Applied Algebra and Trigonometry

Module 1: Exponents and Radicals
- Getting ready for Exponents
- Introduction to Exponents and Scientific Notation
- Simplifying Expressions with Exponents
- Converting Between Decimal and Scientific Notation
- Multiplying and Dividing Numbers in Scientific Notation
- Problem Solving With Scientific Notation
- Problem Set: Exponents and Scientific Notation
- Square Roots
- Problem set: Square roots
- Summary: Exponents, Scientific Notation and Square Roots
Module 2: Linear and Quadratic Equations
- Why It Matters: Linear Equations
- Multi-Step Linear Equations
- Problem Set: Multi-Step Linear Equations
- Why It Matters: Quadratic Equations and Complex Numbers
- Introduction to Quadratic Equations
- Quadratic Equations and Factoring
- Quadratic Formula
- Introduction to Complex Numbers
- Complex Numbers
- Introduction to Quadratic Equations with Complex Solutions
- The Discriminant
- Quadratic Equations With Complex Solutions
- Putting It Together: Quadratic Equations and Complex Numbers
- Problem set: Quadratic Equations
Module 3: Rates, Ratios and Proportions
- Getting ready for Rates and Ratios
- Introduction to Rates, Ratios, and Proportions
- Writing Ratios as Fractions
- Writing Rates and Calculating Unit Rates
- Problem Set: Ratios and Rates
- Getting ready for Proportions
- Introduction to Proportions
- Writing Proportions
- Solving Proportions
Module 4: Variation
- Variation
- Problem Set: Modeling Using Variation
- Solutions: Modeling Using Variation
Module 5: Measurements
- Measurements
- Measurement Uncertainty, Accuracy, and Precision
- Introduction to Systems and Scales of Measurement
- Getting ready for Conversions of Measurements
- Making Unit Conversions in the U.S. System of Measurement
- Making Unit Conversions in the Metric System of Measurement
- Converting Between U.S. and Metric Systems of Measurement
- Mathematical Treatment of Measurement Results
- Problem Set: Measurements
- Solutions: Measurements
Module 6: Introduction to Functions
- Why It Matters: Function Basics
- Functions and Function Notation
- Evaluating functions
- Library of functions and their graphs
- Problem set: Functions and Function Notation
- Solutions: Functions and Function Notation
- Domain and Range of Functions
- Piecewise-defined functions
- One-to-one functions
- Inverse Functions
- Problem set: Domain and Range
- Solutions: Domain and Range
- Functions Practice Test
- Solutions: Functions Practice Test
Module 7: Linear and Quadratic Functions
- Getting ready for Linear Functions
- Linear Functions
- Problem Set: Linear Functions
- Solutions: Linear Functions
- Why It Matters: Modeling with Linear Functions
- Interpreting Slope in Equations and Graphs
- Interpreting the y-Intercept and Making Predictions
- Models and Applications
- Putting It Together: Modeling with Linear Functions
- Problem set: Modeling with Linear Functions
- Solutions: Modeling with Linear Functions
- Linear Functions Practice Test
- Solutions: Linear Functions Practice Test
- Why It Matters: Quadratic Functions
- Equations and Graphs of Quadratic Functions
- Applications of Quadratic Functions
- Putting It Together: Quadratic Functions
- Problem set: Quadratic Functions
- Solutions: Quadratic Functions
Module 8: Systems of Linear Equations
- Why It Matters: Linear Systems
- Introduction to Systems of Equations in Two Variables
- Ordered Pairs as Solutions to Systems
- Classify Solutions for Systems
- Graphing Systems of Equations
- Summary: Solutions to Systems of Equations
- Introduction to Algebraic Methods for Solving Systems
- The Substitution Method
- The Elimination Method Without Multiplication
- The Elimination Method With Multiplication
- Problem set: Systems of Linear Equations in Two Variables
- Solutions: Systems of Linear Equations in Two Variables
- Introduction to Systems of Equations in Three Variables
- Systems of Linear Equations: Three Variables
- Problem Set: Systems of Linear Equations in Three Variables
- Solutions: Systems of Linear Equations in Three Variables
- Why It Matters: Solving Systems with Matrices
- Matrices and Matrix Operations (optional)
