Algebra and Trigonometry

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P: Prerequisites: Fundamental Concepts of Algebra I

P.1: Algebraic Expressions, Mathematical Models, and Real Numbers

 Addition of Polynomials - Activity A

P.2: Exponents and Scientific Notation

 Dividing Exponential Expressions
 Exponents and Power Rules
 Multiplying Exponential Expressions

P.3: Radicals and Rational Exponents

 Operations with Radical Expressions
 Simplifying Radicals - Activity A

P.5: Factoring Polynomials

 Factoring Special Products
 Modeling the Factorization of ax2+bx+c
 Modeling the Factorization of x2+bx+c

1: Equations and Inequalities

1.2: Linear Equations and Rational Equations

 Modeling One-Step Equations - Activity A
 Modeling and Solving Two-Step Equations
 Solving Two-Step Equations

1.3: Models and Applications

 Solving Formulas for any Variable

1.5: Quadratic Equations

 Roots of a Quadratic

1.6: Other Types of Equations

 Polynomials and Linear Factors

1.7: Linear inequalities and Absolute-Value Inequalities

 Compound Inequalities
 Inequalities Involving Absolute Values
 Solving Inequalities Using Multiplication and Division
 Solving Linear Inequalities using Addition and Subtraction

2: Functions and Graphs

2.1: Basics of Functions and Their Graphs

 Introduction to Functions
 Using Tables, Rules and Graphs

2.3: Linear Functions and Slope

 Distance-Time and Velocity-Time Graphs
 Linear Functions
 Slope - Activity A
 Slope-Intercept Form of a Line - Activity A

2.5: Transformations of Functions

 Translating and Scaling Functions

2.6: Combinations of Functions; Composite Functions

 Function Machines 2 (Functions, Tables, and Graphs)
 Function Machines 3 (Functions and Problem Solving)
 Reflections of a Linear Function

2.8: Distance and Midpoint Formulas; Circles

 Distance Formula - Activity A

3: Polynomial and Rational Functions

3.1: Quadratic Functions

 Quadratic Functions
 Quadratics in Factored Form
 Quadratics in Vertex Form - Activity A

3.2: Polynomial Functions and Their Graphs

 Addition and Subtraction of Polynomials
 Cubic Function Activity

3.3: Dividing Polynomials; Remainder and Factor Theorems

 Dividing Polynomials Using Synthetic Division

3.4: Zeros of Polynomial Functions

 Polynomials and Linear Factors

3.5: Rational Functions and Their Graphs

 General Form of a Rational Function
 Rational Functions

4: Exponential and Logarithmic Functions

4.1: Exponential Functions

 Exponential Functions - Activity A

4.2: Logarithmic Functions

 Logarithmic Functions - Activity A

4.5: Exponential Grwoth and Decay; Modeling Data

 Exponential Growth and Decay - Activity A

5: Trigonometric Functions

5.2: Right Triangle Trigonometry

 Sine and Cosine Ratios - Activity A
 Tangent Ratio

5.4: Trigonometric Functions of Real Numbers; periodic Functions

 Translating and Scaling Sine and Cosine Functions - Activity A

5.5: Graphs of Sine and Cosine Functions

 Cosine Function
 Sine Function

5.6: Graphs of Other Trigonometric Functions

 Tangent Function

5.8: Applications of Trigonometric Functions

 Sound Beats and Sine Waves

6: Analytic Trigonometry

6.1: Verifying Trigonometric Identities

 Simplifying Trigonometric Expressions

6.2: Sum and Difference Formulas

 Sum and Difference Identities for Sine and Cosine

7: Additional Topics in Trigonometry

7.3: Polar coordinates

 Points in Polar Coordinates

7.5: Complex Numbers in Polar Form; DeMoivre's Theorem

 Complex Numbers in Polar Form

7.6: Vectors

 Adding Vectors

7.7: The Dot Product


8: Systems of Equations and Inequalities

8.1: Systems of Linear Equations in Two Variables

 Modeling Linear Systems - Activity A
 Special Types of Solutions to Linear Systems
 Systems of Linear Equations - Activity A

8.4: Systems of Nonlinear Equations in Two Variables

 System of Two Quadratic Inequalities

8.5: Systems of inequalities

 Systems of Linear Inequalities (Slope-intercept form) - Activity A

8.6: Linear Programming

 Linear Programming - Activity A

10: Conic Sections and Analytic Geometry

10.1: The Ellipse

 Ellipse - Activity A

10.2: The Hyperbola

 Hyperbola - Activity A

10.3: The Parabola

 Parabolas - Activity A

11: Sequences, induction, and Probability

11.2: Arithmetic Sequences

 Arithmetic Sequences

11.3: Geometric Sequences and Series

 Geometric Sequences

11.5: The Binomial Theorem

 Binomial Probabilities

11.6: Counting Principles, Permutations, and Combinations

 Permutations and Combinations

11.7: Probability

 Compound Independent Events
 Probability Simulations

Content correlation last revised: 12/7/2011