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Functions and Applications, Mixed (MCF3M) UNIT 1: Introduction to Quadratic Functions UNIT 2: The Algebra of Quadratic Expressions UNIT 3: Working with Quadratic Functions: Standard and Factored Forms UNIT 4: Working with Quadratic Models: Standard and Vertex Forms UNIT 5: Trigonometry and Acute Triangles UNIT 6: Sinusoidal Functions UNIT 7: Exponential Functions UNIT 8: Solving Financial Problems Involving Exponential Functions UNIT 1: Introduction to Quadratic Functions 1.1 Characteristics of Functions Pages 6 # Defining which relation are Functions Website Video Clips with Solutions: Mapping a diagram Recognizing Functions by Vertical Line Test 1.2 Comparing Rates of Change in Pages 17 # Linear and Quadratics Website Video Clips with Solutions: 1.3 Function Notation Pages 27 # Introduction to Function Notations Website Video Clips with Solutions: Evaluating Functions Evaluating Functions Example 1 Evaluating Functions Example 2 Function Notation Go to topic “Algebra” and click on “Functions” then click on “Function Notation” Khan Academy Exercises: Functions Practice 1 Functions Practice 2 1.4 Transformations of Quadratic Pages 38 # Functions Vertical Stretch Example Website Video Clips with Solutions: Reflections of a Vertical stretch Horizontal translation example Vertical Translation example 1.5 Graphing Quadratic Functions using Pages 41 # Transformations Types of Sketches and Transformations Website Video Clips with Solutions: Click on “Quadratic Functions” – Sketches and Transformations: M: 43 to 48 (Vertical stretch, Compression, vertical translation, horizontal translation, combining translations) Transformation of Quadratics in vertex form Additional Support tools: This site allows you to explore the effects of stretches and translations on quadratic functions by using a graph creator. This site also allows you to create your own graphs by using the tools under the activity tools section. Graphing Calculator Emulator Download free graphing Calculator software 1.6 Multiple Transformations to graph Pages 51 # Quadratic Functions Website Video Clips with Solutions: Graphing Quadratics example Vertical and horizontal shifts of quadratic graphs 1.7 Domain and Range of a Pages 59 # Quadratic Function Domain and Range Example Website Video Clips with Solutions: Domain and Range Example 2 Restricting Domain and Range application problem example Explaining the domain of a function Domain and Range Go to topic “Algebra” and click on “Functions” then click on “Domain and Range” Khan Academy Exercises: Domain of a Function Range of a Function Review Pages 66 # UNIT 2: The Algebra of Quadratic Expressions 2.1 Quadratic Expressions Pages 78 # Expanding Binomials using the FOIL method Website Video Clips with Solutions: Watch Concept Video and practice problems 1-4 Expanding binomials using algebra area tiles Expanding and simplifying binomials/polynomial examples Click on topic “Algebra” then click on “polynomials” and watch “multiplication of polynomials” Adding and Subtracting Rational Expressions examples Watch concept video and practice problems 1-4 Khan Academy Exercises: 2.2 Factoring Polynomials: Pages 88 # Common Factoring Review of Factoring by Grouping Website Video Clips with Solutions: Polynomial Factoring Examples Go to topic “Algebra” and click on “Factoring” then click on “Grouping” Additional Support tools: Practice problems Guided Instruction and Practice problems for factoring polynomials 2.3 Factoring Quadratic Pages 95 # Expressions: x2 + bx + c Quadratic Functions Website Video Clips with Solutions: Click on Quadratic Functions: Factoring: #13-17 (Common Factoring, Trinomials) Factoring Trinomials with a=1 example Click on topic “Algebra” then click on “factoring” and watch “Trinomials with a=1 examples” Factoring Quadratic example 2 Factoring Quadratic example 3 Review Quadratic Expressions Additional Support: Watch videos #1 to #12 to review these skills Review Quadratic Relations Watch videos #1 to #5 to review these skills Khan Academy Exercises: Find the Greatest Common divisor 2.4 Factoring Quadratic Pages 104 # expressions: ax2 + bx + c Factoring Trinomials with a>1 Click on topic “Algebra” then click on “factoring” and watch “Trinomials” Website Video Clips with Solutions: Solving Quadratics by Factoring Factoring Trinomials with a>1 example 2 Watch Concept Video and practice problems 1-4 Solving Quadratics By Factoring Finding the greatest common divisor (GCD) is necessary when factoring quadratics. Practice this Khan Academy Exercises: skill on Khan Academy. 