Unit 5: Calculus
Topic 5.9: Differentiation rules (HL only) Questions
Practice 20 exam-style questions for IB Math AI SL Topic 5.9. Review the question stems below, then unlock the full Question Bank to access markschemes, model answers, and AI grading.
21 mark
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For the quotient rule (u/v)′, the numerator is:
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If an area A is in m² and time t in seconds, the rate dA/dt has units:
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In a related-rates problem, you should substitute the given numerical value of the variable:
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A particle's position is s(t) = t³ − 6t² + 9t (metres). Find an expression for its velocity v(t) = s′(t).
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A circular wave's radius grows at 4 cm s⁻¹. Find how fast its area grows when r = 6 cm.
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A cube's edge grows at 0.5 cm s⁻¹. Find how fast its volume grows when the edge is 4 cm. (V = x³.)
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Differentiate y = 5eˣ − 4ln x.
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Which rule differentiates y = x³·cos x?
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The derivative of the constant function f(x) = 12 is:
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For a sphere V = (4/3)πr³, the derivative dV/dr is:
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The curve y = x³ − 3x has gradient 0 where:
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Find the equation of the tangent to y = x² − 2x + 1 at the point where x = 4.
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A model gives f(x) = x²·ln x (x > 0). Find f′(x).
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A sound wave is modelled by y = 3sin x + 2cos x (x in radians). Find dy/dx and evaluate it at x = 0.
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2026
Differentiate g(x) = (3x) / (x + 2) using the quotient rule.
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