- Introduction to Solving Systems with Cramer's Rule
- Using Cramer’s Rule to Solve a System of Two Equations in Two Variables
- Using Cramer’s Rule to Solve a System of Three Equations in Three Variables
- Problem Set: Solving Systems with Cramer's Rule
- Solutions: Solving Systems with Cramer's Rule
- Introduction to Problem Solving With Systems
- Cost and Revenue Problems
- Value Problems
- Mixture Problems
- Problem Set: Problem Solving with Systems
- Solutions: Problem Solving with Systems
Module 9: Introduction to Exponential and Logarithmic Functions
- Why It Matters: Exponential and Logarithmic Functions
- Introduction to Exponential Functions
- Exponential Functions
- Exponential functions with base e
- Graphs of exponential functions
- Problem set: Exponential Functions
- Solutions: Exponential Functions
- Introduction to Logarithmic Functions
- Logarithmic vs Exponential form of equation
- Evaluating logarithms
- Identify the domain of a logarithmic function
- Graph logarithmic functions
- Problem Set: Logarithmic Functions
- Solutions: Logarithmic Functions
Module 10: Applications of Exponential and Logarithmic Functions
- Introduction to Logarithmic Properties
- Use the product rule for logarithms
- Use the quotient and power rules for logarithms
- Expand logarithmic expressions
- Condense logarithmic expressions
- Problem Set: Logarithmic Properties
- Solutions: Logarithmic Properties
- Why It Matters: Exponential and Logarithmic Equations and Models
- Introduction to Exponential and Logarithmic Equations
- Use like bases to solve exponential equations
- Use logarithms to solve exponential equations
- Use the definition of a logarithm to solve logarithmic equations
- Use the one-to-one property of logarithms to solve logarithmic equations
- Solve applied problems involving exponential and logarithmic equations
- Problem Set: Exponential and Logarithmic Equations
- Solutions: Exponential and Logarithmic Equations
- Introduction to Exponential and Logarithmic Models
- Model exponential growth and decay
- Use Newton’s Law of Cooling
- Use logistic-growth models
- Problem Set: Exponential and Logarithmic Models
- Solutions: Exponential and Logarithmic Models
Module 11: Unit Circle Trigonometry
- Introduction to Angles
- Angles in standard position
- Converting Between Degrees and Radians
- Coterminal Angles
- Arc Length and Area of a Sector
- Problem Set: Angles
- Solutions: Angles
- Introduction to the Unit Circle and Sine and Cosine Functions
- Unit circle
- Sine and Cosine of all Angles
- Problem Set: Unit Circle
- Solutions: Unit Circle
Module 12: Right Triangle Trigonometry
- Introduction to Right Triangle Trigonometry
- Using Right Triangles to Evaluate Trigonometric Functions
- Pythagorean Theorem
- Applications of Right Triangle Trigonometry
- Problem Set: Right Triangle Trigonometry
- Solutions: Right Triangle Trigonometry
Module 13: Non-Right Triangles
- Introduction to Law of Sines
- Using the Law of Sines to Solve Oblique Triangles
- Solving Applied Problems using Law of Sines
- Problem Set: Law of Sines
- Solutions: Law of Sines
- Introduction to Law of Cosines
- Using the Law of Cosines to Solve Oblique Triangles
- Solving Applied Problems Using the Law of Cosines
- Problem Set: Law of Cosines
- Solutions: Law of Cosines
- Introduction to Vectors
- A Geometric View of Vectors
- Magnitude and Direction of a Vector
- Problem Set: Vectors
- Solutions: Vectors
Appendix

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Table of Contents

Module 1: Exponents and Radicals

Module 2: Linear and Quadratic Equations

Module 3: Rates, Ratios and Proportions

Module 4: Variation

Module 5: Measurements

Module 6: Introduction to Functions

Module 7: Linear and Quadratic Functions

Module 8: Systems of Linear Equations

Module 9: Introduction to Exponential and Logarithmic Functions

Module 10: Applications of Exponential and Logarithmic Functions

Module 11: Unit Circle Trigonometry

Module 12: Right Triangle Trigonometry

Module 13: Non-Right Triangles

Appendix

Copyright

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