Intermediate Algebra

George Woodbury earned a bachelor’s degree in Mathematics from the University of California—Santa Barbara and a master’s degree in Mathematics from California State University—Northridge. He currently teaches at College of the Sequoias in Visalia, CA, just outside of Fresno. George has been honored as an instructor by both his students and his colleagues. Aside from teaching and writing, George served as the department chair of the math/engineering division from 1999 through 2004. He has been a user of MyLab™ Math and Statistics since their inception, continually coming up with creative ways to integrate his teaching methods with technology. He actively blogs on georgewoodbury.com about thoughts on math, statistics, teaching, and study skills. 

R. Review of Real Numbers 

R.1 Integers, Opposites, and Absolute Value 

R.2 Exponents and Order of Operations




1. Linear and Absolute Value Equations and Inequalities

1.1 Introduction to Algebra

1.2 Linear Equations

1.3 Problem Solving: Applications of Linear Equations

1.4 Proportions and Dimensional Analysis

1.5 Absolute Value Equations

1.6 Linear Inequalities

1.7 Absolute Value Inequalities




2. Graphing Linear Equations

2.1 The Rectangular Coordinate System; Equations in Two Variables

2.2 Slope of a Line

2.3 Equations of Lines

2.4 Linear Inequalities

2.5 Linear Functions

2.6 Absolute Value Functions




3. Systems of Equations

3.1 Systems of Two Equations in Two Unknowns

3.2 Applications of Systems of Equations

3.3 Systems of Linear Inequalities

3.4 Systems of Three Equations in Three Unknowns

3.5 Using Matrices to Solve Systems of Equations

3.6 Determinants and Cramer’s Rule




4. Exponents, Polynomials, and Factoring Polynomials

4.1 Exponents

4.2 Negative Exponents; Scientific Notation

4.3 Polynomials; Addition, Subtraction, and Multiplication of Polynomials

4.4 Polynomial Division

4.5 An Introduction to Factoring; The Greatest Common Factor; Factoring by Grouping

4.6 Factoring Trinomials of Degree 2

4.7 Factoring Special Binomials

4.8 Factoring Polynomials: A General Strategy

4.9 Solving Quadratic Equations By Factoring




Chapters 1—4 Cumulative Review




5. Rational Expressions and Equations

5.1 Rational Expressions and Functions

5.2 Multiplication and Division of Rational Expressions

5.3 Addition and Subtraction of Rational Expressions

5.4 Complex Fractions

5.5 Rational Equations

5.6 Applications of Rational Equations




6. Radical Expressions and Equations

6.1 Square Roots; Radical Notation

6.2 Rational Exponents

6.3 Simplifying, Adding, and Subtracting Radical Expressions

6.4 Multiplying and Dividing Radical Expressions

6.5 Radical Equations and Applications of Radical Equations

6.6 The Complex Numbers




7. Quadratic Equations

7.1 Solving Quadratic Equations by Extracting Square Roots; Completing the Square

7.2 The Quadratic Formula

7.3 Equations That Are Quadratic in Form

7.4 Graphing Quadratic Equations and Quadratic Functions

7.5 Applications Using Quadratic Equations

7.6 Quadratic and Rational Inequalities

7.7 Other Functions and Their Graphs




Chapters 5—7 Cumulative Review




8. Logarithmic and Exponential Functions

8.1 The Algebra of Functions

8.2 Inverse Functions

8.3 Exponential Functions

8.4 Logarithmic Functions

8.5 Properties of Logarithms

8.6 Exponential and Logarithmic Equations

8.7 Applications of Exponential and Logarithmic Functions

8.8 Graphing Exponential and Logarithmic Functions




9. Conic Sections

9.1 Parabolas

9.2 Circles

9.3 Ellipses

9.4 Hyperbolas

9.5 Nonlinear Systems of Equations




10. Sequences, Series, and the Binomial Theorem

10.1 Sequences and Series

10.2 Arithmetic Sequences and Series

10.3 Geometric Sequences and Series

10.4 The Binomial Theorem




Chapters 8—10 Cumulative Review




Answers to Selected Exercises*






*Additional Instructor's Answers are given in the Annotated Instructor's Edition.







