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Course Description

Live online instructional time is essential and will be held 11:30 pm – 12:30 pm (Eastern Standard Time) during the section schedule dates. Students can expect to commit an additional 2-3 hours/day of asynchronous work to this course.

UWindsor Prep Advanced Functions and Problem-Solving Strategies is a non-credit online course that reviews grade 12 concepts and problem-solving techniques to help students prepare for calculus at the University of Windsor.

This online 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 review and develop strategies, mathematical processes, and thinking skills during problem-solving sessions. Emphasis will be placed on understanding various mathematical relationships, utilizing mathematical techniques in solving problems, and applying mathematical knowledge into various contexts.

 

Course Outline

To successfully complete this course participants will regularly attend online classes and complete a series of assignments and quizzes. Upon completion students will be awarded a grade of complete or incomplete and successful learners will receive a Certificate of Completion from UWindsor Continuing Education.

Learner Outcomes

Throughout this course, students will:

Exponential and Logarithmic Functions

  • demonstrate an understanding of the relationship between exponential expressions and logarithmic expressions, evaluate logarithms, and apply the laws of logarithms to simplify numeric expressions;
  • identify and describe some key features of the graphs of logarithmic functions, make connections among the numeric, graphical, and algebraic representations of logarithmic functions, and solve related problems graphically;
  • solve exponential and simple logarithmic equations in one variable algebraically, including those in problems arising from real-world applications.

Trigonometric Functions

  • demonstrate an understanding of the meaning and application of radian measure;
  • make connections between trigonometric ratios and the graphical and algebraic representations of the corresponding trigonometric functions and between trigonometric functions and their reciprocals, and use these connections to solve problems;
  • solve problems involving trigonometric equations and prove trigonometric identities.

Polynomial and Rational Functions

  • identify and describe some key features of polynomial functions, and make connections between the numeric, graphical, and algebraic representations of polynomial functions;
  • identify and describe some key features of the graphs of rational functions, and represent rational functions graphically;
  • solve problems involving polynomial and simple rational equations graphically and algebraically;
  • demonstrate an understanding of solving polynomial and simple rational inequalities.

Characteristics of Functions

  • demonstrate an understanding of average and instantaneous rate of change, and determine, numerically and graphically, and interpret the average rate of change of a function over a given interval and the instantaneous rate of change of a function at a given point
  • determine functions that result from the addition, subtraction, multiplication, and division of two functions and from the composition of two functions, describe some properties of the resulting functions, and solve related problems;
  • compare the characteristics of functions, and solve problems by modelling and reasoning with functions, including problems with solutions that are not accessible by standard algebraic techniques.

Notes

No textbook is required. This course is offered through Blackboard Collaborate.

Blackboard Requirements

All course details can be accessed through Blackboard. A link will be provided through email and you will have access the first day of class.

Please activate your UWinID. Your UWinID and password are needed to access Blackboard. If you have any issues, please contact continue@uwindsor.ca.

Blackboard.uwindsor.ca works best with Google Chrome. You can also use Firefox or Safari. It is suggested that you avoid using Internet Explorer. There is a “Navigating Your Online Course” module and technical tutorials that you can review for a brief orientation to Blackboard once you log in. Feel free to review the full Blackboard preferred system requirements.

Prerequisites

Successful completion of MHF4U (Grade 12U Advanced Functions) is recommended.
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