Integrated Review Worksheets for Intermediate Algebra

Jay Lehmann has taught for the past 25 years at College of San Mateo, where he received the “shiny apple award” for excellence in teaching. He has presented at over 80 conferences including AMATYC and ICTCM over the past 16 years. Jay is currently the newsletter editor for California Mathematics Council, Community Colleges (CMC3). Still young at heart, he plays in a rock band appropriately named the Procrastinistas. Jay has authored several algebra textbooks published by Pearson and is has also recently completed a Prestatistics textbook.In the words of the author:Before writing my algebra series, it was painfully apparent that my students couldn't relate to the applications in the course. I was plagued with the question, "What is this good for?" To try to bridge that gap, I wrote some labs, which facilitated my students in collecting data, finding models via curve fitting, and using the models to make estimates and predictions. My students really loved working with the current, compelling, and authentic data and experiencing how mathematics truly is useful.My students' response was so strong that I decided to write an algebra series. Little did I know that to realize this goal, I would need to embark on a 15-year challenging journey, but the rewards of hearing such excitement from students and faculty across the country have made it all worthwhile! I'm proud to have played even a small role in raising people’s respect and enthusiasm for mathematics.I have tried to honor my inspiration: by working with authentic data, students can experience the power of mathematics. A random-sample study at my college suggests that I am achieving this goal. The study concludes that students who used my series were more likely to feel that mathematics would be useful in their lives (P-value 0.0061) as well as their careers (P-value 0.024).The series is excellent preparation for subsequent courses; in particular, because of the curve fitting and emphasis on interpreting the contextual meaning of parameters, it is an ideal primer for statistics. In addition to curve fitting, my approach includes other types of meaningful modeling, directed-discovery explorations, conceptual questions, and of course, a large bank of skill problems. The curve-fitting applications serve as a portal for students to see the usefulness of mathematics so that they become fully engaged in the class. Once involved, they are more receptive to all aspects of the course.

• Linear Equations and Linear Functions 1.1 Using Qualitative Graphs to Describe Situations1.2 Graphing Linear Equations1.3 Slope of a Line1.4 Meaning of Slope for Equations, Graphs, and Tables1.5 Finding Linear Equations1.6 FunctionsModeling With Linear Functions 2.1 Using Lines to Model Data2.2 Finding Equations of Linear Models2.3 Function Notation and Making Predictions2.4 Slope Is a Rate of ChangeTaking It to the Lab: Climate Change Lab • Used-Car Lab • Golf Ball Lab • Walking Student Lab • Linear Lab: Topic of Your ChoiceSystems of Linear Equations and Systems of Linear Inequalities 3.1 Using Graphs and Tables to Solve Systems3.2 Using Substitution and Elimination to Solve Systems3.3 Using Systems to Model Data3.4 Value, Interest, and Mixture Problems3.5 Using Linear Inequalities in One Variable to Make Predictions3.6 Linear Inequalities in Two Variables; Systems of Linear InequalitiesTaking It to the Lab: Climate Change Lab (continued from Chapter 2) • Sports Lab • Truck LabExponential Functions 4.1 Properties of Exponents4.2 Rational Exponents4.3 Graphing Exponential Functions4.4 Finding Equations of Exponential Functions4.5 Using Exponential Functions to Model DataTaking It to the Lab: Stringed Instrument Lab • Cooling Water Lab • Exponential Lab: Topic of Your ChoiceLogarithmic Functions 5.1 Composite Functions5.2 Inverse Functions5.3 Logarithmic Functions5.4 Properties of Logarithms5.5 Using the Power Property with Exponential Models to Make Predictions5.6 More Properties of Logarithms5.7 Natural LogarithmTaking It to the Lab: China and India Populations Lab • Folding Paper Lab • Exponential/Logarithmic Lab: Topic of Your ChoicePolynomial Functions 6.1 Adding and Subtracting Polynomial Expressions and Functions6.2 Multiplying Polynomial Expressions and Functions6.3 Dividing Polynomials: Long Division and Synthetic Division6.4 Factoring Trinomials of the Form x2 + bx + c; Factoring Out the GCF6.5 Factoring Polynomials6.6 Factoring Special Binomials; A Factoring Strategy6.7 Using Factoring to Solve Polynomial EquationsTaking It to the Lab: Climate Change Lab (continued from Chapter 3) • Projectile LabQuadratic Functions 7.1 Graphing Quadratic Functions in Vertex Form7.2 Graphing Quadratic Functions in Standard Form7.3 Using the Square Root Property to Solve Quadratic Equations7.4 Solving Quadratic Equations by Completing the Square7.5 Using the Quadratic Formula to Solve Quadratic Equations7.6 Solving Systems of Linear Equations in Three Variables; Finding Quadratic Functions7.7 Finding Quadratic Models7.8 Modeling with Quadratic FunctionsTaking It to the Lab: Climate Change Lab (continued from Chapter 6) • Projectile Lab (continued from Chapter 6) • Projectile Lab (Using a CBR or CBL) • Water Flow Lab • Quadratic Lab: Topic of Your ChoiceRational Functions 8.1 Finding the Domains of Rational Functions and Simplifying Rational Expressions8.2 Multiplying and Dividing Rational Expressions; Converting Units8.3 Adding and Subtracting Rational Expressions8.4 Simplifying Complex Rational Expressions8.5 Solving Rational Equations8.6 Modeling with Rational Functions8.7 VariationTaking It to the Lab: Climate Change Lab (continued from Chapter 7) • Illumination Lab • Boyle’s Law LabRadical Functions 9.1 Simplifying Radical Expressions9.2 Adding, Subtracting, and Multiplying Radical Expressions9.3 Rationalizing Denominators and Simplifying Quotients of Radical Expressions9.4 Graphing and Combining Square Root Functions9.5 Solving Radical Equations9.6 Modeling with Square Root FunctionsTaking It to the Lab: Pendulum LabSequences and Series 10.1 Arithmetic Sequences10.2 Geometric Sequences10.3 Arithmetic Series10.4 Geometric SeriesTaking It to the Lab: Bouncing Ball Lab • Stacked Cups LabAdditional Topics 11.1 Absolute Value: Equations and Inequalities11.2 Performing Operations with Complex Numbers11.3 Pythagorean Theorem, Distance Formula, and Circles11.4 Ellipses and Hyperbolas11.5 Solving Nonlinear Systems of EquationsAPPENDICES A. Reviewing the Prerequisite MaterialB. Using a TI-83 or TI- 84 Graphing CalculatorC. Using StatCrunch