Course Overview: Deepen your mathematical knowledge with this comprehensive course. Explore advanced topics in algebra, calculus, geometry, and more, while developing problem-solving skills and analytical thinking.

What Will You Learn?

This Year 11 Mathematics course provides a comprehensive understanding of advanced mathematical concepts, equipping students with skills applicable to various fields of study. Through engaging lessons and challenging exercises, students will develop their analytical and problem-solving abilities, preparing them for higher education and beyond.

Course Content

Lesson 1: Course Introduction and Objectives

o Welcome to the course and understand its structure.

Lesson 2: Polynomial and Rational Functions

o Study polynomial and rational functions, including end behavior.
o Analyze the relationship between roots and factors.

Lesson 3: Exponential and Logarithmic Functions

o Explore exponential growth and decay models.
o Understand logarithmic functions and solve related equations.

Lesson 4: Trigonometric Identities and Equations

o Dive into advanced trigonometric identities.
o Solve complex trigonometric equations and prove identities.

Lesson 5: Complex Numbers and Polar Coordinates

o Introduce complex numbers and their operations.
o Represent complex numbers in polar form and perform operations.

Lesson 6: Derivatives and Applications

o Understand the concept of a derivative and its applications.
o Apply differentiation to optimize problems.

Lesson 7: Techniques of Differentiation

o Explore differentiation rules for various functions.
o Differentiate exponential, logarithmic, and trigonometric functions.

Lesson 8: Integration and Antiderivatives

o Introduce integration and antiderivatives.
o Explore the fundamental theorem of calculus.

Lesson 9: Applications of Integration

o Apply integration to calculate areas, volumes, and work.
o Study the concept of definite and indefinite integrals.

Lesson 10: Euclidean Geometry and Proofs

o Explore axiomatic systems and Euclidean geometry.
o Develop geometric proofs and theorems.

Lesson 11: Vectors and Vector Operations

o Introduce vectors, vector operations, and their properties.
o Analyze applications of vectors in geometry and physics.

Lesson 12: Probability Distributions and Statistics

o Study probability distributions and statistical analysis.
o Calculate measures of central tendency and dispersion.

Lesson 13: Probability and Discrete Random Variables

o Explore probability models, discrete random variables, and binomial distribution.
o Analyze probability experiments and solve related problems.