Radford Mathematics AI SL • Topic 5
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IB Mathematics Applications and Interpretation SL

Topic 5: Calculus

A structured path through the finalized Radford Mathematics calculus lessons.

AI SL · Topic 5

Calculus learning path

Work through the lessons in syllabus order. Each page contains an online lesson, worked example, practice prompts and relevant video tutorials. Premium printable handouts are available separately through the Radford Mathematics Store.

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SL 5.1Limits and the DerivativeApproach limits numerically and graphically, then interpret the derivative as gradient and rate of change.SL 5.2Increasing and Decreasing FunctionsRead the sign of the derivative to identify where a function rises, falls or is stationary.SL 5.3Power Rule DifferentiationDifferentiate polynomial terms efficiently and connect the algebra to gradient.SL 5.4Tangents and NormalsUse derivatives to construct tangent and normal lines at a point on a curve.SL 5.5Integration and AreaConnect anti-differentiation, boundary conditions, definite integrals and positive area using technology appropriately.SL 5.6Stationary PointsUse technology to generate the derivative, solve f′(x)=0 and classify local maxima and minima.SL 5.7OptimisationTurn a real context into a one-variable objective function and find the required maximum or minimum.SL 5.8Trapezoidal Rule for IntegrationApproximate area from equally spaced data or function values with the trapezoidal rule.

Related Topic 5 tutorials

▶What is a derivative? Gradient of a curveRadford Mathematics on YouTube▶Plot first and second derivative functions on TI-Nspire CXRadford Mathematics on YouTube▶Power rule for differentiationRadford Mathematics on YouTube▶Definite integrals on TI-Nspire CXRadford Mathematics on YouTube

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