Grade 11 Functions (MCR3U) Course Outline and Syllabus Semester 2 2016-2017 Teacher: Mrs. Vallee Room A7 Email: christina.vallee@ed.amdsb.ca Course Wiki: http://mcr3ugrade11math.pbworks.com This course is made up of 8 Units of Study: Unit 1 Polynomials Unit 5 The Exponential Function Unit 2 Introduction to Functions Unit 6 Financial Applications Unit 3 The Quadratic Function Unit 7 Trigonometry Unit 4 The Rational Function Unit 8 The Sinusoidal Function The course will be evaluated using the following categories and weightings: Knowledge and Understanding Application Thinking Communication 35% 35% 15% 15% Evaluation in this course will be based upon a 70% term mark and 30% final exam. The term mark will be determined by assessments in the form of quizzes, tests and assignments. We will use the following success criteria guidelines to measure progress and achievement in this course. Guidelines for Achieving Success in Senior Mathematics How can you determine if you are meeting the required expectations of this course on a daily basis? You will be given a course syllabus that lists all of the units of study, with descriptions of the key skills identified for each lesson. You should use the course syllabus as part of your daily planner as it will help you keep record of the skills developed as well as help you self-assess your understanding of concepts each day. Fill in the Blank Notes will be provided and posted to our wiki before each lesson. You are expected to use bring these notes with you to class before the lesson, or you may choose to print the completed note that will be posted to the wiki when it is finished. You should also work to meet the following success criteria each day: Success Criteria I have read through the course syllabus for the given lesson of study and have identified the skills and concepts that I need to use, understand and consolidate. I have participated in the lesson and learning activities and have collaborated with my peers in the effort to understand concepts and actively solve problems. I have attempted to use the skill(s) on my own before leaving class each day. I have assessed my understanding of concepts by attempting all practice questions and checking my work. I have asked for help and clarification from my peers and/or teacher if having difficulty with a concept. I have pursued extra help to answer any assigned questions that I could not complete on my own. I have completed all assigned practice and homework before quizzes. I have completed review practice and studied my notes in preparation for tests. I have completed my unit assignment to the best of my ability and submitted it on time. You are expected to complete a minimum of 30 minutes of daily homework in this course.
Achievement Please refer to the Achievement Chart for Mathematics (see below). Communication in this course will be assessed on tests and assignments, using the evaluation guidelines listed in the achievement chart for communication.
Course Syllabus and Skills Checklist UNIT 1 Polynomials Lesson 1 Simplifying Polynomials I can simplify expressions by collecting like terms I can multiply and divide monomials Lesson 2 Expanding Polynomials I can expand polynomials by monomials I can expand binomials using the distribution law and FOIL Lesson 3 Factoring Polynomials I can common factor polynomial expressions I can factor trinomials when a = 1 I can factor trinomials (by grouping) when a 1 I can factor special products Lesson 4 Solving Equations I can solve one- and two-step linear equations. I can solve multi-step equations. I can solve equations involving fractions. Unit 1 Assignment Due Date: Unit 1 Test Date: UNIT 2 Introduction to Functions Lesson 5 Representing and Understanding Functions I can represent relations using equations, words, mapping diagrams, graphs and tables of values I can determine if a relation is a function from its equation, graph, tables of values or mapping diagram I can represent relations that are functions using function notation I can evaluate functions in equation and graphical forms using function notation I can find the domain and range of a function from its equation, graph or tables of values and represent it using proper set notation Lesson 6 Types of Parent Functions I can identify and graph the seven types of parent functions from their graph and equation: linear, quadratic, square root, absolute, rational, exponential, and sinusoidal. I can identify and describe the graphical properties and characteristics of the seven basic parent functions listed above and plot the key points for each Lesson 7 The Inverse of a Function I can determine the inverse of a function for a given parent function I can determine if the inverse of a function is a function or not Lesson 8 Transformations of Functions I can identify how transformations to functions change the shape and location of the graphs of parent functions (stretches, compressions, reflections, translations) I can identify and describe transformations to all of the parent functions using the factors a, k, d and c in y = af[k(x - d)]+c I can sketch graphs of all parent functions using transformations I can map points for a transformed function Lesson 9 Problem Solving with Transformations of Functions I can plot a scatter plot of data, identify the relationship and representative function I can determine the equation of the line/curve of best fit using transformations I can connect a parent function to a scenario/relationship it represents in real-life. Unit 2 Assignment Due Date: Unit 2 Test Date: UNIT 3 The Quadratic Function
Lesson 10 Radicals I can represent radicals as mixed or entire radicals I can add, subtract, multiply and divide radicals I can simplify expressions involving mixed and entire radicals Lesson 11 Solving Quadratic Equations (Finding the Roots) I can use factoring strategies to solve quadratic functions (find the x-intercepts or zeroes) I can use the quadratic formula to solve quadratic functions Lesson 12 Finding the Vertex I can change a quadratic function from standard form to vertex form by completing the square I can identify the vertex of a quadratic function from its equation I can use the vertex form of a quadratic function to solve maximum and minimum problems Lesson 13 Problem Solving and Quadratic Models I can solve problems involving quadratic relationships, such as the motion of a ball, by identifying the vertex and the roots and explaining what they represent in the real-world situation I can create a quadratic model to represent a real situation by identifying key features and using transformations to determine the equation Unit 3 Assignment Due Date: Unit 3 Test Date: UNIT 4 The Rational Function Lesson 14 Operations with Fractions I can