Department of Mathematics
Ascension of Our Lord Secondary School
Course Code:
Course Name:
Level:
MHF 4U
Advanced Functions
Grade 12 University
Student Name: ________________________
Textbook #:
Course Description:
This course extends students’ experience with functions. Students will investigate the properties of
polynomial, rational, logarithmic, and trigonometric 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 who plan to study mathematics in university and for those wishing to consolidate their
understanding of mathematics before proceeding to any one of a variety of university programs.
Overall Course Expectations or Strands:
EXPONENTIAL AND LOGARITHMIC FUNCTIONS
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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 problems arising from real-world
applications
TRIGONOMETRIC FUNCTIONS
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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
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identify and describe some key features of polynomial functions, and make connections between all 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
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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
Overall Catholic Graduate Expectations:
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a discerning believer formed in the catholic faith community
an effective communicator and a reflective, creative and holistic thinker
a self-directed, responsible, life-long learner, a collaborative contributor and a responsible citizen
Efforts will be made to meet the individual learning needs of students to promote student success
with respect to meeting the expectations of this course.
My signature below indicates that I have read the Course Handout, and I am in agreement with its contents.
Parent’s/Guardian’s Signature: _________________________ Date: _______________
Student’s Signature: ________________________________
Date: _______________
Units of Study:
Resources:
The cour se will use a var iety of r esources. The
pr imar y textbook Advanced Functions will be
distr ibuted to students dur ing the fir st week of
the cour se. The text and all other r esour ces
assigned to each student ar e the r esponsibility
of the student. Any damage incur r ed will r esult
in payment for r eplacement. Replacement cost
for the text is $100.00.
Unit 1: Functions: Characteristics and Properties
Unit 2: Functions: Understanding Rates of Change
Unit 3: Polynomial Functions
Unit 4: Polynomial Equations and Inequalities
Unit 5: Rational Functions, Equations and Inequalities
Unit 6: Trigonometric Functions
Unit 7: Trigonometric identities and Equations
Unit 8: Exponential and Logarithmic Functions
Unit 9: Combinations of Functions
Summative Tasks will be administered towards the end of
the course and will be weighted at 30% of the final mark.
These tasks are specifically itemized below.
Evaluation Policies
1. Student marks will be determined by evaluating process & product according to 4 categories (see below) & 4
levels of the Achievement Chart as found in the Ministry Policy document for Mathematics.
Evaluation Str uctur e:
Knowledge/Under standing
Application
Communication
Thinking/Inquir y
30%
30%
20%
20%
Ter m Evaluations = 70% of the final mar k. Final Evaluation = 30% of the final mar k.
Final Evaluations will include: Final Exam 30%
2. Feedback will also be provided for student lear ning skills. Working independently, teamwork, organization, work
habits/homework, and initiative are assessed apart from student achievement in the four categories outlined above
and will conform to the coding:
E – Excellent
G – Good
S – Satisfactor y
N - Needs Impr ovement
3. Assignments submitted after the due date established by the teacher will receive a penalty in accord with our
Board Assessment & Evaluation Policy Document as outlined in the student agenda.
4. Should a student miss an evaluation due to a legitimate absence, in accor d with our Boar d A&E Policy
Document, the student and teacher will make arrangements to address the missed evaluation in a timely manner.
In the cases of extended vacation or pr olonged absence, consultation with the appropriate administrator is
required.
5. In the event that the student does not make up the missed evaluation(s), a zero may be assigned. If it is determined
that the evaluation(s) has/have been missed as a result of a skip/truancy or has/have been plagiarized, a zero may
be assigned.
6. For all other cases of absence and/or missed evaluations (including absence during the final examination period),
please refer to our Board A&E Policy as outlined in the student agenda.