Lemmara logoLemmaraWorked solution

4MA1/1HR Jan 2023, Question 19: Inverse Proportion: y = k/x

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1HR (Higher) · Calculator · 6 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

P varies inversely as y squared, with P = a when y = 4. Use the additional direct proportion between y and √x, plus x = a giving P = 4a, to derive two formulas.

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

Part (a) · 3 marks

Express P as a formula involving y and a, using the inverse square relationship and the given pair of values.

  1. 1P is inversely proportional to y², so P = k/y² for a constant k.
  2. 2When y = 4, P = a: a = k/4² = k/16
  3. 3k = 16a
  4. 4P = 16a/y²

AnswerP = 16a/y²

Part (b) · 3 marks

Using y proportional to √x and the condition x = a, P = 4a, write P as a formula in x and a.

  1. 1When P = 4a: 4a = 16a/y²
  2. 2y² = 16a/(4a) = 4, so y = 2 when x = a
  3. 3y is directly proportional to √x, so y = c√x for a constant c.
  4. 4When x = a, y = 2: 2 = c√a, so c = 2/√a
  5. 5y² = c²x = (4/a)x
  6. 6P = 16a/y² = 16a ÷ (4x/a) = 16a × a/(4x)
  7. 7P = 4a²/x

AnswerP = 4a²/x

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 1HR January 2023 · 4MA1/1HR · 4ma1 jan23 1hr · question 19.
Lemmara is an independent study tool, not affiliated with or endorsed by Pearson Edexcel. The worked solutions are Lemmara’s own.