 ## Foundations for College Mathematics Strands and Subgroups in the Grade 11 Course

• A. EXPONENTIAL AND LOGARITHMIC FUNCTIONS
- Evaluating Logarithmic Expressions
- Connecting Graphs and Equations of Logarithmic Functions
- Solving Exponential and Logarithmic Equations
• B. TRIGONOMETRIC FUNCTIONS
- Understanding and Applying Radian Measure
- Connecting Graphs and Equations of Trigonometric Functions
- Solving Trigonometric Equations
• C. POLYNOMIAL AND RATIONAL FUNCTIONS
- Connecting Graphs and Equations of Polynomial Functions
- Connecting Graphs and Equations of Rational Functions
- Solving Polynomial and Rational Equations
- Solving Inequalities
• D. CHARACTERISTICS OF FUNCTIONS
- Understanding Rates of Change
- Combining Functions
- Using Function Models to Solve Problems

### Chapter 1: Polynomial Functions

1.1: Power Functions
1.2: Characteristics of Polynomial Functions
1.3: Equations and Graphs of Polynomial Functions
1.4: Transformations
1.5: Slopes of Secants and Average Rate of Change
1.6: Slopes of Tangents and Instantaneous Rate of Change

### CHAPTER 2: Polynomial Equations and Inequalities

2.1: The Remainder Theorem
2.2: The Factor Theorem
2.3: Polynomial Equations
2.4: Families of Polynomial Functions
2.5: Solve Inequalities Using Technology
2.6: Solve Factorable Polynomial Inequalities Algebraically

### CHAPTER 3: Rational Functions

3.1: Reciprocal of a Linear Function
Extension: Asymptotes and the TI-83 Plus
or TI-84 Plus Graphing Calculator
3.2: Reciprocal of a Quadratic Function
3.3: Rational Functions
3.4: Solve Rational Equations and Inequalities
3.5: Making Connections With Rational Functions and Equations

### CHAPTER 4: Trigonometry

4.2: Trigonometric Ratios and Special Angles
4.3: Equivalent Trigonometric Expressions
4.4: Compound Angle Formulas
4.5: Prove Trigonometric Identities

### CHAPTER 5: Trigonometric Functions

5.1: Graphs of Sine, Cosine, and Tangent Functions
5.2: Graphs of Reciprocal Trigonometric Functions
5.3: Sinusoidal Functions of the Form
f(x) = a sin [k(x - d)] + c and
f(x) = a cos [k(x - d)] + c 270
Extension: Use a Graphing Calculator to Fit a Sinusoidal Regression to Given Data
5.4: Solve Trigonometric Equations
5.5: Making Connections and Instantaneous Rate of Change

### CHAPTER 6: Exponential and Logarithmic Functions

6.1: The Exponential Function and Its Inverse
6.2: Logarithms
6.3: Transformations of Logarithmic Functions
6.4: Power Law of Logarithms
6.5: Making Connections: Logarithmic Scales in the Physical Sciences

### CHAPTER 7: Tools and Strategies for Solving Exponential and Logarithmic Equations

7.1: Equivalent Forms of Exponential Equations
7.2: Techniques for Solving Exponential Equations
7.3: Product and Quotient Laws of Logarithms
7.4: Techniques for Solving Logarithmic Equations
7.5: Making Connections: Mathematical Modelling With Exponential and Logarithmic Equations

### CHAPTER 8: Combining Functions

8.1: Sums and Differences of Functions
8.2: Products and Quotients of Functions
8.3: Composite Functions
8.4: Inequalities of Combined Functions
8.5: Making Connections: Modelling With Combined Functions

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### Chapter 1: Characteristics and Properties

1.1: Functions
1.2: Exploring Absolute Value
1.3: Properties of Graphs of Functions
1.4: Sketching Graphs of Functions
1.5: Inverse Relations
1.6: Piecewise Functions
1.7: Exploring Operations with Functions

### CHAPTER 2: Functions: Understanding Rates of Change

2.1: Determining Average Rate of Change
2.2: Estimating Instantaneous Rates of Change form Tables of Values and Equations
2.3: Exploring Instantaneous Rates of Change Using Graph
2.4: Using Rates of Change to Create a Graphical Model
2.5: Solving Problems Involving Rates of Change

### CHAPTER 3: Polynomial Functions

3.1: Exploring Polynomial Functions
3.2: Characteristics of Polynomial Functions
3.3: Characteristics of Polynomial Functions in Factored Form
3.4: Transformations of Cubic and Quartic Functions
3.5: Dividing Polynomials
3.6: Factoring Polynomials
3.7: Factoring a Sum or Difference of Cubes

### CHAPTER 4: Polynomial Equations and Inequalities

4.1: Solving Polynomial Equations
4.2: Solving Linear Inequalities
4.3: Solving Polynomial Inequalities
4.4: Rates of Change in Polynomial Functions

### CHAPTER 5: Rational Functions, Equations, and Inequalities

5.1: Graphs of Reciprocal Functions
5.2: Exploring Quotients of Polynomial Functions
5.3: Graphs of Rational Functions of the Form Form f (x) = ax + b / cx + d

### CHAPTER 6: Trigonometric Functions

6.2: Radian Measure and Angles on the Cartesian Plane
6.3: Exploring Graphs of the Primary Trigonometric Functions
6.4: Transformation of Trigonometric Functions
6.5: Exploring Graphs of the Reciprocal Trigonometric Functions
6.6: Modelling with Trigonometric Functions
6.7: Rates of Change in Trigonometric Functions

### CHAPTER 7:Trigonometric Identities and Equations

7.1: Exploring Equivalent Trigonometric Functions
7.2: Compound Angle Formulas
7.3: Double Angle Formulas
7.4: Proving Trigonometric Identities
7.5: Solving Linear Trigonometric Equations

### CHAPTER 8: Exponential and Logarithmic Functions

8.1: Exploring the Logarithmic Functions
8.2: Transformations of Logarithmic Functions
8.3: Evaluating Logarithms
8.4: Laws of Logarithms
8.5: Solving Exponential Equations
8.6: Solving Logarithmic Equations
8.7: Solving Problems with Exponential and Logarithmic Functions
8.8: Rates of Change in Exponential and Logarithmic Functions

### CHAPTER 9: Combinations of Functions

9.1: Exploring Combinations of Functions
9.2: Combining Two Functions: Sums and Differences
9.3: Combining Two Functions: Products
9.4: Exploring Quotients of Functions
9.5: Composition of Functions
9.6: Techniques for Solving Equations and Inequalities
9.7: Modelling with Functions # Strictly Ontario Curriculum

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