IB Math AA HL · Unit 5 of 6

IB Math AA HL Unit 5: Calculus

Unit 5 of IB Mathematics: Analysis and Approaches covers Calculus. This unit contains 19 topics and 38 sub-topics. Below you'll find free study notes, flashcards, and exam preparation resources for every topic in this unit.

Higher Level students should treat this unit page as a route map: revise the shared core, then use the HL notes and topic links to reach the extra depth and evaluation expected at HL.

19 topics38 sub-topics

Exam technique guide

What Unit 5 covers

Differentiation and integration, including limits, implicit and related rates, differential equations and series.

Topics in Unit 5

5.1

Introduction to derivatives

1 sub-topics

5.2

Increasing & decreasing

1 sub-topics

5.3

Differentiating polynomials

2 sub-topics

5.4

Tangents & normals

2 sub-topics

5.5

Introduction to integration

2 sub-topics

5.6

Chain, product & quotient

3 sub-topics

5.7

Second derivative

1 sub-topics

5.8

Optimisation & inflexion

3 sub-topics

5.9

Kinematics

1 sub-topics

5.10

Integration by substitution

2 sub-topics

5.11

Definite integrals & areas

2 sub-topics

5.12

First principles (HL only)

2 sub-topics

5.13

Limits & l'Hopital (HL only)

2 sub-topics

5.14

Implicit & related rates (HL only)

3 sub-topics

5.15

Further calculus (HL only)

2 sub-topics

5.16

Integration by parts (HL only)

2 sub-topics

5.17

Volumes of revolution (HL only)

2 sub-topics

5.18

Differential equations (HL only)

3 sub-topics

5.19

Maclaurin series (HL only)

2 sub-topics

Study tip: Work through the topics in order — each builds on concepts from the one before. Start with notes, then reinforce with flashcards and practice questions.

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