Lester B. Pearson C.I. – Mathematics Department

Grade 12 Advanced Functions (MHF4U1) 1 Credit

Policy Documents: The Ontario Curriculum, Grades 11 and 12; Revised 2007

Prerequisite:Grade 11 University Math - MCR3U1 or Grade 12 College Technology Math - MCT4C1

Textbook:AdvancedFunctions 12, Nelson

Replacement Cost: $90

Course Description:

This course extends students’ experience with functions. Students will investigate the properties of polynomial, rational, exponential, 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 programme and for those wishing to consolidate their understanding of mathematics before proceeding to any one of a variety of university programmes.

Unit Descriptions:

UNIT # / TITLE OF UNIT / Overall Expectations:
By the end of the course students will: / Time
(Hrs)
Assessments / Introductory Unit and Exam /
  • Review
/ 5
Unit 1 / Functions: Characteristics and Properties /
  • Explore functions and their properties, absolute value, inverse, and piecewise functions;
/ 12
Unit 2 / Functions: Rates of Change /
  • Determine average rate of change;
  • Estimate instantaneous rate of change;
/ 9
Unit 3 / Polynomial Functions /
  • Explore characteristics of polynomial functions;
  • Divide and factor polynomials;
/ 11
Unit 4 / Polynomial Equations and Inequalities /
  • Solve polynomial equations;
  • Solve linear and polynomial inequalities;
/ 9
Unit 5 / Rational Functions, Equations, and Inequalities /
  • Sketch graphs of reciprocal and rational functions;
  • Solve rational equations and inequalities;
/ 9
Unit 6 / Trigonometric Equations /
  • Explore graphs of primary trigonometric functions and their transformations;
  • Explore graphs of reciprocal trigonometric functions;
/ 12
Unit 7 / Trigonometric Identities and Equations /
  • Prove trigonometric identities;
  • Solve trigonometric equations;
/ 11
Unit 8 / Exponential and Logarithmic Functions /
  • Explore the logarithmic function and its transformations;
  • Solve exponential equations and problems;
/ 11
Unit 9 / Combinations of Functions /
  • Explore combinations of functions;
  • Explore composition of functions;
/ 6

Attitudes: This course is designed to assist each student to develop:

  • Positive attitude toward mathematics and a feeling of self worth.
  • An appreciation for the place of mathematics and its widespread application in society and its importance in technological development.

Class Work Requirements

Regular attendance and punctuality at all classes are essential. Success in this course will largely depend on diligent completion of all assigned work and daily attendance. Students must always come prepared to class with his/her notebook, textbook and other required items. Daily homework must be completed before the next class. If you were unable to complete it, please speak to the teacher before the class starts. If some work is not understood, see the teacher as soon as possible to make arrangements for extra help.

Teaching/Assessment and Evaluation Strategies:

MHF4U1 EVALUATION POLICY:

The Final Course Mark will be determined from the following weightings:

Term Work 70%

( TESTS = 49%: QUIZZES = 14% : ASSIGNMENTS =7% )

Term Marks will be determined using the following weights:

Knowledge and Content 30% : Application of Content 30%
Thinking and Problem Solving Skills 25% : Communication 15%

Final Exam 30%

All students in the course will write a common exam at the end of the semester.

Term Work + Final Exam = 100%

Missed Evaluation Policy

Take-home assignments or projects

  • Your teacher will assign a deadline for the submission of take home assignments.
  • It is expected that you will submit your work on time and timely submission of assignments will be reflected in the learning skills section of your report card.
  • Your teacher will also give you an ultimate deadline for your assignment. No late marks will be taken off of assignments that are submitted by the ultimate deadline.
  • Assignments submitted after the ultimate deadline will be subject to a maximum 10% late deduction of marks.

In-class assessments (tests, quizzes etc.)

  • If you are going to be absent for any in class assessment you must notify your teacher as soon as possible before the assessment. You and your teacher will make alternate arrangements to write the assessment at a different.
  • If you miss an in class assessment for an unforeseen reason (i.e. illness) Your teacher will require you to write it upon your return.
  • If your teacher decides that it is not appropriate for you to write the assessment on your return then you and your teacher will set time to write an alternate assessment. This may be outside of class time.

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