MCR3U

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TORONTO DISTRICT SCHOOL BOARD

WEST HUMBER COLLEGIATE INSTITUTE

MATHEMATICS COURSE OUTLINE

** Course Title ** : Functions **Course Code**: MCR3U ** Description ** 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
 * Course Type ** : University Preparation **Grade Level**: 11 **Credit Value**: 1.0
 * Ministry Guideline/Date ** : The Ontario Curriculum, Grades 11 and 12, Mathematics, 2007

** OVERALL EXPECTATIONS ** ** A. CHARACTERISTICS OF FUNCTIONS ** By the end of this course, students will: · demonstrate an understanding of functions, their representations, and their inverses, and make connections between the algebraic and graphical representations of functions using transformations; · 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; · demonstrate an understanding of equivalence as it relates to simplifying polynomial, radical, and rational expressions. ** B. EXPONENTIAL FUNCTIONS ** By the end of this course, students will: · evaluate powers with rational exponents, simplify expressions containing exponents, and describe properties of exponential functions represented in a variety of ways; · make connections between the numeric, graphical, and algebraic representations of exponential functions; · identify and represent exponential functions, and solve problems involving exponential functions, including problems arising from real-world applications. ** C. TRIGONOMETRIC FUNCTIONS ** By the end of this course, students will: · 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; · demonstrate an understanding of periodic relationships and sinusoidal functions, and make connections between the numeric, graphical, and algebraic representations of sinusoidal functions; · identify and represent sinusoidal functions, and solve problems involving sinusoidal functions, including problems arising from real-world applications. ** D. DISCRETE FUNCTIONS ** By the end of this course, students will: · demonstrate an understanding of recursive sequences, represent recursive sequences in a variety of ways, and make connections to Pascal’s triangle; · demonstrate an understanding of the relationships involved in arithmetic and geometric sequences and series, and solve related problems; · make connections between sequences, series, and financial applications, and solve problems involving compound interest and ordinary annuities. **__ Evaluation __** Evaluation is based on the Ministry of Education document, //Growing Success: Assessment, Evaluation, and Reporting in Ontario Schools, First Edition, Covering Grades 1 to 12, 2010.// Each student’s grade in this course will be generated as follows:  · ** 70 % of the grade ** will be based on evaluation conducted throughout the course. Such evaluations may take the form of tests, quizzes, and assignments etc.  · ** 30 % of the grade ** will be based on a final exam and/or culminating activity that will be administered at the end of the course. Throughout the course, all evaluations will be divided into categories as set out by the Achievement Chart. Please note that not all categories will be included in a particular evaluation. The categories and their approximate weighting are as follows: Subject-specific content acquired in each course (knowledge), and the comprehension of its meaning and significance (understanding) || 30 %  ||   || The use of critical and creative thinking skills and/or processes || 15 %  ||   || The conveying of meaning through various forms || 10 %  ||   || The use of knowledge and skills to make connections within and between various contexts || 15 %  ||   ||
 * ** Categories ** ||  ** WEIGHTING **  ||   ||
 * ** Knowledge and Understanding **
 * ** Thinking **
 * ** Communication **
 * ** Application **
 * ** Term Evaluation ** || 70%  || 100 % ||
 * ** Final Examination and / or Culminating Activity ** || 30 %  ||^   ||

**__ Learning Skills and Work Habits: __** In addition to a numeric grade, students will be assessed on how well they develop the following learning skills and work habits:


 * Responsibility
 * Organization
 * Independent Work
 * Collaboration
 * Initiative
 * Self-Regulation

For each skill, students will receive a rating of “Excellent”, “Good”, “Satisfactory”, or “Needs Improvement”. This will be reported on a student’s report card.

**__ Student Expectations: __**
 * 1. Students are responsible for their behaviour in the classroom and the school and for providing evidence of their achievement of the overall expectations of the curriculum. **
 * 2. Homework will be assigned on a daily basis. If you have a problem with homework, you are expected to get extra help before the next class. **
 * 3. In order to ensure equity for all students, assignments for evaluation and tests or exams are to be completed, whenever possible, under the supervision of a teacher. **
 * 4. Students are expected to complete all Assessment for/as/of learning for the day noted by the teacher. All math problems are to be answered using proper format, neat and legible. Assignments are always due at the beginning of the period on the due date. Late assignments will not normally be accepted after the assignment has been taken up or handed back. Failure to make arrangements concerning missed assignments will result in a mark of zero. It is the responsibility of the student to catch up on any work they might have missed. **
 * 5. Assessment of learning will be given on a regular basis. If absent on an assessment day, the assessment will be written the first day back unless prior arrangements have been made. Failure to check with the teacher will result in a mark of zero. **
 * 6. Organized notebooks are the key to success! Each lesson should be neatly dated, numbered and include a **
 * record of that day’s homework. **
 * 7. It is the student’s responsibility to seek extra help when needed - it is always available upon request. Don’t forget that keeping up is easier than catching up! **