simplify fractions to lowest terms. I can add and subtract fractions with unlike denominators. I can multiply and divide fractions. Lesson 15 Simplifying Rational Expressions and Restrictions I can add and subtract rational numbers I can multiply and divide rational numbers I can simplify fractions and write them in lowest terms I can simplify rational expressions using factoring strategies I can identify the restrictions for a rational expression Lesson 16 Multiplying and Dividing Rational Expressions I can simplify rational expressions using factoring strategies I can use the rules for multiplying and dividing fractions and apply them to rational expressions Lesson 17 Adding and Subtracting Rational Expressions I can simplify rational expressions using factoring strategies I can use the rules for adding and subtracting fractions and apply them to rational expressions Lesson 18 Applications of Rational Functions I can use and manipulate a rational function to solve a problem or represent a realworld scenario Unit 4 Assignment Due Date: Unit 4 Test Date: ***MIDTERM*** UNIT 5 The Exponential Function Lesson 19 Exponent Laws I understand the definition and properties of exponents I can use the exponent laws for multiplication, division, and a power of a power to simplify algebraic expressions
I can evaluate and/or simplify algebraic expressions involving zero and negative exponents Lesson 20 Rational Exponents I understand the definition of a rational exponent and how it relates to the root of a number I can evaluate and/or simplify algebraic expressions involving rational exponents I can use all of the exponent rules together to simplify algebraic expressions involving powers and radicals Lesson 21 Exponential Growth and Decay Models I can identify an exponential function from its equation or graph I can identify and determine the key features of an exponential function from its equation or graph (starting value, growth or decay rate, number of intervals) Lesson 22 Problem Solving with Exponential Functions I can solve problems involving exponential relationships, such as the depreciation of a car, by relating the function for growth or decay to a realworld situation. Unit 5 Assignment Due Date: Unit 5 Test Date: UNIT 6 Financial Applications Lesson 23 Simple and Compound Interest I can evaluate simple and compound interest and apply these calculations to banking applications, investments and loans Lesson 24 Components of a Budget I understand how to create a budget (fixed expenses, variable expenses, income, taxes etc.) I can create a detailed budget for a variety of different living situations Lesson 25 Annuities Investments and Loans I understand the definition of an annuity I can use financial calculators (TVM Solver or Computer Applications) to determine monthly payments, terms, interest, present and future value I understand how loans, mortgages and credit cards work I understand how to optimize the repayment of loans I understand how investments work and how to maximize dividends Unit 6 Assignment Due Date: Unit 6 Test Date: UNIT 7 Trigonometry Lesson 26 Solving Triangles I can solve for missing sides and angles in right triangles using Pythagorean Theorem and the primary trigonometric ratios sine, cosine and tangent I can identify and use the reciprocal trigonometric ratios cosecant, secant and cotangent I can solve for missing sides and angles in acute and obtuse triangles using the sine law and/or the cosine law Lesson 27 Solving Triangles in Three Dimensions I can solve real-life problems using all concepts from Lesson 26 I can solve three-dimensional problems using the principles of geometry and trigonometry Lesson 28 Angles in Standard Position I can find the exact values of sine, cosine and tangent using special triangles I can identify and represent angles in standard position on the cartesian plane Lesson 29 Evaluating Angles in the Cartesian Plane I can use the cartesian plane and angles in standard position to evaluate the primary trignometric ratios for angles between 0 and 360 I can represent a point in the cartesian plane using an angle in standard position
I can use the CAST rule to predict the sign of a primary trigonometric ratio for a given angle Lesson 30 Trigonometric Identities I can prove trigonometric identities Unit 7 Assignment Due Date: Unit 7 Test Date: UNIT 8 Sinusoidal Functions Lesson 31 Periodic Functions and The Properties of Sine and Cosine Function I can identify and represent a relationship that is repetitive I can identify the key features of a periodic function (amplitude, period, equation of axis) I can identify, plot and characterize the key points/features of sine and cosine function (amplitude, equation of axis, period) I can connect the key features of a sinusoidal function to what they represent in a real-world scenario (ie. Ferris Wheel example) Lesson 32 Transformations of Sine and Cosine Function I can identify the key features of a periodic function (amplitude, period, equation of axis) and relate them to the transformation factors a, k, d and c I can sketch graphs of sine and cosine using the transformation rules I can represent sine and cosine functions directly from an equation and determine the equation from a graph, using transformations Lesson 33 Creating Sinusoidal Models and Problem Solving I can determine the equation of a sinusoidal function from its description, graph or table of values and use it to solve problems I can solve real-world problems using sinusoidal functions I can create sinusoidal models to represent real-world situations Unit 8 Assignment Due Date: Unit 8 Test Date: Please be mindful of the learning skills as you take part in lessons each day. The set of skills outlined below are skills that you need to develop and carry with you beyond the walls of a classroom. In this math class we will be focused on improving our ability to collaborate and self-regulate as these are key skills that will determine your success in your post-secondary endeavours. Learning Skills Responsiblity Organization Independent Work Demonstrates: Demonstrates: Demonstrates: Collaboration Initiative Self-Regulation Demonstrates: Demonstrates: Demonstrates: Active listening Meets all deadlines Accountable for their decisions and actions Uses their planner/agenda Uses class time efficiently Identifies, collects and evaluates information effectively Uses class time appropriately Follows instructions Stays on task Does not disrupt the learning of others Shares work equally Supports peers Shares ideas Resolves conflicts Takes on different roles Open to new ideas Innovation Risk-taking Curiosity Positive Attitude Advocates Sets goals Monitors progress Asks for help when needed Self-assesses strengths and weaknesses