Mathematics DepartmentVictoria Park Collegiate Institute

ADVANCED FUNCTIONS

GRADE 12

Course Code: MHF4U1Credit 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

  • 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;
  • 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 1Review and Introduction to MHF 4UUnit 5Trigonometry

Unit 2Polynomial FunctionsUnit 6Trigonometric Functions

Unit 3Polynomial Equations & InequalitiesUnit 7Exponential & Logarithmic Functions

Unit 4Rational FunctionsUnit 8Combining Functions

Term Mark (70% of Final Grade)Learning Skills

Knowledge 30%Works Independently

Application30%Teamwork

Communication20%Organization

Thinking20%Work Habits / Homework

Initiative

Self Regulation

Summative Mark (30% of Final Grade)Categories are evaluated as:

Final Exam30%Needs Improvement, Satisfactory,

Good, orExcellent

Please refer to the Student Agenda for the Evaluation Policy at Victoria Park C.I.