Elementary & Intermediate Algebra
Functions and Authentic Applications
Inbunden, Engelska, 2014
Av Jay Lehmann
3 979 kr
Finns i fler format (1)
Produktinformation
- Utgivningsdatum2014-02-21
- Mått225 x 285 x 40 mm
- Vikt2 395 g
- FormatInbunden
- SpråkEngelska
- Upplaga2
- FörlagPearson Education (US)
- ISBN9780321922724
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For more than twenty years, Jay Lehmann has taught at College of San Mateo, where he has received the Shiny Apple Award for excellence in teaching. He has worked on a NSF-funded grant to study classroom assessment and has performed research on collaborative directed-discovery learning. Jay has served as the newsletter editor for CMC3 (California Mathematics Council, Community College) for twelve years. He has presented at more than seventy-five conferences, including AMATYC, ICTCM, and T3, where he has discussed curve fitting and sung his "Number Guy" song. Jay plays in a rock band called The Procrastinistas, who play at various clubs in the San Francisco Bay Area, where Jay, his wife Keri, and son Dylan reside. He plays a number of instruments including bass, guitar, piano, violin, and baritone. In addition to his elementary, intermediate, and combined algebra textbooks, Jay is currently writing a heist novel for high school students, which he hopes will be published before Dylan outgrows it. Dylan, a devoted drummer and artist, drafted many of the cartoons that are included in Jay's textbooks. 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 has made it all worthwhile! I'm proud to have played even a small role in raising peoples' respect and enthusiasm for mathematics.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.
- PrefaceAcknowledgmentsIndex of Applications 1. Introduction To Modeling1.1 Variables And Constants1.2 Scattergrams1.3 Exact Linear Relationships1.4 Approximate Linear RelationshipsTaking It To The Lab: Climate Change Lab * Volume Lab * LinearGraphing Lab: Topic Of Your ChoiceChapter SummaryKey Points Of Chapter 1Chapter 1 Review ExercisesChapter 1 Test 2. Operations And Expressions2.1 Expressions2.2 Operations With Fractions2.3 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 OperationsTaking It To The Lab: Climate Change Lab * Stocks LabChapter SummaryKey Points Of Chapter 2Chapter 2 Review ExercisesChapter 2 TestCumulative Review Of Chapters 1 And 2 3. Using Slope To Graph Linear Equations3.1 Graphing Equations Of The Form y = mx + b3.2 Graphing Linear Models; Unit Analysis3.3 Slope Of A Line3.4 Using Slope To Graph Linear Equations3.5 Rate Of ChangeTaking It To The Lab: Climate Change Lab * WorkoutLab * Balloon LabChapter SummaryKey Points Of Chapter 3Chapter 3 Review ExercisesChapter 3 Test 4. Simplifying Expressions And Solving Equations4.1 Commutative, Associative, And Distributive Laws4.2 Simplifying Expressions4.3 Solving Linear Equations In One Variable4.4 Solving More Linear Equations In One Variable4.5 Comparing Expressions And Equations4.6 FormulasChapter SummaryKey Points Of Chapter 4Chapter 4 Review ExercisesChapter 4 TestCumulative Review Of Chapters 1—4 5. Linear Functions And Linear Inequalities In One Variable5.1 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 VariableTaking It To The Lab: Climate Change Lab * Golf Ball Lab *Rope Lab * Shadow Lab * Linear Lab: Topic Of Your ChoiceChapter SummaryKey Points Of Chapter 5Chapter 5 Review ExercisesChapter 5 Test 6. Systems Of Linear Equations And Systems Of Linear Inequalities6.1 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 LinearInequalities In Two VariablesTaking It To The Lab: Climate Change Lab * Sports Lab *Truck LabChapter SummaryKey Points Of Chapter 6Chapter 6 Review ExercisesChapter 6 test 383Cumulative Review of Chapters 1—6 7. Polynomial Functions And