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```					MHF4U                                                                                                          2012 – 2013

Prerequisites: MCR3U (Functions) or MCT4C (Mathematics for College Technology)
Recommended Mark: Level 3- (70%)
Policy Document: The Ontario Curriculum, Grades 11 and 12: Mathematics (2007)
Course Website: http://mrmaloley.pbworks.com
E-mail: thomas.maloley@ocdsb.ca

Course Description
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. The use of graphing calculators is encouraged, particularly to
support the development of concepts.

Topics
i.       Function Models and Rates of Change
ii.      Polynomial Functions
iii.     Rational Function Models
iv.      Trigonometric Function Models
v.       Exponential and Logarithmic Function Models
vi.      Combining Function Models

Mathematical Processes

The mathematical processes are a set of interconnected thinking skills that support lifelong learning in mathematics.
Students develop and apply these skills in all math courses as they work to achieve the expectations outlined within each
course. These skills are developed through problem-solving experiences that incorporate a variety of approaches, including
investigation. The mathematical processes are:

   Problem Solving
   Reasoning and Proving
   Reflecting
   Selecting Tools and Computational Strategies
   Connecting
   Representing
   Communicating

Learning Skills

Learning skills are student habits and behaviours that enable them to learn effectively and achieve their potential. They are
critical to success in all subject areas. Initiative, independent work, organization, self-regulation, collaboration and
responsibility will be assessed throughout the course, and communicated on the report card.

Student Absences

Students are responsible for all work missed regardless of the reason for the absence. If you are away, you WILL miss
something important! Work must be completed before returning to school in order to remain connected to the development
of the concepts.

Students who expect to miss school due to family vacations must notify the Principal in writing, in advance. Vacations
cannot be recognized as legitimate reasons for exemption from formal evaluation. Refer to Math Department policy on
Missed / Late Assessments for more detailed information.

Textbook

Your textbook is Advanced Functions (Nelson). You must return it in the condition that you receive it or you will be
charged a fee for damages.
MHF4U                                                                                                         2012 – 2013

Evaluation

The final mark consists of two components: term work (70%) and summative evaluation (30%).

Term Work

During the term, students will be evaluated against the overall expectations of the course, with respect to the categories of
Knowledge and Understanding, Application, Communication, and Thinking as specified in the achievement chart of
the Ministry of Education curriculum documents. Evaluation should be viewed as an opportunity to demonstrate
achievement of course expectations. Evaluation will be varied, and will include mastery tests (10% of final mark), unit tests
and performance assessments. It may also include other assignments, projects, investigations and classroom activities.

Summative Evaluation

Summative evaluation occurs near the end of the course, and has two components: a final examination (20%) and
summative performance task(s) (10%). Attendance is mandatory for these evaluations.

(from: The Ontario Curriculum, Grades 11 and 12: Mathematics)
By the end of this course, students will:

A: Exponential and Logarithmic Functions
1. demonstrate an understanding of the relationship between exponential expressions and logarithmic expressions,
evaluate logarithms, and apply the laws of logarithms to simplify numeric expressions
2. 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
3. solve exponential and simple logarithmic equations in one variable algebraically, including those in problems
arising from real-world applications

B: Trigonometric Functions
1. demonstrate an understanding of the meaning and application of radian measure
2. 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
3. solve problems involving trigonometric equations and prove trigonometric identities

C: Polynomial and Rational Functions
1. identify and describe some key features of polynomial functions, and make connections between the numeric,
graphical and algebraic representations of polynomial functions
2. identify and describe some key features of the graphs of rational functions, and represent rational functions
graphically
3. solve problems involving polynomial and simple rational equations graphically and algebraically
4. demonstrate an understanding of solving polynomial and simple rational inequalities

D: Characteristics of Functions
1. 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
2. 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
3. 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
MHF4U                                                                                       2012 – 2013

Evaluation Framework

The breakdown of marks is described in the table below:

Evaluation Focus                Achievement Chart Categories       Marks
     Knowledge and Understanding
     Application
Overall Expectations

60%
TERM

Thinking
     Communication

Mastery                    Knowledge and Understanding      10%

     Thinking
SUMMATIVE

     Communication
10%

     Knowledge and Understanding
Final Examination                Application                      20%
     Communication

The Overall Expectation mark (60%) is broken down further according to strand and expectation in
terms of the nature of the expectation and described in the table below:

Strand                Strand Weight        Overall Expectation    Expectation Weight
A1                      3
Exponential and
Logarithmic Functions                       14                      A2                      6
A3                      5
B1                      2
Trigonometric
Functions                    12                      B2                      5
B3                      5
C1                      5
Polynomial and                                              C2                      4
Rational Functions                   17                      C3                      5
C4                      3
D1                      6
Characteristics of
Functions                    17                      D2                      6
D3                      5

For more detailed information about the overall expectations, refer to the course outline or ask your
teacher.

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