Canterbury High School Functions, Grade 11 University Preparation MCR3U

This course introduces the mathematical concept of the function by extending students' experiences with linear and quadratic relations. Students will investigate properties of discrete and continuous functions, including trigonometric and exponential functions; represent functions numerically, algebraically, and graphically; solve problems involving applications of functions; investigate inverse functions; and develop facility in determining equivalent algebraic expressions. Students will reason mathematically and communicate their thinking as they solve multi-step problems.
Prerequisite:Principles of Mathematics, Grade 10, Academic The Term work will be worth 70% of the final mark divided up into the following topics:

CHARACTERISTICS OF FUNCTIONS 1. demonstrate an understanding of functions, their representations, and their inverses, and make connections between the algebraic and graphical representations of functions using transformations; 2. determine the zeros and the maximum or minimum of a quadratic function, and solve problems involving quadratic functions, including problems arising from real-world applications; 3. demonstrate an understanding of equivalence as it relates to simplifying polynomial, radical, and rational expressions.

EXPONENTIAL FUNCTIONS 1. evaluate powers with rational exponents, simplify expressions containing exponents, and describe properties of exponential functions represented in a variety of ways; 2. make connections between the numeric, graphical, and algebraic representations of exponential functions; 3. identify and represent exponential functions, and solve problems involving exponential functions, including problems arising from real-world applications.

DISCRETE FUNCTIONS 1. demonstrate an understanding of recursive sequences, represent recursive sequences in a variety of ways, and make connections to Pascal’s triangle; 2. demonstrate an understanding of the relationships involved in arithmetic and geometric sequences and series, and solve related problems; 3. make connections between sequences, series, and financial applications, and solve problems involving compound interest and ordinary annuities.

TRIGONOMETRIC FUNCTIONS 1. determine the values of the trigonometric ratios for angles less than 360º; prove simple trigonometric identities; and solve problems using the primary trigonometric ratios, the sine law, and the cosine law; 2. demonstrate an understanding of periodic relationships and sinusoidal functions, and make connections between the numeric, graphical, and algebraic representations of sinusoidal functions; 3. identify and represent sinusoidal functions, and solve problems involving sinusoidal functions, including problems arising from real-world applications.

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.

CanterburyHigh SchoolFunctions, Grade 11University Preparation MCR3UThis course introduces the mathematical concept of the function by extending students' experiences with linear and quadratic relations. Students will investigate properties of discrete and continuous functions, including trigonometric and exponential functions; represent functions numerically, algebraically, and graphically; solve problems involving applications of functions; investigate inverse functions; and develop facility in determining equivalent algebraic expressions. Students will reason mathematically and communicate their thinking as they solve multi-step problems.

Prerequisite:Principles of Mathematics, Grade 10, Academic

The Term work will be worth 70% of the final mark divided up into the following topics:

CHARACTERISTICS OF FUNCTIONS1.demonstrate an understanding of functions, their representations, and their inverses, and makeconnections between the algebraic and graphical representations of functions using transformations;

2.determine the zeros and the maximum or minimum of a quadratic function, and solve problemsinvolving quadratic functions, including problems arising from real-world applications;

3.demonstrate an understanding of equivalence as it relates to simplifying polynomial, radical, andrational expressions.

EXPONENTIAL FUNCTIONS1.evaluate powers with rational exponents, simplify expressions containing exponents, and describeproperties of exponential functions represented in a variety of ways;

2.make connections between the numeric, graphical, and algebraic representations of exponentialfunctions;

3.identify and represent exponential functions, and solve problems involving exponential functions,including problems arising from real-world applications.

DISCRETE FUNCTIONS1.demonstrate an understanding of recursive sequences, represent recursive sequences in a variety ofways, and make connections to Pascal’s triangle;

2.demonstrate an understanding of the relationships involved in arithmetic and geometric sequencesand series, and solve related problems;

3.make connections between sequences, series, and financial applications, and solve problems involvingcompound interest and ordinary annuities.

TRIGONOMETRIC FUNCTIONS1.determine the values of the trigonometric ratios for angles less than 360º; prove simple trigonometricidentities; and solve problems using the primary trigonometric ratios, the sine law, and the cosine law;

2.demonstrate an understanding of periodic relationships and sinusoidal functions, and makeconnections between the numeric, graphical, and algebraic representations of sinusoidal functions;

3.identify and represent sinusoidal functions, and solve problems involving sinusoidal functions,including problems arising from real-world applications.

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

Nelson Functions 11 ( $85 if lost or damaged)

Teacher: Mr. Hughsone-mail: darrin.hughson@ocdsb.caWebsite:hughsonmath.wikispaces.comSome helpful websites:Identities: http://www.teaching.martahidegkuti.com/shared/lnotes/trigidentities1/trigidentities1.pdf

Function Notation: http://www.purplemath.com/modules/fcnnot.htm

Transformations: http://cnx.org/content/m11471/latest/

http://math.kennesaw.edu/~sellerme/sfehtml/classes/math1113/transformation.pdf

http://cnx.org/content/m11470/latest/

Factoring Quadratics: http://www.purplemath.com/modules/factquad.htm

Quadratic Functions: http://uncw.edu/courses/mat111hb/pandr/quadratic/quadratic.html

http://faculty.mdc.edu/mmontane/quadratic-models.pdf

Radicals: http://www.themathpage.com/alg/simplify-radicals.htm

Solving Linear-Quadratic systems: http://www.regentsprep.org/Regents/math/ALGEBRA/AE6/PLinQuad.htm

http://mathbits.com/MathBits/TISection/Algebra1/LinQuad.htm

http://www.regentsprep.org/Regents/math/ALGEBRA/AE6/LLinQuad1.htm

Integer and Rational exponents: http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut5_ratexp.htm

http://tutorial.math.lamar.edu/classes/alg/integerexponents.aspx

http://tutorial.math.lamar.edu/Classes/Alg/RationalExponents.aspx

Exponetial Functions: http://www.purplemath.com/modules/expofcns.htm

http://tutorial.math.lamar.edu/Classes/Alg/ExpFunctions.aspx

http://www.analyzemath.com/expfunction/expfunction.html

http://www.algebralab.org/lessons/lesson.aspx?file=Algebra_ExponentialTransformations.xml

Review TestHomeworkMCR 3U Textbook Homework

Ch 7 Sequences & Series

Videos: Sequences and Series

Ch 1 Functions

Videos: Functions, Inverse, Transformations

Ch 2 Algebra

Videos: Expanding and Factoring Quadratics Rational Expressions

Ch 3 Quadratics

Videos: Quadratic Functions

Ch 4 Exponential Functions

Videos: Exponential Functions

Ch 5 Trig

Videos: Trig Videos

Ch 6 Trig Functions

Ch 8 Financial Math