This course extends students’ experience with functions. Students will investigate the properties of polynomial, rational, logarithmic, and trigonometric functions; develop techniques for combining functions; broaden their understanding of 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 both for students taking the Calculus and Vectors course as a prerequisite for a university program and for those wishing to consolidate their understanding of mathematics before proceeding to any one of a variety of university programs.
Pre-requisite(s): • Grade 11 Functions, University preparation, (MCR3U-C) OR • Grade 12 Mathematics for College
Technology, College preparation (MCT4C-B)
Course Syllabus
Unit 1: Exponential and logarithmic functions - Part A
Lesson 1: Exponential functions
Lesson 2: Introduction to logarithms
Unit 2: Exponential and logarithmic functions - Part B
Lesson 3: Graphs of logarithmic functions
Lesson 4: Transformations of logarithmic functions
Lesson 5: Exponential and logarithmic equations
Unit 3: Polynomial and rational functions - Part A
Lesson 6: Polynomial functions
Lesson 7: Polynomial equations and graphs
Lesson 8: Transformations and applications of
polynomial functions
Unit 4: Polynomial and rational functions - Part B
Lesson 9: Rational functions
Lesson 10: Applications of rational functions
Unit 5: Trigonometric functions
Lesson 11: Review of trigonometry
Lesson 12: Radian measures
Lesson 13: Graphs of trigonometric functions
Lesson 14: Applications of periodic functions
Lesson 15: Trigonometric identities and equations
Unit 6: Characteristics of functions - Part A
Lesson 16: Average rate of change
Lesson 17: Instantaneous rate of change
Unit 7: Characteristics of functions - Part B
Lesson 18: Operations on functions
Lesson 19: Composite functions
Lesson 20: Mathematical modelling