Intermediate Algebra: A STEM Approach, 1st edition

• 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 f(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 f(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 f1x2 = 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