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.


Textbook


Nelson Functions 11 ( $85 if lost or damaged)

Teacher: Mr. Hughson e-mail: darrin.hughson@ocdsb.ca

Website: hughsonmath.wikispaces.com



Some 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 Test



Homework

MCR 3U Textbook Homework


Ch 7 Sequences & Series
Videos: Sequences and Series
Page
Numbers
424
1,3 to 13,15
430
1 to 12
439
2,3
447
3,6,9
452
1 to 11
459
1 to 7,11
466
3,5

Ch 1 Functions
Videos: Functions, Inverse, Transformations
Page
Numbers
10
1,2,6,7,10
22
2,4,10,11,17
35
1,2,3,5,12,14
46
1,2(a,b,f),5(odd),6(odd),13
51
2,3
58
2,4 to 7
70
1 to 13,17,18

Ch 2 Algebra
Videos: Expanding and Factoring Quadratics Rational Expressions
Page
Numbers
88
2,5,6,8,13
95
2,4,6,7,10
102
1 to 9,14
112
1 to 7,10
121
1 to 9,13
128
1 to 10,12

Ch 3 Quadratics
Videos: Quadratic Functions
Page
Numbers
145
1 to 9,11,12
153
1 to 4,7,8,11
160
1 to 6
167
1 to 7,10 to 12
177
1,2,4,5,7,8,12
185
1 to 4,6 to 9,14
192
1 to9,17
198
1 to 4,6,8,11

Ch 4 Exponential Functions
Videos: Exponential Functions
Page
Numbers
221
1 to 9,13,16,18
229
1 to 12,14
236
1 to 9,11
251
1 to 10
261
1 to 9,11,12

Ch 5 Trig
Videos: Trig Videos
Page
Numbers
274
1 to 8
281
5 to 8,11,13,15
286
1 to 8,11
292
1,2,4
299
1 to 6,8,12
310
1 to 8,11,12,14
318
1 to 8,12,15
325
1 to 8,10
332
3,4,6,7,8,11

Ch 6 Trig Functions
Page
Numbers
354
1 to 4,6,8
363
2,7,9
370
1,2,5,10
379
1 to 3
383
1 to 9
391
1 to 8,13
398
1,2,4 to 9,13

Ch 8 Financial Math
Page
Numbers
481
1,3,5,8,11
490
1,4,5,8,11
498
1,3,5,8,10
511
2,4,6,9
520
1,3,5,9