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Kirk Trigsted teaches mathematics at the University of Idaho and has been director of the Polya Mathematics Center since its inception in 2001. Kirk has taught with MyMathLab for many years, and has contributed to the videos for several Pearson books. Kirk is also actively involved with the National Center for Academic Transformation (NCAT).
Randy Gallaher is a professor of mathematics at Lewis & Clark Community College, where he has taught since 1997. Prior to this position, Randy taught high school and middle school mathematics for five years in Missouri. He holds a master’s degree in mathematics from Southeast Missouri State University and has completed additional graduate coursework at both Missouri State University and the University of Illinois at Urbana-Champaign. He has coauthored ancillary materials for numerous math and statistics textbooks and has worked as a math author on several grant projects for the Illinois Community College Board. Randy is married with three children and spends most evenings actively involved in their activities. In his limited free time, he loves to fish the small rivers and streams of southern Missouri.
Kevin Bodden is a professor of mathematics at Lewis & Clark Community College where he has taught since 1999. He holds a master’s degree in mathematics from Southern Illinois University at Edwardsville and a master’s degree in engineering from Purdue University. He has authored or co-authored ancillary material for numerous textbooks ranging from basic college math to calculus and statistics. He has contributed videos for several of these textbooks and has authored math content on grant projects for the Illinois Community College Board. Kevin is married with three children and is actively involved in their school and extracurricular activities. In his spare time, he enjoys soccer, camping, and geocaching.
Chapter R. Review
R.1 Sets of Numbers
1 Identify sets
2 Classify real numbers
3 Plot real numbers on a number line
4 Use inequality symbols to order real numbers
5 Compute the absolute value of a real number
R.2 Order of Operations and Properties of Real Numbers
1 Perform operations on real numbers
2 Simplify numeric expressions containing exponents and radicals
3 Identify and use the properties of real numbers
4 Use order of operations to evaluate numeric expressions
R.3 Algebraic Expressions
1 Evaluate algebraic expressions
2 Simplify algebraic expressions
3 Write verbal descriptions as algebraic expressions
Chapter 1. Equations and Inequalities in One Variable
1.1 Linear Equations in One Variable
1 Determine if a given value is a solution to an equation
2 Solve linear equations in one variable
3 Identify equations that are contradictions and those that are identities
4 Use linear equations to solve application problems
1.2 Linear Inequalities in One Variable
1 Determine if a given value is a solution to an inequality
2 Graph the solution set of an inequality on a number line
3 Use interval notation to express the solution set of an inequality
4 Solve linear inequalities in one variable
5 Use linear inequalities to solve application problems
1.3 Compound Inequalities; Absolute Value Equations and Inequalities
1 Find the union and intersection of two sets
2 Solve compound linear inequalities in one variable
3 Solve absolute value equations
4 Solve absolute value inequalities
1.4 Formulas and Problem Solving
1 Solve a formula for a given variable
2 Use formulas to solve application problems
Chapter 2. Graphs and Functions
2.1 The Rectangular Coordinate System and Graphing
1 Plot ordered pairs in the rectangular coordinate system
2 Determine if an ordered pair is a solution to an equation
3 Find unknown coordinates
4 Graph equations by plotting points
5 Find x- and y-intercepts
2.2 Relations and Functions
1 Identify independent and dependent variables
2 Find the domain and range of a relation
3 Determine if relations are functions
4 Determine if graphs are functions
5 Solve application problems involving relations and functions
2.3. Function Notation and Applications
1 Express equations of functions using function notation
2 Evaluate functions
3 Graph simple functions by plotting points
4 Interpret graphs of functions
5 Solve application problems involving functions
2.4 Graphs of Linear Functions
1 Graph linear functions by plotting points
2 Graph linear functions by using intercepts
3 Graph vertical and horizontal lines
2.5 Linear Equations in Two Variables
1 Find the slope of a line
2 Graph a line using the slope and a point
3 Determine the relationship between two lines
4 Write the equation of a line from given information
5 Write equations of parallel and perpendicular lines
6 Use linear models to solve application problems; direct variation
2.6 Linear Inequalities in Two Variables
1 Determine if an ordered pair is a solution to a linear inequality in two variables
2 Graph a linear inequality in two variables
Chapter 3. Systems of Linear Equations and Inequalities
3.1 Systems of Linear Equations in Two Variables
1 Determine if an ordered pair is a solution to a system of linear equations in two variables
2 Solve systems of linear equations in two variables by graphing
3 Solve systems of linear equations in two variables by substitution
4 Solve systems of linear equations in two variables by elimination
5 Solve inconsistent and dependent systems
6 Use systems of linear equations in two variables to solve application problems
3.2 Systems of Linear Equations in Three Variables
