Unit 5: Calculus
Topic 5.3: Differentiating Powers Questions
Practice 16 exam-style questions for IB Math AA SL Topic 5.3. Review the question stems below, then unlock the full Question Bank to access markschemes, model answers, and AI grading.
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2026• Aimnova practice — 5.3.2
A curve has equation y = 2x² − 8x + 3.
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2026• Aimnova practice — 5.3.1
A curve has equation y = x³ − 4x. Find dy/dx, and hence the gradient when x = 2.
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2026• Aimnova practice — 5.3.2
Find the gradient of the curve y = x³ − 5x + 1 at the point where x = 1.
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2026• Aimnova practice — 5.3.2
The curve y = x² + 2x has gradient 10 at one point. Find the x-coordinate of that point.
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2026• Aimnova practice — 5.3.1
Differentiate y = 4x⁵ + 9.
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2026• Aimnova practice — 5.3.1
Differentiate f(x) = 3x⁴ − 7x² + 2x − 5.
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2026• Aimnova practice — 5.3.2
Find the values of x where the curve y = x³ − 12x has gradient 0.
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2026• Aimnova practice — 5.3.2
The curve y = x² − 3x + 2 has a tangent parallel to the line y = 5x − 1. Find the x-coordinate of the point of contact.
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2026• Aimnova practice — 5.3.2
Find the gradient of y = 4√x at the point where x = 4.
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2026• Aimnova practice — 5.3.2
The tangent to y = x² at a point makes an angle of 60° with the positive x-axis. Find the x-coordinate of that point, to 3 s.f.
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2026• Aimnova practice — 5.3.1
Differentiate f(x) = (1/3)x³ − 2x1/2.
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2026• Aimnova practice — 5.3.1
Differentiate y = 5x³ + 6/x².
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2026• Aimnova practice — 5.3.1
Differentiate f(x) = 6√x.
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2026• Aimnova practice — 5.3.1
Differentiate y = x² − 4x + 1/x.
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2026• Aimnova practice — 5.3.1
Differentiate f(x) = 2x³ − 6/√x. Give your answer with positive indices removed (i.e. using powers).
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2026• Aimnova practice — 5.3.2
A curve has gradient function f'(x) = 3x² − 6x. Find the values of x where the gradient is −3.
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