4PM1/02R Jan 2022, Question 8: Connected Rates of Change and Small Changes

Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 2R · Calculator · 7 marks

The question, in short

A stain grows as a circle on cloth from t = 0, with area increasing at 1.5 cm²/s. Find the radius at t = 4 s in terms of π, and the radius growth rate then.

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

Part (a) · 3 marks

Find the stain's radius at t = 4 seconds, giving the answer in terms of π.

1Area at t = 4: 4 × 1.5 = 6 cm²
2πr² = 6
3r = √(6/π)

Answerr = √(6/π) cm

Part (b) · 4 marks

Find how fast the radius is increasing at t = 4 seconds, in cm/s to 3 significant figures.

1A = πr², dA/dr = 2πr
2dr/dt = dr/dA × dA/dt = 1.5/(2πr)
3= 1.5/(2π√(6/π))
4= 0.173 cm/s

Answer0.173 cm/s

Stuck on a step? Read the free lesson: Connected Rates of Change and Small Changes

Practise more connected rates of change and small changes questions

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

Practise free on Lemmara

4PM1/02R Jan 2022, Question 8: Connected Rates of Change and Small Changes

The question, in short

Part (a) · 3 marks

Part (b) · 4 marks

Practise more connected rates of change and small changes questions

More past-paper questions on connected rates of change and small changes