Student Solutions Manual for Elementary & 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.

• Introduction to Modeling 1.1 Variables and Constants1.2 Scatterplots1.3 Exact Linear Relationships1.4 Approximate Linear Relationships Taking It to the Lab: Climate Change Lab • Volume Lab • Linear Graphing Lab: Topic of Your ChoiceOperations and Expressions 2.1 Expressions2.2 Operations with Fractions2.3 Absolute Value and Adding Real Numbers2.4 Change in a Quantity and Subtracting Real Numbers2.5 Ratios, Percents, and Multiplying and Dividing Real Numbers2.6 Exponents and Order of Operations Taking It to the Lab: Climate Change Lab (continued from Chapter 1) • Stocks LabUsing Slope to Graph Linear Equations 3.1 Graphing Equations of the Forms y = mx + b and x = a3.2 Graphing Linear Models; Unit Analysis3.3 Slope of a Line3.4 Using Slope to Graph Linear Equations3.5 Rate of Change Taking It to the Lab: Climate Change Lab (continued from Chapter 2) • Workout Lab • Balloon LabSimplifying Expressions and Solving Equations 4.1 Simplifying Expressions4.2 Simplifying More Expressions4.3 Solving Linear Equations in One Variable4.4 Solving More Linear Equations in One Variable4.5 Comparing Expressions and Equations4.6 FormulasLinear Functions and Linear Inequalities in One Variable 5.1 Graphing Linear Equations5.2 Functions5.3 Function Notation5.4 Finding Linear Equations5.5 Finding Equations of Linear Models5.6 Using Function Notation with Linear Models to Make Estimates and Predictions5.7 Solving Linear Inequalities in One Variable Taking It to the Lab: Climate Change Lab (continued from Chapter 3) • Golf Ball Lab • Rope Lab • Shadow Lab • Linear Lab: Topic of Your ChoiceSystems of Linear Equations and Systems of Linear Inequalities 6.1 Using Graphs and Tables to Solve Systems6.2 Using Substitution to Solve Systems6.3 Using Elimination to Solve Systems6.4 Using Systems to Model Data6.5 Perimeter, Value, Interest, and Mixture Problems6.6 Linear Inequalities in Two Variables; Systems of Linear Inequalities in Two Variables Taking It to the Lab: Climate Change Lab (continued from Chapter 5) • Sports Lab • Truck LabPolynomial Functions and Properties of Exponents 7.1 Adding and Subtracting Polynomial Expressions and Functions7.2 Multiplying Polynomial Expressions and Functions7.3 Powers of Polynomials; Product of Binomial Conjugates7.4 Properties of Exponents7.5 Dividing Polynomials: Long Division and Synthetic Division Taking It to the Lab: Climate Change Lab (continued from Chapter 6) • Projectile LabFactoring Polynomials and Solving Polynomial Equations 8.1 Factoring Trinomials of the Form x2 + bx + c and Differences of Two Squares8.2 Factoring Out the GCF; Factoring by Grouping8.3 Factoring Trinomials of the Form ax2 + bx + c8.4 Sums and Differences of Cubes; A Factoring Strategy8.5 Using Factoring to Solve Polynomial Equations8.6 Using Factoring to Make Predictions with Quadratic ModelsQuadratic Functions 9.1 Graphing Quadratic Functions in Vertex Form9.2 Graphing Quadratic Functions in Standard Form9.3 Simplifying Radical Expressions9.4 Using the Square Root Property to Solve Quadratic Equations9.5 Solving Quadratic Equations by Completing the Square9.6 Using the Quadratic Formula to Solve Quadratic Equations9.7 Solving Systems of Linear Equations in Three Variables; Finding Quadratic Functions9.8 Finding Quadratic Models9.9 Modeling with Quadratic Functions Taking It to the Lab: Climate Change Lab (continued from Chapter 7) • Projectile Lab (continued from Chapter 7) • Projectile Lab (Using a CBR or CBL) • Water Flow Lab • Quadratic Lab: Topic of Your ChoiceExponential Functions 10.1 Integer Exponents10.2 Rational Exponents10.3 Graphing Exponential Functions10.4 Finding Equations of Exponential Functions10.5 Using Exponential Functions to Model Data Taking It to the Lab: Stringed Instrument Lab • Cooling Water Lab • Exponential Lab: Topic of Your ChoiceLogarithmic Functions 11.1 Composite Functions11.2 Inverse Functions11.3 Logarithmic Functions11.4 Properties of Logarithms11.5 Using the Power Property with Exponential Models to Make Predictions11.6 More Properties of Logarithms11.7 Natural Logarithms Taking It to the Lab: China and India Populations Lab • Folding Paper Lab • Exponential/Logarithmic Lab:Topic of Your ChoiceRational Functions 12.1 Finding the Domains of Rational Functions and Simplifying Rational Expressions12.2 Multiplying and Dividing Rational Expressions; Converting Units12.3 Adding and Subtracting Rational Expressions12.4 Simplifying Complex Rational Expressions12.5 Solving Rational Equations12.6 Modeling with Rational Functions12.7 Proportions; Similar Triangles12.8 Variation Taking It to the Lab: Climate Change Lab (continued from Chapter 9) • Illumination Lab • Boyle’s Law Lab • Estimating 5 LabRadical Functions 13.1 Simplifying Radical Expressions13.2 Adding, Subtracting, and Multiplying Radical Expressions13.3 Rationalizing Denominators and Simplifying Quotients of Radical Expressions13.4 Graphing and Combining Square Root Functions13.5 Solving Radical Equations13.6 Modeling with Square Root Functions Taking It to the Lab: Pendulum LabSequences and Series 14.1 Arithmetic Sequences14.2 Geometric Sequences14.3 Arithmetic Series14.4 Geometric Series Taking It to the Lab: Bouncing Ball Lab • Stacked Cups LabAdditional Topics 15.1 Absolute Value: Equations and Inequalities15.2 Performing Operations with Complex Numbers15.3 Pythagorean Theorem, Distance Formula, and Circles15.4 Ellipses and Hyperbolas15.5 Solving Nonlinear Systems of EquationsAPPENDICES A. Using a TI-83 or TI-84 Graphing CalculatorB. Using StatCrunch