 ## Functions and Applications Strands and Subgroups in the Grade 11 Course

• A. QUADRATIC FUNCTIONS
- Solving Quadratic Equations
- Connecting Graphs and Equations of Quadratic Functions
- Solving Problems Involving Quadratic Functions
• B. EXPONENTIAL FUNCTIONS
- Connecting Graphs and Equations of Exponential Functions
- Solving Problems Involving Exponential Functions
- Solving Financial Problems Involving Exponential Functions
• C. TRIGONOMETRIC FUNCTIONS
- Applying the Sine Law and the Cosine Law in Acute Triangles
- Investigating Arithmetic and Geometric Sequences and Series
- Solving Problems Involving Sine Functions

## Table of Contents by Nelson

### Chapter 1: Introduction to Functions

1.1: Relations and Functions
Curious Math
1.2: Function Notation
1.3: Exploring Properties of Parent Functions
1.4: Determining the Domain and Range of a Function
1.5: The Inverse Function and Its Properties
1.6: Exploring Transformations of Parent Functions
1.7: Investigating Horizontal Stretches, Compressions, and Reflections
1.8: Using Transformations to Graph Functions of the Form y = af [k(x - d )] + c

### CHAPTER 2: Equivalent Algebraic Expressions

2.1: Adding and Subtracting Polynomials
2.2: Multiplying Polynomials
Curious Math
2.3: Factoring Polynomials
2.4: Simplifying Rational Functions
2.5: Exploring Graphs of Rational Functions
2.6: Multiplying and Dividing Rational Expressions

### CHAPTER 3: Quadratic Functions

3.1: Properties of Quadratic Functions
3.2: Determining Maximum and Minimum Values of a Quadratic Function
3.3: The Inverse of a Quadratic Function
3.4: Operations with Radicals
Curious Math 3.5: Quadratic Function Models: Solving Quadratic Equations
3.6: The Zeros of a Quadratic Function
3.7: Families of Quadratic Functions
3.8: Linear–Quadratic Systems

### CHAPTER 4: Exponential Functions

4.1: Exploring Growth and Decay
4.2: Working with Integer Exponents
4.3: Working with Rational Exponents
4.4: Simplifying Algebraic Expressions Involving Exponents
4.5: Exploring the Properties of Exponential Functions
4.6: Transformations of Exponential Functions
4.7: Applications Involving Exponential Functions

### CHAPTER 5: Trigonometric Ratios

5.1: Trigonometric Ratios of Acute Angles
5.2: Evaluating Trigonometric Ratios for Special Angles
Curious Math
5.3: Exploring Trigonometric Ratios for Angles Greater than 90°
5.4: Evaluating Trigonometric Ratios for Any Angle Between 0° and 360°
5.5: Trigonometric Identities
5.6: The Sine Law
5.7: The Cosine Law
5.8: Solving Three-Dimensional Problems by Using Trigonometry

### CHAPTER 6: Sinusoidal Functions

6.1: Periodic Functions and Their Properties
6.2: Investigating the Properties of Sinusoidal Functions
6.3: Interpreting Sinusoidal Functions
6.4: Exploring Transformations of Sinusoidal Functions
6.5: Using Transformations to Sketch the Graphs of Sinusoidal Functions
6.6: Investigating Models of Sinusoidal Functions
6.7: Solving Problems Using Sinusoidal Models

### CHAPTER 7: Discrete Functions: Sequences and Series

7.1: Arithmetic Sequences
7.2: Geometric Sequences
7.3: Creating Rules to Define Sequences
7.4: Exploring Recursive Sequences
Curious Math
7.5: Arithmetic Series
7.6: Geometric Series
7.7: Pascal's Triangle and Binomial Expansions

### CHAPTER 8: Discrete Functions: Financial Applications

8.1: Simple Interest
8.2: Compound Interest: Future Value
8.3: Compound Interest: Present Value
Curious Math
8.4: Annuities: Future Value
8.5: Annuities: Present Value
8.6: Using Technology to Investigate Financial Problems

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## Table of Contents by McGraw Hill

### Chapter 1: Review & Quadratic Functions

1.1: Define function and identify a function from a relation that is not a function
1.2: valuate linear and quadratic functions
1.3: Define and identify restrictions domain and range by investigating numerical, graphical and algebraic representations
1.4: Investigate quadratic functions in vertex form, describe the roles of variables in the transformation of f(x) = x² and the corresponding sketch.
1.5: Collect data that represents a quadratic relation and determine the equations of curves of best fit where applicable

### CHAPTER 2: Factor Quadratic Expressions

2.1 - Quadratic Factoring
2.2 & 2.3_Common_Factoring
2.4 Factoring when a is not 1
2.5 Factoring Special Quadratics
2.6 Factoring - Mixing It All Up

### CHAPTER 3: Represent Quadratic Function in Factored and Standard Forms

3.1: Standard and Factored forms
3.2: Solving Quadratic Eqns by Graphing
3.3: Solving_Quadratics_by_factoring
3.4: Solving_Quadratic_Problems
3.5: Creating_a_Quad_Model_from_Data
3.6: Vertex Form

### CHAPTER 4: Vertex to Standard

4.1: Vertex to Standard
4.2: Completing the square
4.3: Quadratic Formula
4.4: Nature_of_the_roots_and_Descriminant
4.5: Applications_of_Functions

### CHAPTER 5: Trigonometry

5.1: Primary trig ratios
5.2: Right Triangle Word Problems
5.3: The Sine Law
5.4: The Cosine Law
5.5: Word Problems

### CHAPTER 6: Exponential Functions

6.1: Sequences
6.2: Arithmetic Sequences
6.3: Geometric Sequences
6.4: Recursion Formulas
6.5: Arithmetic Series
6.6: Geometric Series

### CHAPTER 7: Compound Interest and Annuities

7.1: Investigation: Simple Interest, Arithmetic Sequences, and Linear Growth
7.2: Compound Interest
7.3: Investigation: Compound Interest, Geometric Sequences, and Exponential Growth
7.4: Present Value
7.5: Amount of an Ordinary Annuity
7.6: Present Value of an Ordinary Annuity
7.7: Technology: Amortization Tables and Spreadsheets
7.8: Mortgages

### CHAPTER 8: Loci and Conics

8.1: Technology: Constructing Loci Using The Geometer’s Sketchpad®
8.2: Equations of Loci
8.3: Technology: Loci and Conics
8.4: The Circle
8.5: The Ellipse
8.6: The Hyperbola
8.7: The Parabola
8.8: Conic Sections With Equations in the Form ax2 + by2 + 2gx + 2fy + c = 0
8.9: Intersections of Lines and Conics # Strictly Ontario Curriculum

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