Lemmara logoLemmaraWorked solution

4MA1/2H Jun 2021, Question 16: Inverse Proportion: y = k/x

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2H (Higher) · Calculator · 6 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

Given A inversely proportional to r squared, with A = 5 when r = 0.3, derive the formula and then find A for a new r value.

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

Part (a) · 3 marks

Find a formula expressing A in terms of r using the inverse square relationship and the given pair of values.

  1. 1Inversely proportional to r²: A = k/r²
  2. 25 = k/0.3² = k/0.09
  3. 3k = 5 × 0.09 = 0.45
  4. 4A = 0.45/r²

AnswerA = 0.45/r²

Part (b) · 3 marks

Using the proportionality, find A when r = 7.5A.

  1. 1A = 0.45 / r² and r = 7.5A
  2. 2A = 0.45 / (7.5A)²
  3. 3(7.5A)² = 56.25A², so A = 0.45 / (56.25A²)
  4. 4Multiply both sides by 56.25A²: 56.25A³ = 0.45
  5. 5A³ = 0.45 ÷ 56.25 = 0.008
  6. 6A = ∛0.008
  7. 7A = 0.2

Answer0.2

Stuck on a step? Read the free lesson: Inverse Proportion: y = k/x

Practise more inverse proportion: y = k/x questions

Real 4MA1 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 inverse proportion: y = k/x

Also searched as: 4MA1 2H June 2021 · 4MA1/2H · 4ma1 jun21 2h · question 16.
Lemmara is an independent study tool, not affiliated with or endorsed by Pearson Edexcel. The worked solutions are Lemmara’s own.