# Grade 11 MCF3M Functions and Applications by I14TpTUD

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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 #

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

1.6 Multiple Transformations to graph                                           Pages 51 #

Website Video Clips with Solutions:                               Graphing Quadratics example
Vertical and horizontal shifts of quadratic graphs

1.7 Domain and Range of a                                                Pages 59 #
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

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”

Guided Instruction and Practice problems for factoring polynomials
2.3 Factoring Quadratic                                                     Pages 95 #
Expressions: x2 + bx + c
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”

Additional Support:                                     Watch videos #1 to #12 to review these skills
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
Finding the greatest common divisor (GCD) is necessary when factoring quadratics. Practice this

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

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

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
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)
Click on “Quadratic Functions” - Solving by Factoring: #26-33 (Number and Type of roots,

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 #
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 #

Website Video Clips with Solutions:                            Watch Concept Video and practice problems 1-3
Select topic “Algebra” then click on “quadratic equations” and then on “quadratic formula”

4.4 Investigating the nature of Roots                                            Pages 227 #

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

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

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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