**__ Plagiarism __** Plagiarism is a very serious offence. Any work that the student submits as an evaluation must be his or her original work. Students who are caught plagiarizing will receive a mark of zero, and further disciplinary action may be taken. **__ Materials Required __** Pencil, pen, eraser, ruler, scientific calculator, lined or grid paper, three-ring binder. **__ Contact Information __** Parent(s) and/or guardian(s) may contact the school at (416) 394-7570 at any time to find out how students are progressing in their classes.

 Quizzes Assignments Mid-Chapter and Chapter Test Key Question :Achievement Check || 1.1 Relations and Functions || p.10-11 #1-11 || Read p.38-39 p.40 # 1-8 || y = af(k(x-c)) +d || p.70-73 #1-13,16-20 || p.76-77# 1-19 p.78 # 1-8 || Quizzes Assignments Chapter Test Key Question :Achievement Check || 2.1 Adding and Subtracting Polynomials || p.88-89 # 1-12 Do every other letter #1-8 || Do every other letter # 1-6 || Do every other letter # 1-7 p.107 # 1-9 Do every other letter # 1,2,5,7,8 || Do every other letter || p.132-133 # 1-17 || Quizzes Assignments Chapter Test Key Question :Achievement Check || 3.1 Properties of Quadratic Functions || p.145-147- # 1-13 || Read p.169 p.170 # 1-14 || Do every other letter p.202-203 # 1-23 || Quizzes Assignments Chapter Test Key Question :Achievement Check || 4.1 Exponential Growth || p.216 # 1-2 || Read p.238 Do every other letter p.239 #1-12 || 4.6 Transformations of Exponential Functions || p.243 # 1-2 p.251#1-11 || p.267-268 #1-12 ||
 * ** Chapter/Unit ** || Sections || Homework ||
 * **__ UNIT 1: CHARACTERISTICS OF FUNCTIONS __**
 * Chapter 1 **
 * Introduction to Functions **
 * Evaluation **
 * ^  || 1.2 Function Notation || p.22-24 #1-17,20 ||
 * ^  || 1.3 Investigating Properties of Parent Functions || p.28 # 1-3 ||
 * ^  || 1.4 Determining the Domain and Range of a Function || p.35-37 # 1-15,17
 * ^  || 1.5 The Inverse Function and Its Properties || p.46-48 #1-12,15 ||
 * ^  || 1.6 Exploring Transformations of Parent Functions || p.51 #1-4 ||
 * ^  || 1.7 Transformations: Reflections, Stretches and Compressions y = kf(x) and y = f(-kx) || p.58-60 #1-11 ||
 * ^  || 1.8Using Transformations to Graph Functions
 * ^  || ** Chapter review ** || Read p.74-75
 * ** Chapter 2 **
 * Equivalent Algebraic Expressions **
 * Evaluation **
 * ^  || 2.2 Multiplying Polynomials || p.95-96 # 1-13
 * ^  || 2.3 Factoring Polynomials || p.102-103 # 1-12,14
 * ^  || 2.4 Simplifying Rational Expressions || p.112-113 # 1-10 ||
 * ^  || 2.5 Exploring Graphs of Rational Functions || Read p.115-116 ||
 * ^  || 2.6 Multiplying and Dividing Rational Expressions || p.121-123 #1-10 ||
 * ^  || 2.7 Adding and Subtracting Rational Expressions || p.128-129 # 1-10
 * ^  || ** Chapter Review ** || Read p.131
 * ** Chapter 3 **
 * Quadratic Functions **
 * Evaluation **
 * ^  || 3.2 Determining Optimal Value of a Quadratic Function || p.153-154 # 1-12 ||
 * ^  || 3.3 The Inverse of a Quadratic Function || p.160-162#1-13 ||
 * ^  || 3.4 Operations with Radicals || p.167-168# 1-17
 * ^  || 3.5 Quadratic Function Models: Solving Quadratic Equations || p.177-178 # 1-14 ||
 * ^  || 3.6 The Zeroes of Quadratic Functions || p.185-186 # 1-13 ||
 * ^  || 3.7 Finding the Algebraic Model for a Quadratic Function || p.192-193 # 1-13 ||
 * ^  || 3.8 Linear Quadratic Systems || p.198-199 #1-12 ||
 * || ** Chapter Review ** || Read p.200-201
 * **__ UNIT 2: EXPONENTIAL FUNCTIONS __**
 * Chapter 4 **
 * Exponential Functions **
 * Evaluation **
 * ^  || 4.2 Working with Integer Exponents || p.221-223 # 1-18 ||
 * ^  || 4.3 Working with Rational Exponents || p.229 -230 # 1-14,18 ||
 * ^  || 4.4 Simplifying Algebraic Expressions Involving Exponents || p.235-237 #1-15
 * ^  || 4.5 Investigating the Properties of Exponential Functions
 * ^  || 4.7 Applications Involving Exponential Functions || p.261-264 #1-16 ||
 * ^  || ** Chapter Review ** || Read p.265-266
 * **__ UNIT 3:TRIGONOMETRIC FUNCTIONS __**