Properties Of Exponents7.1 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 DivisionTaking It To The Lab: Climate Change Lab * Projectile LabChapter SummaryKey Points Of Chapter 7Chapter 7 Review ExercisesChapter 7 TestMaking Sure You’re Ready For Intermediate Algebra:A Review Of Chapters 1—7 8. Factoring Polynomials And Solving Polynomial Equations8.1 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 ModelsChapter SummaryKey Points Of Chapter 8Chapter 8 Review ExercisesChapter 8 TestMaking Sure You’re Ready For Intermediate Algebra:A Review Of Chapters 1—8 9. Quadratic Functions9.1 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 FunctionsTaking It To The Lab: Climate Change Lab * ProjectileLab * Projectile Lab (Using A CBR Or CBL) * Water FlowLab * Quadratic Lab: Topic Of Your ChoiceChapter SummaryKey Points Of Chapter 9Chapter 9 Review ExercisesChapter 9 TestCumulative Review Of Chapters 1—9 10. Exponential Functions10.1 Integer Exponents10.2 Rational Exponents10.3 Graphing Exponential Functions10.4 Finding Equations Of Exponential Functions10.5 Using Exponential Functions To Model DataTaking It To The Lab: Stringed Instrument Lab * Cooling WaterLab * Exponential Lab: Topic Of Your ChoiceChapter SummaryKey Points Of Chapter 10Chapter 10 Review ExercisesChapter 10 Test 11. Logarithmic Functions11.1 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 LogarithmsTaking It To The Lab: China And India Populations Lab * FoldingPaper Lab * Exponential/Logarithmic Lab: Topic Of Your ChoiceChapter SummaryKey Points Of Chapter 11Chapter 11 Review ExercisesChapter 11 TestCumulative Review Of Chapters 1—11 12. Rational Functions12.1 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 VariationTaking It To The Lab: Climate Change Lab * IlluminationLab * Boyle’s Law Lab * Estimating P LabChapter SummaryKey Points Of Chapter 12Chapter 12 Review ExercisesChapter 12 Test 13. Radical Functions13.1 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 FunctionsTaking It To The Lab: Pendulum LabChapter SummaryKey Points Of Chapter 13Chapter 13 Review ExercisesChapter 13 Test 14. Sequences And Series14.1 Arithmetic Sequences14.2 Geometric Sequences14.3 Arithmetic Series14.4 Geometric SeriesTaking It To The Lab: Bouncing Ball Lab * Stacked Cups LabChapter SummaryKey Points Of Chapter 14Chapter 14 Review ExercisesChapter 14 TestCumulative Review Of Chapters 1—14 15. Additional Topics15.1 Absolute Value: Equations And InequalitiesKey Points Of Section 15.115.2 Performing Operations With Complex NumbersKey Points Of Section 15.215.3 Pythagorean Theorem, Distance Formula, And CirclesKey Points Of Section 15.315.4 Ellipses And HyperbolasKey Points Of Section 15.415.5 Solving Nonlinear Systems Of EquationsKey Points Of Section 15.5 A. Using A TI-83 Or TI-84 Graphing Calculator (Available Online Only)A.1 Turning A Graphing Calculator On Or OffA.2 Making The Screen Lighter Or DarkerA.3 Entering An EquationA.4 Graphing An EquationA.5 Tracing A Curve Without A ScattergramA.6 ZoomingA.7 Setting The Window FormatA.8 Plotting Points In A ScattergramA.9 Tracing A ScattergramA.10 Graphing Equations With A ScattergramA.11 Tracing A Curve With A ScattergramA.12 Turning A Plotter On Or OffA.13 Creating A TableA.14 Creating A Table For Two EquationsA.15 Using “Ask” In A TableA.16 Finding The Regression Curve For Some DataA.17 Plotting Points In Two ScattergramsA.18 Finding The Intersection Point(S) Of Two CurvesA.19 Finding The Minimum Point(S) Or Maximum Point(S) Of A CurveA.20 Storing A ValueA.21 Finding Any X-Intercepts Of A CurveA.22 Turning An Equation On Or OffA.23 Finding Coordinates Of PointsA.24 Graphing Equations With Axes “Turned Off”A.25 Entering An Equation By Using Yn ReferencesA.26 Responding To Error Messages Answers To Odd-Numbered ExercisesIndex