Unit 5: Calculus
Topic 5.2: Tangent and Normal Lines Questions
Practice 17 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.
1identify1 mark
2024
For f(x) = x² − 6x + 8, which interval is correct?
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2022
f(x) = 3x² − 12x + 5. On which interval is f decreasing?
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Unlock Question3state2 marks
2024
A function satisfies f'(x) = (x−1)(x−4). State the values of x where f has a stationary point.
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2024
f(x) = −x² + 4x. For what values of x is f increasing?
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2023
If f'(3) = −5, what can you conclude about f near x = 3?
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2024
f(x) = −2x² + 8x. Find where f is increasing.
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2023
If f'(x) > 0 on (2, 5), what can you say about f on that interval?
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2026
Sketch a curve with this behaviour.
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Unlock Question9determine3 marks
2022
Determine whether h(x) = x³ + 2 is ever decreasing. Justify your answer.
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Unlock Question10find6 marks
2024
The value of an investment V(t) = 1000 + 200t − 10t² (in dollars, t in years).
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Unlock Question11find5 marks
2023
The population P(t) = 500 + 60t − 3t² models a town.
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2022
g(x) = x³ − 6x. Show that g is decreasing on (−√2, √2).
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Unlock Question13find5 marks
2023
The velocity of a particle is v(t) = t² − 6t + 5.
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Unlock Question14find2 marks
2023
f(x) = x³ − 3x² − 9x. Find the intervals where f is increasing.
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Unlock Question15find4 marks
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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Unlock Question16show4 marks
2022
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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2022
f(x) = x⁴ − 8x². Find all intervals where f is decreasing.
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