Integrated Review Topics:




Chapter 1

Build variable expressions - sections 1.3, 1.6

Evaluate variable expressions - 1.2

Find the absolute value of an integer - 1.5, 1.7

Find the least common multiple (LCM) of two natural numbers - 1.2

Graph integers on a number line - 1.6

Identify linear equations with no solution - 1.5

Multiply fractions - 1.4

Perform arithmetic operations with integers - 1.2

Present the solutions of an inequality on a number line and using interval notation - 1.7

Simplify a fraction to lowest terms - 1.2, 1.4

Simplify variable expressions - 1.2

Solve compound linear inequalities - 1.7

Solve linear equations using the five-step general strategy - 1.3, 1.5, 1.6

Solve linear equations using the multiplication property of equality - 1.4

Solve linear inequalities - 1.7




Chapter 2

Determine whether a value is a solution of an equation - 2.1

Determine whether an ordered pair is a solution of an equation in two variables - 2.4

Determine whether two lines are parallel - 2.3

Determine whether two lines are perpendicular - 2.3

Evaluate variable expressions - 2.5

Find the absolute value of an integer - 2.6

Find the slope of a line passing through two points using the slope formula - 2.3

Graph a line using its slope and y-intercept - 2.4, 2.5

Graph horizontal lines and vertical lines - 2.4

Graph integers on a number line - 2.1

Graph linear equations using their intercepts - 2.4

Graph linear functions - 2.6

Interpret the slope and y-intercept in real-world applications - 2.5

Plot ordered pairs on a rectangular coordinate plane - 2.2

Simplify a fraction to lowest terms - 2.2

Solve linear equations using the five-step general strategy - 2.1

Solve literal equations for a specified variable - 2.2, 2.3

Subtract integers - 2.2




Chapter 3

Build variable expressions - 3.2

Complete ordered pairs for a linear equation in two variables - 3.1, 3.5

Create an augmented matrix for a system of three equations in three unknowns - 3.6

Create an augmented matrix for a system of two equations in two unknowns - 3.6

Determine if an ordered pair is a solution of an equation - 3.1

Determine if an ordered pair is a solution to a system of equations - 3.4

Graph a line using its slope and y-intercept - 3.3

Graph a line using the most efficient strategy - 3.1

Graph a linear inequality in two variables - 3.3

Graph linear equations using their intercepts 3.3

Identify linear equations that are contradictions or identities - 3.1

Solve linear equations containing fractions - 3.1

Solve linear equations using the five-step general strategy - 3.1

Solve systems of linear equations by using the addition method - 3.2

Solve systems of linear equations by using the substitution method - 3.2

Solve systems of linear equations using the addition method - 3.4, 3.5

Solve systems of three linear equations in three unknowns - 3.5




Chapter 4

Evaluate functions - 4.1

Factor a difference of squares - 4.8

Factor a difference or sum of cubes - 4.8

Factor a polynomial by grouping - 4.6, 4.8

Factor a trinomial of the form ax2 + bx + c - 4.8

Factor a trinomial of the form x2 + bx + c - 4.8

Factor the GCF out of each term of a polynomial - 4.6, 4.7, 4.8

Find special products - 4.7

Find the prime factorization of a natural number - 4.5

Multiply a monomial by a polynomial - 4.4, 4.5

Multiply polynomials - 4.4, 4.5, 4.6

Perform arithmetic operations with decimals - 4.2

Simplify a fraction to lowest terms - 4.1

Simplify exponents - 4.1

Simplify variable expressions - 4.3

Solve linear equations containing fractions - 4.9

Solve linear equations using the five-step general strategy - 4.9

Solve problems involving consecutive integers - 4.9

Subtract integers - 4.2

Understand the strategy for factoring a general polynomial - 4.9

Use the distributive property of real numbers - 4.3

Use the product rule for exponents - 4.3

Use the quotient rule for exponents - 4.2, 4.4

Use unit factors for dimensional analysis - 4.2




Chapter 5

Add and subtract fractions with the same denominator - 5.3

Add and subtract fractions with unlike denominators - 5.3

Add and subtract polynomials - 5.3

Divide fractions - 5.2

Evaluate algebraic expressions - 5.1

Evaluate functions - 5.1

Factor polynomials - 5.1

Find the least common denominator (LCD) of two or more rational expressions - 5.4

