Unit 5: Calculus
Topic 5.15: Further calculus (HL only) Questions
Practice 20 exam-style questions for IB Math AA SL Topic 5.15. Review the question stems below, then unlock the full Question Bank to access markschemes, model answers, and AI grading.
11 mark
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d/dx(eˣ) is the special case of d/dx(aˣ) = aˣ ln a because:
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To differentiate y = (sin x)/(2ˣ) you use:
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Write down the derivative of y = tan x, and find dy/dx at x = 0.
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Find the derivative of f(x) = 3ˣ, and evaluate f′(2). Give an exact answer.
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Show that the gradient of y = loga x can be written as 1/(x ln a), and hence find dy/dx for y = log10 x.
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Which derivative is NEGATIVE for all x in its domain?
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Differentiate f(x) = eˣ sec x and write your answer in factored form.
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The curve y = arctan x passes through the origin. Find the gradient of the tangent at x = 0, and state the equation of that tangent.
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Write down d/dx(arccos x) and d/dx(arctan x), then state which is always negative.
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Find the gradient of y = sec x at x = π/3.
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Differentiate y = x tan x.
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Differentiate y = tan(x²) and hence find the gradient at x = 0.
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