0580/43 May/Jun 2026, Question 11: Exponential Functions
Cambridge IGCSE Mathematics 0580 · Paper 43 (Extended) · Calculator · 10 marks
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The question, in short
Table of values for y = 3 × 2ˣ − 5, rounded to 1 decimal place. Fill in missing entries, plot the curve for −2 ≤ x ≤ 2, use a line to solve 3 × 2ˣ = 7, and state the asymptote.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Part (a) · 3 marks
Work out the y-values missing from the table for the given x-values, giving each to 1 decimal place.
- 1x = −2: 3 × 0.25 − 5 = −4.25 ≈ −4.3
- 2x = −1: 3 × 0.5 − 5 = −3.5
- 3x = 0: 3 × 1 − 5 = −2
Answer−4.3, −3.5, −2
Part (b) · 4 marks
Plot the curve y = 3 × 2ˣ − 5 on the grid for x from −2 to 2.
- 1Plot all 9 points from the completed table
- 2Join them with a smooth curve (not ruled)
- 3Curve rises more and more steeply to the right
AnswerCorrect smooth curve through (−2, −4.3), (−1.5, −3.9), (−1, −3.5), (−0.5, −2.9), (0, −2), (0.5, −0.8), (1, 1), (1.5, 3.5), (2, 7)
Part (c) · 2 marks
Add a straight line to the graph and use where it meets the curve to solve 3 × 2ˣ = 7.
- 13 × 2ˣ = 7 ⇒ 3 × 2ˣ − 5 = 2
- 2Draw the line y = 2
- 3Read x where it meets the curve: x ≈ 1.2
Answer1.2 (accept 1.15 to 1.3)
Part (d) · 1 mark
State the equation of the horizontal line that the curve approaches.
- 1As x → −∞, 2ˣ → 0
- 2So y → 3 × 0 − 5 = −5
- 3Asymptote: y = −5
Answery = −5
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