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4PM1/02 Jun 2021, Question 7: Exponentials, Logarithms, e and ln

Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 2 · Calculator · 9 marks

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The question, in short

Complete a table for y = 3^(x/4) + 2, plot its graph for 0 ≤ x ≤ 5, then use a straight line to estimate a root of log₃(6 − 2x)⁴ − x = 0.

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

Part (a) · 2 marks

Fill in the missing y values for y = 3^(x/4) + 2 at the given x values, rounding to 2 decimal places.

  1. 1x = 2: 3^0.5 + 2 = 3.73
  2. 2x = 3: 3^0.75 + 2 = 4.28
  3. 3x = 4: 3¹ + 2 = 5

Answerx = 2: 3.73; x = 3: 4.28; x = 4: 5

Part (b) · 2 marks

Draw the curve y = 3^(x/4) + 2 on the grid for x from 0 to 5.

  1. 1Plot the six points from the table
  2. 2Join them with a smooth curve

AnswerSmooth increasing curve through (0, 3), (1, 3.32), (2, 3.73), (3, 4.28), (4, 5), (5, 5.95)

Part (c) · 5 marks

Draw a suitable straight line on the grid and use it to estimate, to 1 decimal place, the root of log₃(6 − 2x)⁴ − x = 0 between 0 and 5.

  1. 1log₃ (6 − 2x)⁴ = x ⇒ 4 log₃ (6 − 2x) = x ⇒ log₃ (6 − 2x) = x/4
  2. 26 − 2x = 3^(x/4)
  3. 38 − 2x = 3^(x/4) + 2
  4. 4Draw y = 8 − 2x on the grid
  5. 5The line meets the curve at x ≈ 2.1

Answerx = 2.1

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