Quizzes Assignments Chapter Test Key Question :Achievement Check || 5.1 The Trigonometric Ratios of an Acute Angle || p.280-282 # 1-17 || Read p.302-303 Do every other letter p.304 || p.338-339 || Quizzes Assignments Chapter Test Key Question :Achievement Check || 6.1 Periodic Functions and Their Properties || p.352-356 # 1-13 || Read p.374-375 p.376 # 1-6 || Handout || 6 .  7 Applications Involving Sinusoidal Functions || p.391-393 # 1-11 p.398-401 #1-10 || p.404-405#1-14 ||
 * Chapter 5 **
 * Trigonometric Ratios **
 * Evaluation **
 * ^  || 5.2 Evaluating Trigonometric Ratios for Special Angles || p.286-287 # 1-12 ||
 * ^  || 5.3 Exploring Trigonometric Ratios for Angles > 90° that involve Special Triangles || p.292 # 1-4 ||
 * ^  || 5.4 Evaluating Trigonometric Ratios for Angles between 0o and 360o || p.299 -301 # 1-12,17
 * ^  || 5.5 Trigonometric Identities || p.310-311 # 1-12 ||
 * ^  || 5.6 Using the Sine Law || p.318-320 # 1-13 ||
 * ^  || 5.7 Using the Cosine Law || p.325-327 # 1-11,14 ||
 * ^  || 5.8 Solving Triangle Problems || p.332-335 # 1-12 ||
 * ^  || ** Chapter Review ** || Read p.336-337
 * ** Chapter 6 **
 * Sinusoidal Functions **
 * Evaluation **
 * ^  || 6.2 The Graphs of f(x) = sin x and f(x) = cos x || p.363-364 # 1-14,16 ||
 * ^  || 6.3 Interpreting Sinusoidal Functions || p.370-373 #1-13
 * ^  || 6.4 Investigating Transformations of Sinusoidal Functions || p.379 # 1-3
 * ^  || 6.5 Using Transformations to Sketch the Graphs of Sinusoidal Functions || p.383-385 # 1-11,13 ||
 * ^  || 6.6 Exploring Sinusoidal Function Models
 * ^  || ** Chapter review ** || Read p.403
 * **__ UNIT 4:DISCRETE FUNCTIONS __**

Quizzes Assignments Chapter Test Key Question :Achievement Check || 7.1 The Arithmetic Sequence || p.424-425 # 1-16 || Read p.445-446 p.447 # 1-10 || p.468-469 # 1-23 || Quizzes Assignments Chapter Test Key Question :Achievement Check || 8.1 Simple Interest || p.481-482 # 1-11 || p.535-535 # 1-20 ||
 * Chapter 7 **
 * Discrete Functions: Sequences and Series **
 * Evaluation **
 * ^  || 7.2 The Geometric Sequence || p.430-432 # 1-1-16,19 ||
 * ^  || 7.3 Creating Rules to Define Sequences || p.439-440 # 1-7,9 ||
 * ^  || 7.4 Exploring Recursive Sequences || p.443 # 3
 * ^  || 7.5 Arithmetic Series || p.452-453 # 1-13,15-16 ||
 * ^  || 7.6 Geometric Series || p.459-461 # 1-7,11-13,16 ||
 * ^  || 7.7 Pascal’s Triangle and Binomial Expansion || p.466 # 1-10 ||
 * ^  || ** Chapter Review ** || Read p.467
 * ** Chapter 8 **
 * Discrete Functions: Financial Applications **
 * Evaluation **
 * ^  || 8.2 Compound Interest: Future Value || p.490-492 # 1-12,15-17 ||
 * ^  || 8.3 Compound Interest: Present Value || p.498-499 # 1-11,13,15 ||
 * ^  || 8.4 Annuities: Future Value || p.511-512 # 1-10 ||
 * ^  || 8  .  5 Annuities: Present Value || p.520-522 # 1-15 ||
 * ^  || 8.6 Using Technology to Investigate Financial Applications || p.530-531 # 1-10 ||
 * ^  || ** Chapter Review ** || Read p.532-533