Unit 5: Calculus
Topic 5.12: First principles (HL only) Questions
Practice 20 exam-style questions for IB Math AA SL Topic 5.12. Review the question stems below, then unlock the full Question Bank to access markschemes, model answers, and AI grading.
2Find3 marks
2026
Find, from first principles, the derivative of f(x) = 5x.
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The gradient of the chord joining the points on y = f(x) at x and x + h is:
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As h → 0, the chord through two points of a curve becomes the:
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From first principles, the derivative of f(x) = x² is:
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For f(x) = x³ + 2x² − 5x, find f'(x) and f''(x).
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Given y = x⁴ − 3x² + 7, find d²y/dx².
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Which notation means the SAME as f''(x)?
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Unlock Question11Differentiate4 marks
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Differentiate f(x) = x² from first principles.
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Show that is not continuous at .
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Why must you simplify (f(x+h) − f(x))/h before substituting h = 0?
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From first principles, the derivative of the constant function f(x) = 7 is:
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Explain what the notation d²y/dx² means, and find it for y = 5x³.
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Write down limx→3 (x² − x), justifying that you may substitute.
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For f(x) = 2x³ − 9x² + 12x, find f''(1).
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A function is continuous at x = a when:
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