Course Overview: Deepen your understanding of advanced mathematical concepts and applications. This course covers topics in calculus, algebra, statistics, and more, preparing you for higher education and real-world challenges.

What Will You Learn?

This Year 12 Mathematics course delves into advanced mathematical concepts and applications, preparing students for higher-level studies and professional pursuits. Through engaging lessons and challenging assignments, students will develop critical thinking skills and a deep appreciation for the beauty and applicability of mathematics.

Course Content

Lesson 1: Course Introduction and Objectives

o Welcome to the course and understand its structure.

Lesson 2: Techniques of Integration

o Explore integration by parts, trigonometric substitution, and partial fractions.
o Apply integration techniques to solve complex integrals.

Lesson 3: Applications of Differential Equations

o Study first-order and second-order differential equations.
o Analyze real-world applications, including growth and decay models.

Lesson 4: Matrices and Systems of Equations

o Introduce matrices, matrix operations, and systems of linear equations.
o Solve systems of equations using matrix methods.

Lesson 5: Matrix Transformations and Eigenvalues

o Explore linear transformations and matrix representations.
o Study eigenvalues, eigenvectors, and diagonalization.

Lesson 6: Hyperbolic Functions and Their Properties

o Introduce hyperbolic functions and their properties.
o Explore hyperbolic identities and applications.

Lesson 7: Complex Analysis and Residue Theorem

o Study complex numbers, complex functions, and contour integration.
o Apply the residue theorem to calculate complex integrals.

Lesson 8: Set Theory and Logic

o Explore set theory, set operations, and Venn diagrams.
o Understand propositional and predicate logic.

Lesson 9: Proof Techniques and Mathematical Induction

o Develop skills in proof writing and logic.
o Study mathematical induction and its applications.

Lesson 10: Probability Distributions and Sampling

o Study continuous and discrete probability distributions.
o Explore sampling methods and Central Limit Theorem.

Lesson 11: Hypothesis Testing and Confidence Intervals

o Understand hypothesis testing, p-values, and significance.
o Calculate confidence intervals and perform statistical tests.

Lesson 12: Multivariable Calculus and Partial Derivatives

o Explore functions of several variables and partial derivatives.
o Analyze critical points and optimize multivariable functions.

Lesson 13: Applications of Calculus to Physics and Engineering

o Apply calculus concepts to physics and engineering problems.
o Study applications in kinematics, work, and fluid dynamics.