2.5 Factoring Quadratic Pages 111 # Expressions: Special Cases Factoring Special Cases: Perfect Squares Website Video Clips with Solutions: Watch Concept Video and practice problems 1-4 Factoring Special Cases: By Grouping Watch Concept Video and practice problems 1-4 Factoring Special Cases: By difference of cubes and sums Watch Concept Video and practice problems 1-4 Review Pages 118 # Different Ways to Factor Review Video Website Video Clips with Solutions: Watch Concept Video and practice problems 1-5 UNIT 3: Working with Quadratic Functions: Standard and Factored Forms 3.1 Situations involving Quadratic Pages 130 # Functions Practice Shifting and Reflecting Functions Khan Academy Exercises: Transformation of Quadratics in vertex form This site allows you to explore the effects of stretches and translations on quadratic Additional Support tools: functions by using a graph creator. This site also allows you to create your own graphs by using the tools under the activity tools section. Graphing Calculator Emulator Download free graphing Calculator software 3.2 Standard and Factored Forms Pages 132 # Vertex to standard form Website Video Clips with Solutions: Click on “Quadratic Functions” – Quadratic Relations: J: 34 (Vertex to standard form) Analyzing Vertex and Standard form Click on “Quadratic Functions” – Completing the Square: N: 49 – Analyzing vertex/standard form 3.3 Solving Quadratic equations by Pages 143 # graphing Dilation of Quadratic Graphs Website Video Clips with Solutions: Quadratic Relations Graphs Click on “Quadratic Relations” and watch examples 1 to 5: (Graphing Quadratic Functions, Features of Parabolas, Interpreting parabolas 1, Interpreting parabolas 2, Interpreting parabolas 3) Quadratic Functions Click on “Quadratic Functions” - Solving by Factoring: #26-33 (Number and Type of roots, Min/Max value, Sketching Quadratic relations) 3.4 Solving Quadratic Equations by Pages 156 # Factoring Factoring complicated expressions Website Video Clips with Solutions: Watch the concept video only Different Ways to Factor Review Video Watch Concept Video and practice problems 1-5 3.5 & 3.6 Solving Problems Involving Pages 164 & 170 # Quadratic Functions and Models Factoring complicated expressions Website Video Clips with Solutions: Watch the concept video only Different Ways to Factor Review Video Watch Concept Video and practice problems 1-5 Review Pages 181 # UNIT 4: Working with Quadratic Models: Standard and Vertex Forms 4.1 Vertex form of Quadratic Functions Pages 196 # Vertex to standard form Website Video Clips with Solutions: Click on “Quadratic Functions” – Quadratic Relations: J: 34 (Vertex to standard form) Analyzing Vertex and Standard form Click on “Quadratic Functions” – Completing the Square: N: 49 – Analyzing vertex/standard form Vertex to Standard Form example Vertex to standard form example 2 4.2 Completing the Square Pages 206 # Completing the Square Examples Website Video Clips with Solutions: Click on “Quadratic Functions”- watch Quadratics: M: 50 – 53: Completing the Square Explanation Completing the square example Select topic “Algebra” then click on “quadratics” and then on “completing the square” Completing the Square example 2 Watch Concept Video and practice problems 1-4 4.3 Quadratic Formula Pages 216 # The quadratic Formula explanation Website Video Clips with Solutions: Watch Concept Video and practice problems 1-3 The Quadratic Formula explanation #2 Select topic “Algebra” then click on “quadratic equations” and then on “quadratic formula” Khan Academy Exercises: Quadratic Formula Practice Problems 4.4 Investigating the nature of Roots Pages 227 # Discriminant of Quadratic Equations Explanation Website Video Clips with Solutions: Solving using the discriminant Solving using the discriminant 2 Solving using the discriminant 3 Finding the Vertex, finding axis symmetry example Finding the intercepts, vertex, axis of symmetry, 4.5 & 4.6 Application problems involving Quadratics and Quadratic Models Pages 234 & 242 # Website Video Clips with Solutions: Application of Quadratic Examples Watch Concept Video and practice problems 1-2 Review Pages 253 # UNIT 5: Trigonometry and Acute Triangles 5.1 Primary Trigonometric Ratios Pages 264 # Trigonometric Ratios example Website Video Clips with Solutions: Finding the length of the side of a triangle example Finding an angle given Two angles Solving a right angle triangle Trigonometric Ratio of Sine Example Watch concept video and problems 1-2 Trigonometric Ratio of Cosine Watch concept video and problems 1-2 Trigonometric Ratio of Tangent Watch concept video and problems 1-2 5.2 Solving Right Angle Triangle Pages 274 # Problems Application Problem for Triangles example 1 Website Video Clips with Solutions: Application Problem example 2 Application Problem example 3 Application problem #4 Application Problem #5 Area of a Triangle Explanation and Formula 5.3 Sine Law and Acute triangles Pages 283 # Sine Law examples Website Video Clips with Solutions: Click on topic “Trig Functions” – Sine Law B: 4 to 7 – watch and work through the examples Sine Law example 2 Click on topic “Trigonometry” then click on “Triangles” - Law of Sines examples #1-2 The Law of Sines Examples 3 Watch concept video and problems 1-2 5.4 Cosine Law and acute triangles Pages 294 # Cosine Law Examples Website Video Clips with Solutions: Click on topic “Trig Functions” – Cosine Law C: 8 to 10 – watch and work