Unit 2: Functions
Topic 2.9: Exponential and Logarithmic Functions Questions
Practice 14 exam-style questions for IB Math AA SL Topic 2.9. Review the question stems below, then unlock the full Question Bank to access markschemes, model answers, and AI grading.
1State2 marks
2026• Aimnova practice — 2.9.1
State whether y = (3/4)ˣ shows growth or decay, and give a reason.
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2026• Aimnova practice — 2.9.2
Write down (a) the x-intercept and (b) the vertical asymptote of y = log x.
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2026• Aimnova practice — 2.9.2
State the domain and range of y = log x.
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2026• Aimnova practice — 2.9.2
Explain why y = log x has no value at x = −3.
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2026• Aimnova practice — 2.9.1
Write down (a) the y-intercept and (b) the horizontal asymptote of y = 5ˣ.
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2026• Aimnova practice — 2.9.1
A radioactive sample decays as M(t) = 80·(0.5)ᵗ grams, t in hours. Find (a) the initial mass and (b) the mass after 3 hours.
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2026• Aimnova practice — 2.9.1
A bacteria count is N = 500·2ᵗ where t is in hours. (a) State the initial count. (b) Find the count after 4 hours.
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2026• Aimnova practice — 2.9.1
The value of a car is V = 24000·(0.85)ᵗ dollars after t years. Find (a) the value after 2 years and (b) by what percentage it decreases each year.
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2026• Aimnova practice — 2.9.1
State the horizontal asymptote and y-intercept of y = 3ˣ − 2.
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2026• Aimnova practice — 2.9.1
The graph of y = 4ˣ is translated up by 5 units. Write down
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2026• Aimnova practice — 2.9.2
The graph of y = log₂(x + 1) is given. (a) State the vertical asymptote. (b) Find its x-intercept.
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2026• Aimnova practice — 2.9.2
The function y = log x is the inverse of which function? Explain the connection to the line y = x.
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2026• Aimnova practice — 2.9.2
State the vertical asymptote and domain of y = log(x − 5).
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2026• Aimnova practice — 2.9.2
On the same axes, the curve y = aˣ passes through (0, 1) and its inverse passes through (1, 0). Name the inverse and state its vertical asymptote.
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