Course Title: Advanced Functions
Course Code: MHF4U
Grade: 12
Course Type: University Preparation
Credit Value: 1
Prerequisite: Functions, MCR3U; or Mathematics for College Technology, MCT4C
Department: Mathematics

Course Description

This course extends students’ knowledge with functions. Students will investigate the properties of polynomial, rational, logarithmic, and trigonometric functions as well as develop techniques for combining functions, understand the rates of change, and develop facility in applying these concepts and skills. Students will also refine their use of the mathematical processes necessary for success in senior mathematics. This course is intended for students taking the Calculus and Vectors course as a prerequisite for university programs.

Course Outline
  • MHF4U Unit1 Overview
  • Accessibility to MHF4U Unit1 Assignment
  • U1L1 Polynomial functions (C1.1)
  • U1L2 Properties of polynomial functions (C1.1)
  • U1L3 Graphs of polynomial functions (Part 1) (C1.2)
  • U1L4 Graphs of polynomial functions (Part 2) (C1.3)
  • U1L5 Sinusoidal, polynomial and exponential functions (C1.4)
  • U1L6 Graphs of sinusoidal, polynomial and exponential functions (C1.4)
  • U1L7 Factored form and the x-intercepts (C1.5)
  • U1L8 Graphing functions based on features (Part 1) (C1.5)
  • U1L9 Graphing functions based on features (Part 2) (C1.5)
  • U1L10 The form y = af (k(x – d)) + c (C1.6)
  • U1L11 Properties and parameters a, k, d, and c (C1.7 C1.8)
  • U1L12 Even and odd polynomialfunctions (C1.9)
  • U1L13 Dividing polynomials (Part 1) (C3.1)
  • U1L14 Dividing polynomials (Part 2) (C3.1)
  • U1L15 Factoring polynomials (C3.2)
  • U1L16 Rate of change (D1.1)
  • U1L17 Graphing rate of change (D1.3)
  • U1L18 Properties of rate of change (D1.2)
  • U1L19 Average rates of change (D1.4)
  • U1L20 Instantaneous rates of change (Part 1) (D1.5)
  • U1L21 Instantaneous rates of change (Part 2) (D1.5)
  • U1L22 Instantaneousrates of change – real world application (Part 1) (D1.6)
  • U1L23 Instantaneousrates of change – real world application (Part 2) (D1.6)
  • U1L24 Unit 1 Review
  • Finish and hand in MHF4U Unit1 Assignment at the end of lesson
  • MHF4U Unit1 Online Test
  • MHF4U Unit2 Overview
  • Accessibility to MHF4U Unit2 Assignment
  • U2L1 Slope of the tangent (Part 1) (D1.8)
  • U2L2 Intervals of increase and decrease (Part 2) (D1.8)
  • U2L3 Solving problems related to rate of change (D1.9)
  • U2L4 Polynomial equations (C3.3)
  • U2L5 Roots and x-intercepts (C3.4)
  • U2L6 Equition and inequity (C4.1)
  • U2L7 Solutions to polynomial inequalities (C4.2)
  • U2L8 Graphsof rational functions (C2.1)
  • U2L9 Graphs of reciprocals of linear and quadratic functions (C2.1)
  • U2L10 Connections between the algebraic and graphical representations of rational functions (C2.2)
  • U2L11 The slope of a secant and the average rate of change (D1.7)
  • U2L12 Graph a simple rational function using its features (C2.3)
  • U2L13 Linear inequalities and factorable polynomial inequalities (Part 1) (C4.3)
  • U2L14 Linear inequalities and factorable polynomial inequalities (Part 2) (C4.3)
  • U2L15 Roots and x-intercepts in rational funtions (C3.5)
  • U2L16 Solve simple rational equations in one variable (C3.6)
  • U2L17 Applications of polynomial and simple rational functions and equations (C3,7)
  • U2L18 Radian (B1.1)
  • U2L19 Conversion between radians and degrees (B1.2)
  • U2L20 Primary trigonometric ratios (B1.3 B1.4)
  • U2L21 Reciprocal trigonometric ratios (B1.3 B1.4)
