Course

IB Mathematics SL – Calculus – Free

International Baccalaureate
Mathematics Standard Level

Topic 6 - Calculus

6.1 Differential Calculus
6.2 Properties of Curves
6.3 Applications of Differentiation
6.4 Integration
6.5 Applications of Integration

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Course Materials

6.1 DIFFERENTIAL CALCULUS

Limits at Constants

Limits at Infinity

First Principles

First Principles at a Given x-Value

Basic Differentiation Rules

Chain Rule

Product Rule

Quotient Rule

Derivatives of Exponential Functions

Derivatives of Logarithmic Functions

Derivatives of Trigonometric Functions

Higher Derivatives

6.2 PROPERTY OF CURVES

Tangents

Normals

Increasing and Decreasing Functions

Turning Points

Points of Inflection and Concavity

6.3 APPLICATIONS OF DIFFERENTIATION

Kinematics

Velocity and Acceleration

Rates of Change

Optimisation

Application of Derivatives of Trigonometric Functions

6.4 INTEGRATION

Basic Integration Rules

Integration of Exponential Functions

Integration of Sine and Cosine

Integration of Rational Functions

Integration using Double Angle Formula

Particular Values

Integration of Power Functions

Integration by Substitution

Sine and Cosine Integration by Substitution

Upper and Lower Rectangles

Area Under a Curve

Definite Integrals

Definite Integral of Exponential Functions

Definite Integral of Rational Functions

Definite Integration of Power Functions

Definite Integration by Substitution

6.5 APPLICATIONS OF INTEGRATION

Area between Two Functions

Kinematics using Integration

Volumes using Integration

Volumes for Two Functions