Find the least common multiple (LCM) of two natural numbers - 5.4

Identify factors that are opposites of each other - 5.2

Multiply fractions - 5.2

Simplify a fraction to lowest terms - 5.1

Simplify rational expressions to lowest terms - 5.2, 5.3, 5.4

Solve a quadratic equation by factoring - 5.1, 5.5

Solve linear equations containing fractions - 5.5

Solve literal equations for a specified variable - 5.5

Solve linear equations using the five-step general strategy - 5.1, 5.5

Solve problems involving motion - 5.6

Solve rational equations - 5.6

Understand the six steps for solving applied problems - 5.6




Chapter 6

Evaluate functions - 6.1

Find nth roots - 6.2, 6.3

Find the prime factorization of a number - 6.1, 6.3

Find the square root of a number - 6.2, 6.3, 6.6

Multiply polynomials - 6.4, 6.5, 6.6

Multiply radical expressions - 6.4

Rationalize a denominator with one term - 6.6

Rationalize a denominator with two terms - 6.6

Simplify variable expressions - 6.3, 6.4, 6.6

Simplify expressions using the rules of exponents - 6.2

Solve a quadratic equation by factoring - 6.5

Solve linear equations - 6.5

Solve linear inequalities - 6.1

Use the power rule for exponents - 6.1




Chapter 7

Determine the domain and range of a function from its graph - 7.7

Factor trinomials of degree 2 - 7.1

Find the square root of a number - 7.1, 7.2, 7.5

Find the x- and y-intercepts of a line from its equation - 7.4

Graph absolute value functions by shifting - 7.4, 7.7

Graph quadratic functions of the form ƒ(x) = a(x - h)2 + k by shifting - 7.7

Present the solutions of an inequality on a number line and using interval notation - 7.6

Solve a quadratic equation by factoring - 7.1, 7.2

Solve applied geometry problems - 7.5

Solve applied work-rate problems - 7.3

Solve radical equations - 7.3

Solve rational equations - 7.3

Solve quadratic equations by completing the square - 7.2, 7.4

Solve quadratic equations by factoring or by using the quadratic formula - 7.4, 7.5, 7.6

Solve quadratic equations by using the quadratic formula - 7.3




Chapter 8

Add and subtract polynomials - 8.1

Convert an equation from logarithmic form to exponential form - 8.6

Evaluate exponential functions - 8.4

Evaluate functions - 8.1, 8.3

Evaluate logarithms and logarithmic functions - 8.5

Find the composite function of two functions ƒ(x) and g(x) - 8.2

Find the inverse of a one-to-one function - 8.6

Graph exponential functions - 8.4, 8.8

Graph linear functions - 8.3

Graph logarithmic functions - 8.8

Interpret graphs of functions - 8.3

Multiply polynomials - 8.1

Simplify expressions with exponents - 8.4

Simplify rational expressions to lowest terms - 8.1

Solve a logarithmic equation by converting it to exponential form - 8.7

Solve an exponential equation by using logarithms - 8.7

Solve linear equations - 8.6

Solve literal equations for a specified variable - 8.2

Solve quadratic equations by factoring - 8.6

Use the product and quotient rules for logarithms - 8.6

Use the product rule for exponents - 8.5

Use the quotient rule for exponents - 8.5




Chapter 9

Find a vertex by completing the square - 9.2

Find the center of a circle and its radius by completing the square - 9.3

Find the center of an ellipse and the lengths of its axes by completing the square - 9.4

Find the square root of a number - 9.2, 9.3

Graph circles centered at a point (h, k) - 9.3

Graph ellipses centered at a point (h, k) - 9.4

Graph equations of the form y = a(x - h)2 + k - 9.2

Graph quadratic equations in standard form - 9.1

Graph quadratic functions of the form ƒ1x2 = 1x - h22 + k by shifting - 9.1

Solve a quadratic equation by factoring - 9.1

Solve quadratic equations by completing the square - 9.1

Solve quadratic equations by extracting square roots - 9.1

Solve quadratic equations by using the quadratic formula - 9.1

Solve systems of linear equations by using the addition method - 9.5

Solve systems of linear equations by using the substitution method - 9.5




Chapter 10

Add, subtract, multiply, and divide integers - 10.1

Evaluate functions - 10.1

Find partial sums of a sequence - 10.2

Find partial sums of an arithmetic sequence - 10.3

Find special products - 10.4

Find the general term of a sequence - 10.2

Find the general term of an arithmetic sequence - 10.3

Multiply polynomials - 10.4