G12 Advanced Functions - Mhf4U

Foundations for Calculus & Advanced Math

What you'll learn

Analyze and graph polynomial, rational, exponential, logarithmic, and trigonometric functions.

Solve equations and inequalities involving advanced algebraic and transcendental functions.

Apply transformations to functions and interpret their effects on graphs and equations.

Investigate properties of functions, including domain, range, inverses, and rates of change.

Model real-world scenarios using functions and solve applied problems.

Requirements

G11 Functions (MCR3U)

Description

This course builds upon your previous experience with functions, diving deeper into the mathematical concepts that are fundamental to higher education in STEM and business fields. You will investigate the properties and applications of advanced functions, including polynomial, rational, exponential, logarithmic, and trigonometric functions. A significant focus is placed on developing your ability to model real-world phenomena with mathematics, translating situations involving rates of change, periodic motion, and exponential growth or decay into functional models.You will continue to hone essential mathematical reasoning and problem-solving skills by solving complex problems through a multi-representational approach. This involves mastering the connections between algebraic, numerical, graphical, and verbal representations of functions. Key topics include mastering transformations, combining functions, understanding rates of change, and solving intricate equations and inequalities.The course is strategically designed to establish the crucial conceptual and procedural foundation required for success in calculus and other university-level mathematics courses. The skills you develop—in modelling, analysis, and logical reasoning—are highly transferable and valued in numerous academic and professional disciplines. MHF4U is intended for students pursuing university programs in mathematics, physics, engineering, economics, and commerce, preparing them to think critically about the mathematical structures that describe our world.– This couse is oriented to seondary school students of G10 - G12 and to be purchased by their parents or guardian. –Prerequisite: Functions, Grade 11 (MCR3U)

Overview

Section 1: Introduction to Functions

Lecture 1 Recap Functions' Theory

Lecture 2 Functions’ Verification and Absolute Value Function

Lecture 3 Graphing Functions

Lecture 4 Inverse Functions

Lecture 5 Piecewise Functions

Lecture 6 Operation of Functions

Section 2: Understanding Rates of Change

Lecture 7 Average Rate of Change

Lecture 8 Instantaneous Rates of Change

Lecture 9 Applications of Rates of Change

Section 3: Polynomial Functions

Lecture 10 Characteristics of Polynomial Functions

Lecture 11 Characteristics of Polynomial Functions in Factored Form

Lecture 12 Transformations of Cubic and Quartic Functions

Lecture 13 Dividing Polynomials

Lecture 14 Factoring Polynomials

Section 4: Polynomial Equations and Inequalities

Lecture 15 Solving Polynomial Equations

Lecture 16 Solving Linear Inequalities

Lecture 17 Solving Polynomial Inequalities

Lecture 18 Rates of Change in Polynomial Functions

Section 5: Rational Functions, Equations and Inequalities

Lecture 19 Graph of Reciprocal Functions

Lecture 20 Exploring Quotients of Polynomial Functions

Lecture 21 Solving Rational Equations

Lecture 22 Solving Rational Inequalities

Lecture 23 Rates of Change in Rational Functions

Section 6: Trigonometric Functions

Lecture 24 Radian Measure

Lecture 25 Radian Measure and Angles on the Cartesian Plane

Lecture 26 Graphs of Primary Trigonometric Functions

Lecture 27 Transformation of Trigonometric Functions

Lecture 28 Modeling with Trigonometric Functions

Section 7: Trigonometric Identities and Equations

Lecture 29 Equivalent Trigonometric Functions and Compound Angles’ Formula

Lecture 30 Double Angle Formulars

Lecture 31 Proving Trigonometric Identities

Lecture 32 Solving Linear Trigonometric Equations

Lecture 33 Solving Quadratic Trigonometric Equations

Section 8: Exponential and Logarithmic Functions

Lecture 34 Logarithmic Functions

Lecture 35 Laws of Logarithms

Lecture 36 Solving Exponential Equations

Lecture 37 Solve Logarithmic Equations

Lecture 38 Applications of Exponential and Logarithmic Functions

Secondary School Students who are going to learn Advanced Functions (MHF4U) at G12 or before G12