Grade 11 MCF3M Functions and Applications by I14TpTUD

VIEWS: 175 PAGES: 14

									                              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 #

								
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