Lemmara logoLemmaraWorked solution

4PM1/01 Nov 2023, Question 3: Integration: Undoing Differentiation

Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 1 · Calculator · 8 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

Given g′(x) = mx² − 10x − 37 with integer m, curve through (1, 20) and factor (x − 5), show the cubic form of g(x) then solve g(x) = 0.

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

Part (a) · 5 marks

Show that g(x) = 2x³ − 5x² − 37x + 60 using the gradient, the point (1, 20) and the factor (x − 5).

  1. 1g(x) = mx³/3 − 5x² − 37x + c
  2. 2g(1) = 20: m/3 − 5 − 37 + c = 20, so m/3 + c = 62
  3. 3g(5) = 0: 125m/3 − 125 − 185 + c = 0, so 125m/3 + c = 310
  4. 4Subtract: (124/3)m = 248, so m = 6, c = 60
  5. 5g(x) = 2x³ − 5x² − 37x + 60

Answerg(x) = 2x³ − 5x² − 37x + 60 shown

Part (b) · 3 marks

Use algebra, using part (a) or otherwise, to solve the equation g(x) = 0.

  1. 1Divide by (x − 5): g(x) = (x − 5)(2x² + 5x − 12)
  2. 22x² + 5x − 12 = (2x − 3)(x + 4)
  3. 3x = 5, 3/2, −4

Answerx = 5, x = 3/2, x = −4

Stuck on a step? Read the free lesson: Integration: Undoing Differentiation

Practise more integration: undoing differentiation questions

Real 4PM1 past-paper questions, marked on your working like the exam, with a worked solution for every part.

Practise free on Lemmara

More past-paper questions on integration: undoing differentiation

Also searched as: 4PM1 1 November 2023 · 4PM1/01 · 4pm1 nov23 1 · question 3.
Lemmara is an independent study tool, not affiliated with or endorsed by Pearson Edexcel. The worked solutions are Lemmara’s own.