through the examples Cosine Law example 2 Click on topic “Trigonometry” then click on “Triangles” - Law of Cosine example #1 The Law of Cosines Example 3 Watch concept video and problems 1-2 5.5 Acute Triangle Application Problems Pages 302 # Application Problem: Finding an angle of an Airplane Website Video Clips with Solutions: Application Problem: finding the length of a Fence Application Problem: Finding the height Application Problem: Finding the distance between cities Review Pages 313 # UNIT 6: Sinusoidal Functions 6.1 Periodic Motion Pages 324 # Properties of Periodic Functions Website Video Clips with Solutions: 6.2 Periodic Behaviour Pages 326 # Properties of Periodic Functions Website Video Clips with Solutions: 6.3 Sine Functions Pages 335 # Sine Function Graphs Website Video Clips with Solutions: Application of Sine Problem 6.4 Comparing Sinusoidal Pages 344 # Functions Basic Sine and Cosine Graphs Website Video Clips with Solutions: Go to topic “Trigonometry” and click on “Graphing and Inverse functions” then click on “amplitude and period” and “phase shift” (Only watch Sine Examples) Sine Graphs Watch the concept video and the problems #1 (skip 2 and 3) 6.5 Transformations of Sine Pages 359 # Functions Transformations of Sinusoidal Graphs Website Video Clips with Solutions: Click on topic “Trig Functions” – E: Graphing 15 to 20 – watch and work through the examples of transformations Transformations of Sine Graphs Watch the concept video and the problems #1 (skip 2 and 3) 6.6 More Transformations of Sine Pages 368 # More Transformation of Sine Graphs Website Video Clips with Solutions: Watch the concept video and the problems #1 (skip 2 and 3) Finding an Equation from the Graph Example Watch the concept video and the problems #1 (skip 2 and 3) Review Pages 377 # UNIT 7: Exponential Functions 7.1 Exponential Data (exploration) Pages 392 # Website Video Clips with Solutions: 7.2 Laws of Exponents Pages 395 # Introduction to Exponents Explanation Website Video Clips with Solutions: Watch the concept video and the problems #1-2 Multiplying Exponents Dividing Exponents Simplifying Exponents Multiplication and Division Properties of exponents Watch the concept video and the problems #1-3 7.3 Working with Integer Exponents Pages 402 # Exponent Properties Website Video Clips with Solutions: Go to topic “Algebra” and click on “Exponents” then click on the videos Integer Exponent Explaining Negative Exponents Exponent Rules Exponent Practice 1 Khan Academy Exercises: Exponent Practice 2 Exponent Rules Exponent Practice 3 7.4 Working with Rational Pages 410 # Exponents Rational Exponent Examples Website Video Clips with Solutions: Click on “Exponential Functions” then Basics: Watch #8-11 Khan Academy Exercises: Exponent Practice 3 7.5 Exploring the Properties of Pages 420 # Exponential Functions Graphing exponential Functions example Website Video Clips with Solutions: Graphing Exponential Functions Graphing Exponential functions using technology 7.6 Solving Problems Involving Pages 425 # Exponential Growth Exponential Application Example 1 Website Video Clips with Solutions: Exponential Application Example 2 Exponential Application Example Growth and Decay 7.7 Exponential Decay Pages 433 # Exponential Application Example 1 Website Video Clips with Solutions: Exponential Application Example 2 Exponential Application Example Growth and Decay Review Pages 442 # UNIT 8: Solving Financial Problems Involving Exponential Functions 8.1 Interest and Rates of Change Pages 454 # Introduction to simple interests Website Video Clips with Solutions: Calculating simple interest example 1 Calculating simple interest example 2 Calculating simple interest example 3 Calculating simple interest example 4 Calculating simple interest example 5 Compound interest example 8.2 Compound Interest: Future Pages 462 # Compound Interest example 1 Website Video Clips with Solutions: Only look at Problem #1 Compound Interest future value example Graphing compound interest 8.3 Compound Interest: Present Pages 471 # Compound interest example Website Video Clips with Solutions: Compound interest example annually Calculating money earned example 8.4 Compound Interest Problems Pages 479 # Compound interest example semi-annually Website Video Clips with Solutions: Compound interest example monthly Compound interest example quarterly 8.5 Annuities: Future Pages 493 # Website with online annuity calculator Website Video Clips with Solutions: Use this website as a tool to check your answers Annuity future value example 8.6 Annuities: Present Pages 501 # Simple Annuities Website Video Clips with Solutions: Website with online annuity calculator Use this website as a tool to check your answers 8.7 Saving Plans and Loans Pages 509 # Using a TVM solver video Website Video Clips with Solutions: Interest earned on an account example Determining service charges example Compound interest example semi-annually Compound interest example monthly Compound interest example quarterly Review Pages 442 #