IB Math AI HL · Unit 5 of 6

IB Math AI HL Unit 5: Calculus

Unit 5 of IB Mathematics: Applications and Interpretation covers Calculus. This unit contains 18 topics and 25 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.

18 topics25 sub-topics

Exam technique guide

What Unit 5 covers

Differentiation and integration, kinematics, differential equations, slope fields and Euler's method.

Topics in Unit 5

5.1

Introduction to limits

1 sub-topics

5.2

Increasing and decreasing functions

1 sub-topics

5.3

Introduction to derivatives

2 sub-topics

5.4

Tangents and normals

2 sub-topics

5.5

Introduction to integration

3 sub-topics

5.6

Stationary points, local maximum and minimum

1 sub-topics

5.7

Optimization

1 sub-topics

5.8

Trapezoid rule

1 sub-topics

5.9

Differentiation rules (HL only)

3 sub-topics

5.10

Second derivatives (HL only)

1 sub-topics

5.11

Integration techniques (HL only)

1 sub-topics

5.12

Areas & volumes of revolution (HL only)

2 sub-topics

5.13

Kinematics (HL only)

1 sub-topics

5.14

Differential equations (HL only)

1 sub-topics

5.15

Slope fields (HL only)

1 sub-topics

5.16

Euler's method (1st order) (HL only)

1 sub-topics

5.17

Phase portraits (HL only)

1 sub-topics

5.18

Euler's method (2nd order) (HL only)

1 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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