Lemmara logoLemmaraWorked solution

4MA1/2H Jun 2024, Question 15: Rearranging Complex Formulas

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2H (Higher) · Calculator · 7 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

Rearrange a formula involving a square root to make g the subject, then solve a quadratic inequality in y, showing working.

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

Part (a) · 4 marks

Rearrange e = √((7g + 5)/(11 + 2g)) to make g the subject.

  1. 1Square both sides: e² = (7g + 5)/(11 + 2g).
  2. 2Multiply out: 11e² + 2e²g = 7g + 5.
  3. 3Collect the g terms: 2e²g − 7g = 5 − 11e².
  4. 4Factorise: g(2e² − 7) = 5 − 11e², so g = (5 − 11e²)/(2e² − 7)

Answerg = (5 − 11e²)/(2e² − 7)

Part (b) · 3 marks

Solve 3y² + 4y − 32 > 0, showing your working clearly.

  1. 1Factorise: (3y − 8)(y + 4) > 0.
  2. 2Critical values: y = 8/3 and y = −4.
  3. 3The graph of 3y² + 4y − 32 is a ∪ shape, so it is above 0 outside the critical values.
  4. 4y < −4 or y > 8/3

Answery < −4, y > 8/3

Stuck on a step? Read the free lesson: Rearranging Complex Formulas

Practise more rearranging complex formulas 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 rearranging complex formulas

Also searched as: 4MA1 2H June 2024 · 4MA1/2H · 4ma1 jun24 2h · question 15.
Lemmara is an independent study tool, not affiliated with or endorsed by Pearson Edexcel. The worked solutions are Lemmara’s own.