Calculus (AHL)
The HL extension of Topic 5, complete: continuity, differentiability and the derivative from first principles; limits and l'Hopital's rule; implicit differentiation with related rates; the extended derivative library and its integrals with partial fractions; integration by substitution and by parts; areas between a curve and the y-axis with volumes of revolution about both axes; differential equations by separation, homogeneous substitution, integrating factor and Euler's method; and Maclaurin series. Every subtopic code from AHL 5.12 to AHL 5.19.
SL Topic 5 end to end — limits informally, the power/product/quotient/chain rules, tangents and normals, optimisation, kinematics, and definite integrals for area. HL widens the library of functions, adds three genuinely new techniques (implicit differentiation, parts, substitution), and turns calculus back on itself with differential equations and series.
- 01Continuity, Differentiability & First Principles
- 02Limits & l'Hôpital's Rule
- 03Implicit Differentiation & Related Rates
- 04The Extended Derivative Library
- 05Integrating the Library & Partial Fractions
- 06Integration by Substitution
- 07Integration by Parts
- 08Areas & Volumes of Revolution
- 09Differential Equations
- 10Maclaurin Series