Unit 5: Calculus
Topic 5.1: Introduction to Differentiation Questions
Practice 20 exam-style questions for IB Math AA SL Topic 5.1. Review the question stems below, then unlock the full Question Bank to access markschemes, model answers, and AI grading.
1Explain2 marks
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Explain the difference between the gradient of a straight line and the gradient of a curve.
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The gradient function of a curve is f'(x) = 4x − 1. Find the gradient of the curve at x = 2.
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The gradient function of a curve is . Find the gradient of the curve at .
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A curve has . Find the value of at its stationary point.
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The gradient function of a curve is . Find the gradient of the curve at .
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A curve has . Determine whether the curve is rising or falling at .
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A club's membership changes with at months, while a second club has . Compare the two clubs.
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Explain why a curve with rises for every value of .
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The gradient function of a curve is f'(x) = 6 − 2x. Find the value of x where the gradient is 0, and state what kind of point this is.
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A curve has gradient function . Determine whether the curve is increasing or decreasing at .
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The temperature of a cooling drink after t minutes has dT/dt = −1.5 at . Interpret this value in context.
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The gradient function of a curve is . Find the value of x where the gradient is 0, and state what kind of point this is.
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The temperature T (°C) of a cooling drink after t minutes has dT/dt = −1.5 at t = 4. Interpret this value in context.
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A population P (thousands) grows so that dP/dt = 0.8 at years. A second population has dP/dt = 0.3 at the same time. Which is growing faster, and by how much (per year)?
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A curve has gradient function f'(x) = 3x2 − 12. Determine whether the curve is increasing or decreasing at x = 1.
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A population P (thousands) grows so that dP/dt = 0.8 at t = 10 years. A second population has dP/dt = 0.3 at the same time. Which is growing faster, and by how much (per year)?
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Find from first principles, using .
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The gradient function of a curve is . Explain why the curve is increasing for every value of x.
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