CanterburyHigh School Advanced Functions, Grade 12 University Preparation MHF4U

This course extends studentsâ€™ experience with functions. Students will investigate the properties of polynomials, 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 considered a prerequisite for Calculus and Vectors as well as for those wishing to consolidate their understanding of the mathematics before proceeding to any of the university programs.

Prerequisite: MCR3U

The Term work will be worth 70% . The methods of evaluation will include tests, quizzes, and in class tasks.

The topics to be studied and evaluated in this course are:

A. EXPONENTIAL AND LOGARITHMIC FUNCTIONS 1. demonstrate an understanding of the relationship between exponential expressions and logarithmic expressions, evaluate logarithms, and apply the laws of logarithms to simplify numeric expressions; 2. 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; 3. solve exponential and simple logarithmic equations in one variable algebraically, including those in problems arising from real-world applications.

B. TRIGONOMETRIC FUNCTIONS 1. demonstrate an understanding of the meaning and application of radian measure; 2. 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; 3. solve problems involving trigonometric equations and prove trigonometric identities.

C. POLYNOMIAL AND RATIONAL FUNCTIONS 1. identify and describe some key features of polynomial functions, and make connections between the numeric, graphical, and algebraic representations of polynomial functions; 2. identify and describe some key features of the graphs of rational functions, and represent rational functions graphically; 3. solve problems involving polynomial and simple rational equations graphically and algebraically; 4. demonstrate an understanding of solving polynomial and simple rational inequalities.

D. CHARACTERISTICS OF FUNCTIONS 1. 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; 2. 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; 3. 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.

The Final Evaluation will be worth 30% of the course.

Required materials

All students are required to have a scientific calculator, pencils, pens, an eraser, paper, graph paper, and a ruler for each class. Borrowing from other students in class during tests, exams, and quizzes is not permitted. Please come to class prepared.

Textbook cost

The textbook for this course costs $95. A textbook will be loaned to you. If you lose or damage the textbook you will be required to pay for it.

Grade 12 FunctionsCourse outline:

CanterburyHigh SchoolAdvanced Functions, Grade 12University Preparation MHF4UThis course extends studentsâ€™ experience with functions. Students will investigate the properties of polynomials, 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 considered a prerequisite for Calculus and Vectors as well as for those wishing to consolidate their understanding of the mathematics before proceeding to any of the university programs.

Prerequisite: MCR3U

The

. The methods of evaluation will include tests, quizzes, and in class tasks.Term work will be worth 70%The topics to be studied and evaluated in this course are:

A.EXPONENTIAL AND LOGARITHMIC FUNCTIONS1.demonstrate an understanding of the relationship between exponential expressions and logarithmic expressions, evaluate logarithms, and apply the laws of logarithms to simplify numeric expressions;2.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 solverelated problems graphically;

3.solve exponential and simple logarithmic equations in one variable algebraically, including those in problems arising from real-world applications.B.TRIGONOMETRIC FUNCTIONS1.demonstrate an understanding of the meaning and application of radian measure;2.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;3.solve problems involving trigonometric equations and prove trigonometric identities.C.POLYNOMIAL AND RATIONAL FUNCTIONS1.identify and describe some key features of polynomial functions, and make connections between the numeric, graphical, and algebraic representations of polynomial functions;2.identify and describe some key features of the graphs of rational functions, and represent rational functions graphically;3.solve problems involving polynomial and simple rational equations graphically and algebraically;4.demonstrate an understanding of solving polynomial and simple rational inequalities.D.CHARACTERISTICS OF FUNCTIONS1.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;2.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;3.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.The

of the course.Final Evaluation will be worth 30%## Required materials

Borrowing from other students in class during tests, exams, and quizzes is not permitted. Please come to class prepared.## Textbook cost

The textbook for this course costs $95. A textbook will be loaned to you. If you lose or damage the textbook you will be required to pay for it.

Teacher: Mr. Hughsone-mail: darrin.hughson@ocdsb.caWebsite:hughsonmath.wikispaces.comWolframAlpha: http://www.wolframalpha.com/

University of waterloo video lessons and exercises with solutions:http://courseware.cemc.uwaterloo.ca/8?gid=122

videos: Go to the second page of this link to start seeing lessons for this course http://www.yourepeat.com/g/MHF4U

Textbook Homework

Ch 3

Ch 4

16

3 to 10

Ch 5

Ch 6

Ch 7

Ch 8

Ch 2

Chs 1 and 9

Trig identities

http://www.oame.on.ca/main/files/Gr12-2007/MHF4U/MHF4U-unit4.doc

Page. 11 #'s 1,3,4,5

Page. 24 #'s 8,9

Page. 35 #'s 1,2,4,5,9,14

Page 76 #'s 1ac,2,8

Page 112 #'s 5ac,6ace,10

Page 146 #'s 1 to 8, 12, 13

Page 204. #'s 1 to 9

Page 213 #1 to 7,9, 11

Ch 4 Quiz postponed until tuesday.

Do Numbers 1 to 14 and 16 on Page 235.

Page 295. #'s 1 to 7, 9, 11, 13

Page 353 #'s 1,2,3,5,6,7

Page 343 # 1(graph each function)

Page 435 # 1

Page 466 #'s 1,2,3

Page 475 #'s 1 to 13