differentiate x²: 2x
  3. 3Differentiate −20x: −20
  4. 4Combine: 12x² + 2x − 20

Answer12x² + 2x − 20

Part (b) · 4 marks

Solve for the x coordinates on C where the gradient is 4, showing clear algebraic working.

  1. 1Set dy/dx = 4: 12x² + 2x − 20 = 4
  2. 2Rearrange and divide by 2: 6x² + x − 12 = 0
  3. 3Factorise: (3x − 4)(2x + 3) = 0
  4. 4x = 4/3 or x = −3/2

Answer4/3, −3/2

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