  • U2L22 Graphs of primary trigonometric functions (B2.1 B2.2)
  • U2L23 Properties of sinusoidal functions (B2.4)
  • U2L24 Transformations of the primary trigonometric functions (B2.5 B2.6)
  • Finish and hand in MHF4U Unit2 Assignment at the end of lesson
  • MHF4U Unit3 Overview
  • Accessibility to MHF4U Unit3 Assignment
  • U3L1 Graphs of reciprocal trigonometric functions (Part 1) (B2.3)
  • U3L2 Graphs of reciprocal trigonometric functions (Part 2) (B2.3)
  • U3L3 Applications of trigonometric functions (Part 1) (B2.7)
  • U3L4 Applications of trigonometric functions (Part 2) (B2.7)
  • U3L5 Rates of change in trigonometric functions (Part 1) (B2.7)
  • U3L6 Rates of change in trigonometric functions (Part 2) (B2.7)
  • U3L7 Equivalent trigonometric expressions (B3.1)
  • U3L8 Compound angle formulas (Part 1) (B3.2)
  • U3L9 Compound angle formulas (Part 2) (B3.2)
  • U3L10 Double angle formulas (Part 1) (B3.3)
  • U3L11 Double angle formulas (Part 2) (B3.3)
  • U3L12 Trigonometric identities (B3.3)
  • U3L13 Linear trigonometric equations (Part 1) (B3.4)
  • U3L14 Linear trigonometric equations (Part 2) (B3.4)
  • U3L15 Quadratic trigonometric equations (B3.4)
  • U3L16 Graphs of logarithmic functions (Part 1) (A2.1)
  • U3L17 Graphs of logarithmic functions (Part 2) (A2.1)
  • U3L18 Exponential function and the corresponding logarithmic function (Part 1) (A2.2)
  • U3L19 Exponential function and the corresponding logarithmic function (Part 2) (A2.2)
  • U3L20 Parameters and transformations on the graph of logarithmic functions (Part 1) (A2.3)
  • U3L21 Parameters and transformations on the graph of logarithmic functions (Part 2) (A2.3)
  • U3L22 Evaluating logarithms (A1.1 A1.2)
  • U3L23 Laws of logarithms (Part 1) (A1.3 A1.4)
  • U3L24 Laws of logarithms (Part 2) (A1.4)
  • Finish and hand in MHF4U Unit3 Assignment at the end of lesson
  • MHF4U Unit3 Online Test
  • MHF4U Unit4 Overview
  • Accessibility to MHF4U Unit4 Assignment
  • U4L1 Simplify logrithm expressions (A3.1)
  • U4L2 Exponential equations (A3.2)
  • U4L3 Common base (A3.2)
  • U4L4 Logarithmic equations (Part 1) (C4.2)
  • U4L5 Logarithmic equations (Part 2) (A3.3)
  • U4L6 Solve exponential and logarithmic functions using graphs (C4.2)
  • U4L7 Exponential and logarithmic functions – Real-world application (Part 1) (A2.4 A3.4)
  • U4L8 Exponential and logarithmic functions – Real-world application (Part 2) (A3.4)
  • U4L9 Rate of change in exponential and logarithmic functions (Part 1) (A2.4)
  • U4L10 Rate of change in exponential and logarithmic functions (Part 2) (A2.4)
  • U4L11 Combinations of functions (D2.1)
  • U4L12 Features of combined functions (Part 1) (D2.1)
  • U4L13 Features of combined functions (Part 2) (D2.3)
  • U4L14 Real-world applications of combinations of functions (Part 1) (D2.2)
  • U4L15 Real-world applications of combinations of functions (Part 2) (D2.2)
  • U4L16 Composition of two functions (Part 1) (D2.4)
  • U4L17 Composition of two functions (Part 2) (D2.5)
  • U4L18 Composition of two functions – real-world application (D2.6)
  • U4L19 Inverse function of the composition of functions (D2.7)
  • U4L20 Transformation and composition of functions (D2.8)
  • U4L21 Solve equations and inequalities (D3.2)
  • U4L22 Characteristics of functions (D3.1)
  • U4L23 Real-world applications – concepts and procedure (Part 1) (D3.3)
  • U4L24 Real-world applications – concepts and procedure (Part 2) (D3.3)
  • Finish and hand in MHF4U Unit4 Assignment at the end of lesson
  • MHF4U Final Project
  • MHF4U Final Exam
Related Courses