Waterloo Collegiate Institute

300 Hazel Street, Waterloo ON, N2L 3P2(519) 884-9590wci.wrdsb.ca

Advanced Functions, Grade 12, 2016-2017

Course Code / MHF 4UI / Teacher / Mrs. Schnute-Klaassen
Period / A and C / Additional Availability / 20 min before school starts
Classroom / 408 / Contact Info / 519-884-9590 ext. 402Math Office
Office Location / 402 / Important Website /

Course Description/Big Ideas

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 (MCV 4UI) 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

POLYNOMIAL AND RATIONAL FUNCTIONS: By the end of this course, students will:

  • 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.

CHARACTERISTICS OF FUNCTIONS: By the end of this course, students will:

  • 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.

EXPONENTIAL AND LOGARITHMIC FUNCTIONS: By the end of this 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.

TRIGONOMETRIC FUNCTIONS: By the end of this course, students will:

  • 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.

Course Text

Nelson: Advanced Functions (Barbara Alldred et al.)

Units

Unit Title
/
Semester 1
/
Semester 2
/ Timing
(approx)
Functions: Characteristics and Properties
/ September / February / 12 classes
Polynomials: Mathematical Properties
/ October / February / 12 classes
Polynomials and Rational Equations and Inequalities
/ October / March / 7 classes
Understanding Rates of Change
/ November / March / 9 classes
Sketching Rational Functions
/ November / April / 7 classes
Exponential and Logarithmic Functions
/ Nov/Dec / April / 14 classes
Trigonometric Functions
/ December / May / 11 classes
Trigonometric Identities and Equations
/ December / May / 11 classes
Combinations of Functions
/ January / June / 4classes
Final Exam Review
/ January / June / 6 classes

Course Evaluation

Overall, coursework will be worth 70% and summative evaluations 30%. A specific breakdown of assessments is below:

Assessment Breakdown
/
Exponential and Logarithmic Functions
/
Trigonometric Functions
/
Polynomial and Rational Functions
/
Characteristics of Functions
/
Weight (%)
Unit Tests / ✭ / ✭ / ✭ / ✭ / 70

Quizzes

/ ✭ / ✭ / ✭ / ✭

Final Exam

/ ✭ / ✭ / ✭ / ✭ / 30

Total

/

100

Late and Missed Assessments

See the “Late and Missed Assessments” policy in the WCI Student Planner.

If you miss an assessment in this course due to a valid absence, you will complete a make-up test. See the teacher immediately upon your return to school to schedule the make-up test.

Cheating and Plagiarism

See the “Cheating and Plagiarism” policy in the WCI Student Planner.

Learning Skills

The development of learning skills and work habits is an integral part of your learning. The achievement of these skills is officially reported on the Provincial Report Card. The learning skills on which you are evaluated are Responsibility, Organization, Independent Work, Collaboration, Initiative, and Self-Regulation. The scale that is used for this evaluation are E - Excellent, G - Good, S - Satisfactory, and N - Needs Improvement.

In this course, excellent learning skills look like this:

  1. Responsibility:

○Being prepared at the start of class with a pencil, eraser, ruler, paper and calculator.

○Letting your teacher know if you will be away during a test, quiz or assignment.

○Completing class work and homework.

○Takes responsibility for and manages own behaviour.

○Takes responsibility for missed classes.

  1. Organization:

○Keeping your notebook and study notes organized.

○Keeping track of important dates.

  1. Independent Work:

○Follows instructions to complete tasks.

○Uses class time effectively to complete tasks.

  1. Collaboration:

○Sharing your ideas, resources, expertise and listening to group discussions.

○Working well with others when asked or offering help to another student.

  1. Initiative:

○Approaches new tasks with a positive attitude.

○Arranging times to make up tests, quizzes or assignments outside of class.

○Demonstrates curiosity and interest in learning.

  1. Self-Regulation:

○Seeks clarification or assistance when needed.

○Being respectful of all people in the class.

○Perseveres and makes an effort when responding to challenges.