IB Mathematics Analysis and Approaches HL Calculus
Course

IB Mathematics Analysis and Approaches 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 Differentiation of Inverse Trigonometric Functions
5.7 Integration of Inverse Trigonometric Functions
5.8 Differential Equations

68 Lessons

Course Materials

RATES OF CHANGE

Average Rates of Change

Gradient using Rates of Change

Limits at Constants

Limits at Infinity

Trigonometric Ratios and Limit Values

DIFFERENTIATION

Basic Differentiation Rules

Differentiation of Surds

First Principles

First Principles at a Given x-Value

Derivative of Sine Functions

Derivatives of Cosine Functions

Derivatives of Tangent Functions

Derivatives of Exponential Functions

Derivatives of Logarithmic Functions

Higher Derivatives

Implicit Differentiation

APPLICATION OF DIFFERENTIATION

Tangents

Normals

Increasing and Decreasing Functions

Turning Points

Points of Inflection and Concavity

Curves of Rational Functions in Quadratics by Linear Form

Curves of Rational Functions in Quadratics by Quadratic Form

Sketching Graphs Containing Stationary Points

Gradient Functions

Sketching Curves from Derivatives

Optimisation

Application of Derivatives of Trigonometric Functions

Kinematics using Differentiation

Maxima and Minima with Trigonometry

INTEGRATION

Basic Integration Rules

Basic Integration Rules involving Algebra

Integration of Power Functions

Particular Values

Upper and Lower Rectangles

Definite Integrals

Integration of Sine and Cosine

Integrations involving Tangent

Sine and Cosine Integration by Substitution

Integration by Partial Fractions

Indefinite Integration by Recognition

Integration by Substitution

Indefinite Integration by Parts

Calculating Integrals using Trapezoidal Rule

APPLICATION OF INTEGRATION

Area Between Y-axis

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