Radford Mathematics AA HL • Topic 5

Radford Mathematics

Contact / enquiry

Send a question about tutoring, revision courses, website resources or anything else. Your message will be sent to info@radfordmathematics.com.

IB Mathematics Analysis and Approaches HL

Topic 5: Calculus

A structured path through the finalized Radford Mathematics calculus lessons.

AA HL · Topic 5

Calculus learning path

Work through the finalized lessons currently available for this topic. Each lesson page follows the corresponding approved Radford Mathematics handout and includes accessible online notes, worked examples, practice and relevant tutorial videos. Premium printable handouts are available separately through the Radford Mathematics Store.

Search Topic 5 practice Related videos Premium notes in the Store
SL 5.1 Limits and the DerivativeApproach limits numerically and graphically, then interpret the derivative as gradient and rate of change. SL 5.2 Increasing and Decreasing FunctionsRead the sign of the derivative to identify where a function rises, falls or is stationary. SL 5.3 Power Rule DifferentiationDifferentiate polynomial terms efficiently and connect the algebra to gradient. SL 5.4 Tangents and NormalsUse derivatives to construct tangent and normal lines at a point on a curve. SL 5.5 Anti-Differentiation and Boundary ConditionsReverse the power rule, include the constant of integration and use a point to determine a particular function. SL 5.6 Differentiation RulesDifferentiate standard functions and combinations using chain, product and quotient rules. SL 5.7 Second Derivative and Graphical BehaviourUse the second derivative to describe concavity and identify changes of curvature. SL 5.8 Stationary Points and Derivative TestsClassify stationary points reliably with first- and second-derivative tests. SL 5.8 OptimisationBuild and analyse an objective function, including closed-domain endpoint checks. SL 5.9 KinematicsMove fluently between displacement, velocity and acceleration and distinguish displacement from total distance. SL 5.10 Standard IntegralsRecognise standard antiderivatives and integrate linear composites with correct scale factors. SL 5.10 Integration by SubstitutionRecognise an inner function and its derivative, then change variable to simplify the integral. SL 5.11 Definite Integrals: Evaluation and PropertiesEvaluate definite integrals analytically, then use reversing limits, interval splitting, linearity and symmetry. SL 5.11 Areas Using Definite IntegralsFrom signed area and its applications to total geometrical area and area between two curves. AHL 5.12 Limits, Continuity and First PrinciplesUnderstand limits and informal continuity/differentiability, derive polynomial derivatives from first principles, and interpret higher derivatives. AHL 5.13 L’Hôpital’s RuleEvaluate indeterminate limits with l’Hôpital’s rule, repeated use, algebraic rewriting and a Maclaurin-series check. AHL 5.14 Implicit DifferentiationDifferentiate relations where y is not isolated, using the chain rule on every y-term. AHL 5.14 Related RatesDifferentiate a geometric/physical constraint with respect to time and connect simultaneous rates of change. AHL 5.14 AA HL OptimisationOptimise models with implicit constraints and endpoint possibilities. AHL 5.15 Further Derivatives and AntiderivativesExtend the standard derivative/integral toolkit and use partial fractions to create integrable forms. AHL 5.16 Advanced Integration: Substitution and Integration by PartsChoose between substitution and integration by parts, including repeated/cyclic applications. AHL 5.17 Areas with the y-Axis and Volumes of RevolutionUse horizontal or vertical strips to model area and volume about either coordinate axis. AHL 5.18 Differential EquationsSolve separable, homogeneous and linear first-order equations and approximate solutions with Euler’s method. AHL 5.19 Maclaurin SeriesBuild and manipulate series near x=0 for approximation, limits and differential equations.

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 ▶Sum/difference and constant multiple rulesRadford Mathematics on YouTube

Practice across the topic

Search lesson practice by syllabus code, keyword or course. Published worksheet PDFs include answers at the end. Premium lesson handouts are sold separately and are not hosted as free downloads.

Worksheet & practice library

Prefer video?

Browse worked examples, calculator guidance and topic tutorials.

Video library