1 Determine if an ordered triple is a solution to a system of linear equations in three variables
2 Solve systems of linear equations in three variables
3 Use systems of linear equations in three variables to solve application problems
3.3 More Problem Solving with Systems of Linear Equations
1 Use systems of linear equations to solve uniform motion problems
2 Use systems of linear equations to solve geometry problems
3 Use systems of linear equations to solve mixture problems
3.4 Systems of Linear Inequalities in Two Variables
1 Determine if an ordered pair is a solution to a system of linear inequalities in two variables
2 Graph systems of linear inequalities in two variables
Chapter 4. Polynomial Expressions and Functions
4.1 Rules for Exponents
1 Simplify exponential expressions using the product rule
2 Simplify exponential expressions using the quotient rule
3 Use the zero-power rule
4 Use the negative-power rule
5 Use the power-to-power rule
6 Use the product-to-power and quotient-to-power rules
7 Simplify exponential expressions using a combination of rules
8 Use rules for exponents with scientific notation
4.2 Introduction to Polynomial Functions
1 Find the coefficient and degree of a monomial
2 Find the leading coefficient and degree of a polynomial
3 Evaluate a polynomial function for a given value
4 Add polynomials
5 Subtract polynomials
6 Add and subtract polynomial functions
4.3 Multiplying Polynomials
1 Multiply monomials
2 Multiply a polynomial by a monomial
3 Multiply two binomials
4 Multiply two binomials using special product rules
5 Multiply two or more polynomials
6 Multiply polynomial functions
4.4 Dividing Polynomials
1 Divide a polynomial by a monomial
2 Divide polynomials using long division
3 Divide polynomials using synthetic division
4 Divide polynomial functions
5 Use the Remainder and Factor theorems
Chapter 5. Factoring
5.1 Greatest Common Factor and Factoring by Grouping
1 Factor out the greatest common factor from a polynomial
2 Factor by grouping
5.2 Factoring Trinomials
1 Factor trinomials of the form x^{2} + bx + c
2 Factor trinomials of the form ax^{2} + bx + c using trial-and-error
3 Factor trinomials of the form ax^{2} + bx + c using the ac method
4 Factor trinomials using substitution
5.3 Special-Case Factoring; A General Factoring Strategy
1 Factor the difference of two squares
2 Factor perfect square trinomials
3 Factor the sum or difference of two cubes
4 Factor polynomials completely
5.4 Polynomial Equations and Models
1 Solve polynomial equations by factoring
2 Find the zeros of a polynomial function
3 Use polynomial equations and models to solve application problems
Chapter 6. Rational Expressions, Equations, and Functions
6.1 Introduction to Rational Expressions and Functions
1 Find the domain of a rational function
2 Evaluate rational functions
3 Simplify rational expressions
6.2 Multiplying and Dividing Rational Expressions
1 Multiply rational expressions
2 Divide rational expressions
6.3 Adding and Subtracting Rational Expressions
1 Add and subtract rational expressions with common denominators
2 Find the least common denominator of rational expressions
3 Add and subtract rational expressions with unlike denominators
6.4 Complex Rational Expressions
1 Simplify complex rational expressions by first simplifying the numerator and denominator
2 Simplify complex rational expressions by multiplying by a common denominator
6.5 Rational Equations and Models
1 Identify rational equations
2 Solv e rational equations
3 Find the zeros of a rational function
4 Us e rational equations to solve application problems
6.6 Variation
1 Solve application problems involving direct variation
2 Solve application problems involving inverse variation
2 Solve application problems involving combined variation
Chapter 7. Radicals and Rational Exponents
7.1 Radical Expressions
1 Find square roots of perfect squares
2 Approximate square roots
3 Simplify radical expressions of the form √(a^{2})
4 Find cube roots
5 Find and approximate nth roots
7.2 Radical Functions
1 Evaluate radical functions
2 Find the domain of a radical function
3 Graph functions that contain square roots or cube roots
7.3 Rational Exponents and Simplifying Radical Expressions
1 Use the definition for rational exponents of the form a^{1/n}
2 Use the definition for rational exponents of the form a^{m/n}
3. Simplify exponential expressions involving rational exponents
4 Use rational exponents to simplify radical expressions
5 Simplify radical expressions using the product rule
6 Simplify radical expressions using the quotient rule
7.4 Operations with Radicals
1 Add and subtract radical expressions
2 Multiply radical expressions
3 Rationalize denominators of radical expressions
7.5 Radical Equations and Models
1 Solve equations involving one radical expression
2 Solve equations involving two radical expressions
3 Use radical equations and models to solve application problems
7.6 Complex Numbers
1 Simplify powers of i
2 Add and subtract complex numbers
3 Multiply complex numbers
4 Divide complex numbers
5 Simplify radicals with negative radicands
Chapter 8. Quadratic Equations and Functions; Circles
8.1 Solving Quadratic Equations
1 Solve quadratic equations using factoring
2 Solve quadratic equations using the square root property
3 Solve quadratic equations by completing the square
4 Solve quadratic equations using the quadratic formula
5 Use the discriminant to determine the number and type of solutions to a quadratic equation
6 Solve equations that are quadratic in form
