Algebra & Trigonometry
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Algebra and Trigonometry Course Outline

What are the prerequisite to algebra and trigonometry?

Concepts Covered:

Why are real numbers an algebra essentials?
What is the difference between exponents and scientific notation?
What is the difference between radicals and rational expressions?
What are polynomials?
How are polynomials factored?
What are rational expressions?

How do equations relate to inequalities?

Concepts Covered:

How are rectangular coordinate systems applied to graphs?
How to use linear equations with one variable?
How are models and applications in algebra and trigonometry apply to real-world situations?
What are different ways to solve complex numbers?
What are different ways to solve quadratic equations?
What are other types of equations used in algebra and trigonometry?
What is the difference between linear inequalities and absolute value inequalities?

What are functions?

Concepts Covered:

How are function notation applied in functions?
What is the difference between domain and range?
How does the rate of change affect the behavior of graphs?
How do you find the composition of functions?
How can functions be transformed?
How do you find absolute value functions?
What are inverse functions?

What are linear functions?

Concepts Covered:

How do we use linear functions?
How do we model linear functions?
How do we fit linear models to data?

How are polynomials related to rational functions?

Concepts Covered:

How are quadratic functions applied in parabolas?
What is the difference between power functions and polynomial functions?
Why do we graph polynomial functions?
How do we divide polynomials?
How do we find zeros in polynomial functions?
Why are rational functions important?
What is the difference between inverses and radical functions?
How do we model using variations?

What are exponential and logarithmic functions?

Concepts Covered:

How are exponential functions used?
How do we graph exponential functions?
How do we find logarithmic functions?
How do we graph logarithmic functions?
What are logarithmic properties?
What is the difference between exponential and logarithmic equations?
How do we use exponential and logarithmic models?
How do we use data to fit exponential models?

What is the difference between sine and cosine functions?

Concepts Covered:

How are angles used in algebra and trigonometry?
How do we use right triangles in algebra and trigonometry?
What is a unit circle?
What are some other trigonometric functions?

What are periodic functions?

Concepts Covered:

How do you make graphs with sine and cosine functions?
How do you make graphs with other trigonometric functions?
What are inverse trigonometric functions?

How do trigonometric identities affect equations?

Concepts Covered:

How do we solve trigonometric equations with identities?
How do we compare sum and difference identities?
How do we differentiate double-angle, half-angle, and reduction formula identities?
What is the difference between sum-to-product and product-to-sum formulas?
How do we solve trigonometric equations?

What else is there in trigonometry?

Concepts Covered:

How do non-right triangles relate to the law of sines?
How do non-right triangles relate to the law of cosines?
How are polar coordinates used?
How are polar coordinates graphed?
What is the polar form of complex numbers?
How are parametric equations formed?
How are parametric equations graphed?
What are vectors?

How do the systems of equations and inequalities operate?

Concepts Covered:

How do you use the systems of linear equations using two variables?
How do you use the systems of linear equations using three variables?
What are the two variables in the systems of nonlinear equations and inequalities?
Why do we get partial fractions?
What is the difference between the matrices and matrix operations?
How do we solve different systems with the Gaussian elimination?
How do we solve different systems with inverses?
How do we solve different systems using Cramer’s rule?

What is analytic geometry?

Concepts Covered:

How is an ellipse formed?
What is a hyperbola?
How do we form parabolas?
What are the rotation of axes?
Where are the conic sections in the polar coordinates?

How do sequences, probability, and counting theory relate to each other?

Concepts Covered:

How do we find sequences and their notations?
How do we find arithmetic sequences?
How do we find geometric sequences?
How do we find series and their notations?
How do we count problems with principles?
What is binomial theorem?
What is probability?

About the book

Algebra & Trigonometry

Algebra and Trigonometry provides a comprehensive exploration of algebraic principles and meets scope and sequence requirements for a typical introductory algebra and trigonometry course. The modular approach and the richness of content ensure that the book meets the needs of a variety of courses. Algebra and Trigonometry offers a wealth of examples with detailed, conceptual explanations, building a strong foundation in the material before asking students to apply what they’ve learned.

About the authors:

Senior Contributing Authors

Jay Abramson, Arizona State University

Contributing Authors

Valeree Falduto, Palm Beach State College
Rachael Gross, Towson University
David Lippman, Pierce College
Melonie Rasmussen, Pierce College
Christina Fernandez
Harold Whipple, Formerly of Columbia College
Jean-Marie Magnier, Springfield Technical Community College
Rick Norwood, East Tennessee State University
Nicholas Belloit, Florida State College at Jacksonville

Assessment Question Author

Dr. Angela Everett
Professor of Mathematics
Chattanooga State Community College

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