Preston High School, Mathematics Department
MHF 4UI, Advanced Functions
Course Handout, 2013 - 14
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.
Course Code:
MHF 4UI
Course Type: University Preparation
Grade:
12
Credit Value:
1
Course Name:
Advanced Functions
Prerequisite:
Functions, Grade 11, University Preparation (MCR3U), or Mathematics for College Technology, Grade
12 (MCT 4CI)
Ministry Guidelines:
The Ontario Curriculum, Grades 11 and 12: Mathematics 2007
Textbook:
Advanced Functions & Introductory Calculus, Nelson, 2002
Mathematics 12, Addison Wesley, 1988
Course Outline
Unit Title and Essential Learning Requirements
Exponential and Logarithmic Functions
 Demonstrate an understanding of exponential and logarithmic expressions, and apply laws of logarithms
to simplify numeric expressions
 Identify key feature of log functions, make connections between the various representations of log
functions and solve problems graphically
 Solve exponential and log equations in one variable
Trigonometric Functions
 Demonstrate an understanding of radian measure
 Make connections between the graphical and algebraic representations of trig functions, between trig
functions and their reciprocals
 Solve problems involving trig equations and prove trig identities
Polynomial and Rational Functions
 Describe key features of polynomial functions and make connections between the various
representations of polynomial functions
 Identify key features of rational functions and represent them graphically
 Solve problems involving polynomial and simple rational expressions
 Demonstrate an understanding of solving polynomial and simple rational inequalities
Characteristics of Functions
 Understand average and instantaneous rate of change of a function
 Determine functions that result from the addition, subtraction, multiplication, and division of two
functions and from the composition of two functions
 Compare the characteristics of functions and solve problems including problems that are not accessible
by standard algebraic techniques
Essential Course Components
To be successful in this course you must be able to demonstrate all of the essential learning requirements as stated in
the table above.
Assessment/Evaluation:
Tests/Quizzes/Assignments/Gizmos
70%
Final Evaluation
30%
The assessment/evaluation methods are based on the achievement chart found in the Provincial Curriculum documents.
Procedures
Late and Missing Assignments: It is important for students to develop good personal management skills (such
as time management and planning). These skills will be reflected in the learning skills area of the report card.
All of the above listed skills/assignments in the core elements checklist must be submitted and/or
demonstrated in order to earn this credit.
Attendance: Attendance in classes is an important part of learning, and absences should be avoided. When a
student is absent, a parent/guardian must call the school’s attendance line on the date of absence, or provide
a note explaining the absence for the student to submit the following day. Students are responsible for what
they missed during their absence.
Cheating and Plagiarism: It is important for students to do their own best work. Most assignments for this
class are done within the classroom, observed by the teacher, and this helps to minimize the chances of
cheating and plagiarism. In the event that cheating or plagiarism occurs, the following consequences may be
implemented, in consultation with administration, depending on the situation:
1. The student may be required to redo all or part of the assignment or assessment.
2. The student may be required to complete an alternate assignment or assessment.
3. The student’s work may be treated as a missed assignment.
There may also be other consequences that are determined to be appropriate (e.g. detention, suspension,
etc.) as per the school’s progressive discipline process. Parents/guardians will be informed about the
infraction and the consequences.
Please refer to your student handbook for more details on these policies and other academic procedures.
Topic
U1: Polynomials Functions_Algebra
U2: Polynomial Functions_Geometry
U3: Rational Functions
U4: Trigonometric Functions
U5: Trigonometric Identities and Equations
U6: Exponential and Logarithmic Functions
U7: Characteristics of Functions
U8: Average and Instantaneous Rates of Change
Summative Review
Total
Approximate Number of Days
11
9
9
13
11
12
9
6
4
84
Equipment: Bring a pen, pencil, eraser, paper, notebook, calculator, and textbook to every class.
Website: The following website will have a general outline of daily work along with some notes,
seatwork, and other helpful activities: noorduynmathhelp.com
Expectations: The completion of homework is an essential ingredient for success in this course. Use common
sense and common courtesy. Be on time!! Don’t disrupt others! Be present! Study!! Ask for help if
you need it!
Extra Help is available everyday, second half of lunch.
Signatures
Please sign below indicating you have read and understand the requirements for successful completion of this
course.
Student (Date)
Parent/Guardian (Date)