IB Mathematics Applications and Interpretation HL Calculus
Course

IB Mathematics Applications and Interpretation HL – Calculus

5.1 Rate of Change
5.2 Differentiation
5.3 Application of Differentiation
5.4 Integration
5.5 Application of Integration
5.6 Differential Equations

55 Lessons

Course Materials

RATES OF CHANGE

Average Rates of Change

Gradient using Rates of Change

Related Rates

Limits at Constants

DIFFERENTIATION

Limits at Infinity

Basic Differentiation Rules

Chain Rule

Product Rule

Quotient Rule

Higher Derivatives

Tangents

Normals

Increasing and Decreasing Functions

Turning Points

Points of Inflection and Concavity

Curves of Rational Functions

Sketching Graphs Containing Stationary Points

Derivative of Sine Functions

Derivatives of Cosine Functions

Derivatives of Exponential Functions

Derivatives of Logarithmic Functions

APPLICATION OF DIFFERENTIATION

Optimisation

Application of Derivatives of Trigonometric Functions

Maxima and Minima with Trigonometry

Kinematics

Velocity and Acceleration

Differentiation and Displacement, Velocity and Acceleration

INTEGRATION

Basic Integration Rules

Integration of Power Functions

Particular Values

Upper and Lower Rectangles

Definite Integrals

Integration by Substitution

Further Integration of Trigonometric Functions by Substitution

Further Integration of Trigonometric Functions using Properties

Integration of Sine and Cosine

Integrating Trigonometric Functions by Recognition

Sine and Cosine Integration by Substitution

Integrations involving Tangent

APPLICATION OF INTEGRATION

Area Under a Curve

Area between Two Functions

Calculating Integrals using Trapezoidal Rule

Kinematics using Integration

Volumes using Integration

Volumes for Two Functions

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