AFNorth International School            

 


COURSE OVERVIEW 2007-2008

 

 


Course Name:            Advanced Functions

 

Course Code:             MHF 4U

                                                                                               

Course Type:             University Preparation   Grade Level:  12               Credit Value:  1.0

 

Textbook(s):               Selection of resources, pending the creation of textbooks for the 2007 Grade 12 Mathematics Curriclum

 

Required Supplies:    Protractor, ruler, calculator, binder, lined paper, pens, pencils, eraser, graph paper       

 

Overall Expectations of the Course   

By the end of the 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 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.

•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 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.

•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.

 

 

Course Units in Sequence:

 

1.                  Introductory Unit

2.                  Polynomial Functions

3.                  Rational Functions

4.                  Radian Measure and Trigonometric Functions

5.                  Trigonometric Functions

6.                  Exponential and Logarithmic Functions

7.                  Combining Functions

8.                  Summative Review and Assessment

                       

 

Assessment and Evaluation Strategies:

 

The focus of this course is on inquiry, problem solving, communication, and acquisition of high levels of knowledge and skills and applications of mathematics.

 

Assessment strategies will address the variety of teaching and learning styles as well as the variety of expectations.

 

The assessment program will include tests, quizzes, observation of performance tasks, performance assessment, conferencing, journals and presentations.

 

Assessment tools to be used throughout the course will include the four level achievement chart, rubrics (both teacher-created and student generated), checklists, rating scales, anecdotal comments, and analytic marking schemes.

 

There will be several short assignments, quizzes and task opportunities in each unit of this course that do not “count” toward the final mark for the unit.  These tasks are opportunities for teacher feedback about what you are doing well and what you need to improve.  In some cases, you will be encouraged to work on the improvements, and hand the assignment in for further feedback.  These tasks will be related to the final summative assignment and test for the unit.  Therefore, despite the fact that you will not lose marks for not completing these tasks, you are encouraged to take advantage of these opportunities for very useful teacher feedback.

 

 

Evaluation:  Weighting of Marks

 

The final grade for the course will be distributed based on the following:

 

            Knowledge                                                       35%

            Thinking, Inquiry and Problem Solving   15%    

            Communication                                     15%

            Applications                                                     35%    

 

 

 

A.        Unit/chapter tests will take place at the end of each unit of work. Students will be notified in advance of their occurrence.

 

B.         Quizzes will be unannounced and will usually cover the previous day's work.

 

C.        Students will be required to complete journal entries as part of their regular assignment. They may also have to present to class their findings from various assignments.

 

D.        The 6+1 Trait is the model selected to improve school-wide writing in all subject areas.  The 6+1 Trait writing framework is a powerful way to learn and use a common language to refer to characteristics of writing as well as establish a common vision of what “strong” writing looks like.  Teachers and students will use the 6+1 Trait model to identify areas of strength and weakness as they continue to strive towards continued writing improvement.  Success of all students requires that the 6+1 Trait become a consistent and integral component of each course taught at AFNORTH High School.

 

E.         A culminating assignment will be part of the final evaluation which also includes the final examination. During this assignment students will be required to demonstrate that they have met the overall expectations of the course. This assignment will make up 10% of the students’ final mark.

 

F.         The final examination will cover the full year's work and will take place at the conclusion of the course. All students will be required to write this examination. The final examination will make up 20% of the students’ final mark.

 

G.        Work habits/homework, organization, initiative, teamwork, and independent work are learning skills which will be evaluated separately from academic achievement.  These are very important skills for you to learn at school and at home, and they are crucial in determining how successful you will be in your future employment or post-secondary schooling. 

 

H.        Much of the students’ work, particularly for complex tasks and assignments, will be marked using a rubric and the final mark will be given as a level (1 to 4).  For this work, the rubric will be provided to students ahead of time so it is very clear what criteria must be met in order to get a particular level.  In other cases, numerical marks will be given.  In both cases, the mark assigned will reflect very specific standards and criteria that are outlined in the curriculum documents for the course.