Lemmara logoLemmaraWorked solution

0606/12 May/Jun 2025, Question 8: The Product and Quotient Rules

Cambridge IGCSE Additional Mathematics 0606 · Paper 12 (Non-calculator) · Non-calculator · 6 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

Given y = ln(3x² + 16)/(x + 2), find the derivative at x = 0 in the form ln p, then approximate the change in y when x increases from 0 to small h.

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

Part (a) · 5 marks

Find dy/dx at x = 0 and express the result as ln p for a constant p.

  1. 1Quotient rule: dy/dx = ((x + 2) × 6x/(3x² + 16) − ln(3x² + 16))/(x + 2)²
  2. 2At x = 0: dy/dx = (0 − ln 16)/4
  3. 3= −(ln 16)/4 = −ln 2
  4. 4= ln(1/2)

Answerln(1/2)

Part (b) · 1 mark

For small h, state the approximate change in y as x goes from 0 to h.

  1. 1δy ≈ (dy/dx) × δx
  2. 2δy ≈ ln(1/2) × h = h ln(1/2)

Answerh ln(1/2)

Stuck on a step? Read the free lesson: The Product and Quotient Rules

Practise more the product and quotient rules questions

Real 0606 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 the product and quotient rules

Also searched as: 0606/12/M/J/25 · 0606_s25_qp_12 · 0606 s25 12 · question 8.
Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education. The worked solutions are Lemmara’s own.