Lemmara logoLemmaraWorked solution

4MA1/1HR Jan 2021, Question 12: Exponential Equations

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1HR (Higher) · Calculator · 9 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

Simplify a square-root power expression, combine two algebraic fractions into one, and solve an index equation for k showing working.

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

Part (a) · 2 marks

Simplify (16e¹⁰f⁶)^(1/2), giving the result in its simplest form.

  1. 1A power of ½ is a square root, so take the square root of each part
  2. 2√16 = 4, √(e¹⁰) = e⁵ and √(f⁶) = f³
  3. 3So the answer is 4e⁵f³

Answer4e⁵f³

Part (b) · 3 marks

Express (2x + 1)/4 + (x − 2)/3 as a single fraction in simplest form.

  1. 1The common denominator of 4 and 3 is 12
  2. 2(2x + 1)/4 = 3(2x + 1)/12 and (x − 2)/3 = 4(x − 2)/12
  3. 3Add them: (3(2x + 1) + 4(x − 2))/12
  4. 4Expand the top: 6x + 3 + 4x − 8 = 10x − 5
  5. 5So the answer is (10x − 5)/12

Answer(10x − 5)/12

Part (c) · 4 marks

Given 4^(k + 3) = 16 × 2^k, find k, showing your working clearly.

  1. 1Write both sides as powers of 2: 4 = 2², so 4^(k+3) = 2^(2k+6)
  2. 216 × 2^k = 2⁴ × 2^k = 2^(k+4)
  3. 3So 2^(2k+6) = 2^(k+4), which means 2k + 6 = k + 4
  4. 4k = −2

Answer−2

Stuck on a step? Read the free lesson: Exponential Equations

Practise more exponential equations 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 exponential equations

Also searched as: 4MA1 1HR January 2021 · 4MA1/1HR · 4ma1 jan21 1hr · question 12.
Lemmara is an independent study tool, not affiliated with or endorsed by Pearson Edexcel. The worked solutions are Lemmara’s own.