8.2 Quadratic Functions and Their Graphs
1 Identify the characteristics of a quadratic function from its graph
2 Graph quadratic functions by using translations
3 Graph quadratic functions of the form f(x) = a(x-h)^{2} + k
4 Find the vertex of a parabola by completing the square
5 Graph quadratic functions of the form f(x) = ax^{2} + bx + c by completing the square
6 Find the vertex of a parabola by using the vertex formula
7 Graph quadratic functions of the form f(x) = ax^{2} + bx + c by using the vertex formula
8.3 Applications and Modeling of Quadratic Functions
1 Solve applications involving unknown numbers
2 Solve applications involving projectile motion
3 Solve applications involving geometric formulas
4 Solve applications involving distance, rate, and time
5 Solve applications involving work
6 Maximize quadratic functions to solve application problems
7 Minimize quadratic functions to solve application problems
8.4 Circles
1 Find the distance between two points
2 Find the midpoint of a line segment
3 Write the standard form of an equation of a circle
4 Sketch the graph of a circle
5 Find the center and radius of a circle
8.5 Polynomial and Rational Inequalities
1 Solve polynomial inequalities
2 Solve rational inequalities
Chapter 9. Exponential and Logarithmic Functions and Equations
9.1 Transformations of Functions
1 Use vertical shifts to graph functions
2 Use horizontal shifts to graph functions
3 Use reflections to graph functions
4 Use vertical stretches and compressions to graph functions
5 Use horizontal stretches and compressions to graph functions
6 Use a combination of transformations to graph functions
9.2 Composite and Inverse Functions
1 Form and evaluate composite functions
2 Determine the domain of composite functions
3 Determine if a function is one-to-one using the horizontal line test
4 Verify inverse functions
5 Sketch the graphs of inverse functions
6 Find the inverse of a one-to-one function
9.3 Exponential Functions
1 Use the characteristics of exponential functions
2 Sketch the graph of exponential functions using transformations
3 Solve exponential equations by relating the bases
4 Solve applications of exponential functions
9.4 The Natural Exponential Function
1 Use the characteristics of the natural exponential function
2 Sketch the graph of natural exponential functions using transformations
3 Solve natural exponential equations by relating the bases
4 Solve applications of natural exponential functions
9.5 Logarithmic Functions
1 Use the definition of a logarithmic function
2 Evaluate logarithmic expressions
3 Use the properties of logarithms
4 Use the common and natural logarithms
5 Use the characteristics of logarithmic functions
6 Sketch the graph of logarithmic functions using transformations
7 Find the domain of logarithmic functions
9.6 Properties of Logarithms
1 Use the product rule, quotient rule, and power rule for logarithms
2 Expand and condense logarithmic expressions
3 Solve logarithmic equations by using the logarithm property of equality
4 Use the change-of-base formula
9.7 Exponential and Logarithmic Equations
1 Solve exponential equations
2 Solve logarithmic equations
9.8 Applications of Exponential and Logarithmic Functions
1 Solve compound interest applications
2 Solve exponential growth and decay applications
3 Solve logistic growth applications
4 Use Newton’s Law of Cooling
Appendix A. Conic Sections
Introduction to Conic Sections
A.1 The Parabola
1 Work With the Equation of a Parabola with a Vertical Axis of Symmetry
2 Work With the Equation of a Parabola with a Horizontal Axis of Symmetry
3 Find the Equation of a Parabola Given Information about the Graph
4 Complete the Square to Find the Equation of a Parabola in Standard Form
5 Solve Applications Involving Parabolas
A.2 The Ellipse
1 Sketch the Graph of an Ellipse
2 Find the Equation of an Ellipse Given Information about the Graph
3 Complete the Square to Find the Equation of an Ellipse in Standard Form
4 Solve Applications Involving Ellipses
A.3 The Hyperbola
1 Sketch the Graph of a Hyperbola
2 Find the Equation of a Hyperbola in Standard Form
3 Complete the Square to Find the Equation of a Hyperbola in Standard Form
4 Solve Applications Involving Hyperbolas
Appendix B Sequences and Series
B.1 Introduction to Sequences and Series
1 Write the terms of a sequence
2 Write the terms of a recursive sequence
3 Write the general term for a given sequence
4 Compute partial sums of a series
5 Determine the sum of a finite series written in summation notation
6 Write a series using summation notation
B.2 Arithmetic Sequences and Series
1 Determine if a sequence is arithmetic
2 Find the general term or specific term of an arithmetic sequence
3 Compute the nth partial sum of an arithmetic series
4 Solve applications of arithmetic sequences and series
B.3 Geometric Sequences and Series
1 Write the terms of a geometric sequence
2 Determin e if a sequence is geometric
2 Find the general term or specific term of a geometric sequence
3 Comput e the nth partial sum of a geometric series
5 Determine if an infinite geometric series converges or diverges
4 Solve applications of geometric sequences and series
B.4 The Binomial Theorem
1 Expand binomials raised to a power using Pascal’s Triangle
2 Evaluate binomial coefficients
3 Expand binomials raised to a power using the Binomial Theorem
4 Find a particular term or a particular coefficient of a binomial expansion
Appendix C Basic Math Review - Fractions, Decimals, Proportions, Percents
C.1 Fractions
C.2 Decimals
C.3 Proportions
C.4 Percents