Unit 5: Calculus
Topic 5.2: Tangent and Normal Lines Questions
Practice 16 exam-style questions for IB Math AI SL Topic 5.2. Review the question stems below, then unlock the full Question Bank to access markschemes, model answers, and AI grading.
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2024• IB AI SL P1
f(x) = −x² + 4x. For what values of x is f increasing?
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2024• IB AI SL P1
For f(x) = x² − 6x + 8, which interval is correct?
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2024• IB AI SL P1
f(x) = −2x² + 8x. Find where f is increasing.
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2023• IB AI SL P1
If f'(3) = −5, what can you conclude about f near x = 3?
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2023• IB AI SL P1
If f'(x) > 0 on (2, 5), what can you say about f on that interval?
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2022• IB AI SL P1
f(x) = 3x² − 12x + 5. On which interval is f decreasing?
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2024• IB AI SL P1
A function satisfies f'(x) = (x−1)(x−4). State the values of x where f has a stationary point.
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2023• IB AI SL P2
The velocity of a particle is v(t) = t² − 6t + 5.
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2022• IB AI SL P2
Determine whether h(x) = x³ + 2 is ever decreasing. Justify your answer.
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2024• IB AI SL P2
The value of an investment V(t) = 1000 + 200t − 10t² (in dollars, t in years).
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2023• IB AI SL P2
The population P(t) = 500 + 60t − 3t² models a town.
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2022• IB AI SL P2
g(x) = x³ − 6x. Show that g is decreasing on (−√2, √2).
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2023• IB AI SL P2
f(x) = x³ − 3x² − 9x. Find the intervals where f is increasing.
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The population of a town is modelled by P(t) = −t³ + 12t² + 100, where t is the time in years.
Find the values of t for which the population is increasing.
Find the values of t for which the population is increasing.
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2022• IB AI SL P2
f(x) = x⁴ − 8x². Find all intervals where f is decreasing.
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2022• IB AI SL P2
f(x) = 2x³ − 9x² + 12x. Show that f is always increasing for x < 1 and x > 2, and decreasing for 1 < x < 2.
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