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0580/43 May/Jun 2023, Question 10: Exponential Functions

Cambridge IGCSE Mathematics 0580 · Paper 43 (Extended) · Calculator · 12 marks

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The question, in short

Using y = 2^x − 3 with a partly filled table, complete values, plot and sketch the curve, then use graphs to solve two related equations.

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

Part (a) · 3 marks

Calculate the missing y values in the table for y = 2^x − 3 at the given x values.

  1. 1x = −1: 2⁻¹ − 3 = 0.5 − 3 = −2.5
  2. 2x = 0: 2⁰ − 3 = 1 − 3 = −2
  3. 3x = 1: 2¹ − 3 = −1

Answer−2.5, −2, −1

Part (b) · 4 marks

Plot the completed points and draw the curve y = 2^x − 3 on the grid for −2 ≤ x ≤ 2.5.

  1. 1Plot (−2, −2.75), (−1, −2.5), (0, −2), (0.5, −1.58), (1, −1), (1.5, −0.17), (2, 1), (2.5, 2.66)
  2. 2Join with a smooth increasing curve

AnswerCorrect smooth curve through the 8 plotted points

Part (c) · 1 mark

Use your graph of y = 2^x − 3 to find the x value where 2^x − 3 = 2.

  1. 1Draw across from y = 2 to the curve
  2. 2Read down: x ≈ 2.3

Answer2.3 to 2.4

Part (d) · 4 marks

Draw a suitable straight line on the graph to solve 2^x − x − 1.5 = 0.

  1. 12ˣ − x − 1.5 = 0 → 2ˣ − 3 = x − 1.5
  2. 2Draw the line y = x − 1.5, e.g. through (0, −1.5) and (2, 0.5)
  3. 3Read the x-coordinates where it meets the curve
  4. 4x = −1 or x = 1.65

Answerx = −1.05 to −0.95 or x = 1.55 to 1.7

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Also searched as: 0580/43/M/J/23 · 0580_s23_qp_43 · 0580 s23 43 · question 10.
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