Mathematics Department
Victoria Park Collegiate Institute
ADVANCED FUNCTIONS
GRADE 12
Course Code:
MHF4U1
Credit Value: 1 Credit
Textbooks:
Advanced Functions 12, McGraw-Hill Ryerson (2008)
Replacement Cost is $80
Prerequisites:
Grade 11U Functions (MCR3U) OR
Grade 12C Mathematics for College Technology (MCT4C)
Ministry Policy:
The Ontario Curriculum: Grades 11 and 12; Mathematics, 2007
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. 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.
Overall Expectations
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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
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;
Mathematics Department
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Victoria Park Collegiate Institute
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 modeling and reasoning with
functions, including problems with solutions not accessible by standard algebraic techniques.
Where To Get Extra Help:
Teachers are available for extra help by appointment or during announced scheduled times.
Mathematics Office:
Room 225
Telephone Number:
(416) 395 3310 ext. 20080
Absences and Evaluations:
1. If you know prior to the evaluation that you will be absent, make other arrangements with
your teacher regarding that particular assessment.
2. If for some reason you are absent on the day of an evaluation:
a)
Call the Math Office before 8:45 a.m. and speak to or leave a message for
your teacher
b)
On the first day back, a note from your parent/guardian is required to explain
your absence.
Teaching, Assessment, and Evaluation Strategies
Throughout this course, students will develop their understanding of essential mathematical
knowledge and procedures. This knowledge becomes meaningful in reasoning, communicating,
and solving problems based on real-life situations. Technology, calculators and/or computer
software will be used to complement the teaching and application of mathematical skills and
explore concepts where appropriate.
Student success is greatly enhanced by good attendance, behaviour, and class participation.
Completion of daily homework exercises and writing all evaluations will provide feedback on
student learning. For courses with multiple sections, summative evaluations will assess common
expectations.
Quizzes and assignments will be scheduled throughout the course. A summative test will
conclude a unit or group of related units. The following is an overview of the units in this course:
Unit 1
Unit 2
Unit 3
Unit 4
Review and Introduction to MHF 4U
Polynomial Functions
Polynomial Equations & Inequalities
Rational Functions
Term Mark (70% of Final Grade)
Knowledge
Application
Communication
Thinking
30%
30%
20%
20%
Summative Mark (30% of Final Grade)
Final Exam
30%
Unit 5
Unit 6
Unit 7
Unit 8
Trigonometry
Trigonometric Functions
Exponential & Logarithmic Functions
Combining Functions
Learning Skills
Works Independently
Teamwork
Organization
Work Habits / Homework
Initiative
Self Regulation
Categories are evaluated as:
Needs Improvement, Satisfactory,
Good, or Excellent
Please refer to the Student Agenda for the Evaluation Policy at Victoria Park C.I.