Course Title: Advanced Functions Online
Course Type: University Preparation
Course Code: MHF 4U
Credit Value: 1
Curriculum Policy Document: Mathematics, The Ontario Curriculum, Grades 11 and 12, 2007 (Revised)
Prerequisite: MCR3U (or MCT4C)
This course is based on the expectations and guidelines set by Ministry of Education’s Ontario Curriculum documents for Grade 11 and 12 Mathematics.
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.
By the end of this course, students will:
- 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 between 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 arising from real-world applications;
- 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;
- Identify and describe some key features of polynomial functions, and make connections between the numeric, graphical, and algebraic representations of polynomial;
- 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 demonstrate an understanding of solving polynomial and simple rational inequalities;
- 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.
Advanced Functions is broken down into the following units:
|1||Understanding Rates of Change|
|6||Trigonometric Identities and Equations|
|7||Exponential and Logarithmic Functions|
|8||Combinations of Functions|
The overall course is broken into Term Work and the Final Exam:
Both the Term work and the Final Exam are broken into the following skill categories:
Each activity accumulates the following mark total (Note: Marks are weighted by skill categories, not by activities):
There is no required textbook for this course.
For additional resources, the recommended textbooks are:
- Advanced Functions 12, McGraw-Hill Ryerson, 2008.
- Advanced Functions, Nelson Education Ltd., 2009.
Student Achievement Levels
Assessment and evaluation is guided by the Ministry of Education’s Growing Success policy document. Student achievement will be communicated formally to parent(s)/guardian(s) by means of the Provincial Report Card for grades 9 – 12 courses. Information about student reporting, along with yearly communication timelines, can be found on the ‘Programs’ page of the Ministry of Education website. The levels of achievement are associated with percentage grades, and are defined as follows:
|Percentage||Achievement of the Provincial Curriculum Expectations|
|80-100%||The student has demonstrated the required knowledge and skills with a high degree of effectiveness. Achievement surpasses the provincial standard. (Level 4)|
|70-79%||The student has demonstrated the required knowledge and skills with considerable
effectiveness. Achievement meets the provincial standard. (Level 3)
|60-69%||The student has demonstrated the required knowledge and skills with some
effectiveness. Achievement approaches the provincial standard. (Level 2)
|50-59%||The student has demonstrated the required knowledge and skills with limited
effectiveness. Achievement falls much below the provincial standard. (Level 1)
|Below 50%||The student has not demonstrated the required knowledge and skills. Extensive
remediation is required.