HSC Year 12 Mathematics Advanced Calculus
Course

HSC Year 12 Mathematics Advanced – Calculus

3.1 Differentiation
3.2 Application of Differentiation
3.3 Integration
3.4 Application of Integration

36 Lessons

Course Materials

DIFFERENTIATION

Derivative of Sine Functions

Derivatives of Cosine Functions

Derivatives of Tangent Functions

Derivatives of Exponential Functions

Derivatives of Logarithmic Functions

APPLICATION OF DIFFERENTIATION

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

Kinematics using Differentiation

INTEGRATION

Basic Integration Rules

Basic Integration Rules involving Algebra

Integration of Power Functions

Particular Values

Indefinite Integration by Recognition

Integration of Sine and Cosine

Integration of Exponential Functions

Definite Integral of Exponential Functions

Integration of Rational Functions

Integrations Resulted in Natural Log Functions by Substitutions

Definite Integral of Rational Functions

APPLICATION OF INTEGRATION

Area Under a Curve

Signed Areas

Area between Two Functions

Area between Two Functions involving Signed Areas

Area under Trigonometric Curves

Kinematics using Integration

Calculating Integrals using Trapezoidal Rule