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Contents
Introduction to Modeling
1.1 Variables and Constants
1.2 Scatterplots
1.3 Exact Linear Relationships
1.4 Approximate Linear Relationships
Taking It to the Lab: Climate Change Lab • Volume Lab • Linear Graphing Lab: Topic of Your Choice
Operations and Expressions
2.1 Expressions
2.2 Operations with Fractions
2.3 Absolute Value and Adding Real Numbers
2.4 Change in a Quantity and Subtracting Real Numbers
2.5 Ratios, Percents, and Multiplying and Dividing Real Numbers
2.6 Exponents and Order of Operations
Taking It to the Lab: Climate Change Lab (continued from Chapter 1) • Stocks Lab
Using Slope to Graph Linear Equations
3.1 Graphing Equations of the Forms y = mx + b and x = a
3.2 Graphing Linear Models; Unit Analysis
3.3 Slope of a Line
3.4 Using Slope to Graph Linear Equations
3.5 Rate of Change
Taking It to the Lab: Climate Change Lab (continued from Chapter 2) • Workout Lab • Balloon Lab
Simplifying Expressions and Solving Equations
4.1 Simplifying Expressions
4.2 Simplifying More Expressions
4.3 Solving Linear Equations in One Variable
4.4 Solving More Linear Equations in One Variable
4.5 Comparing Expressions and Equations
4.6 Formulas
Linear Functions and Linear Inequalities in One Variable
5.1 Graphing Linear Equations
5.2 Functions
5.3 Function Notation
5.4 Finding Linear Equations
5.5 Finding Equations of Linear Models
5.6 Using Function Notation with Linear Models to Make Estimates and Predictions
5.7 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 Choice
Systems of Linear Equations and Systems of Linear Inequalities
6.1 Using Graphs and Tables to Solve Systems
6.2 Using Substitution to Solve Systems
6.3 Using Elimination to Solve Systems
6.4 Using Systems to Model Data
6.5 Perimeter, Value, Interest, and Mixture Problems
6.6 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 Lab
Polynomial Functions and Properties of Exponents
7.1 Adding and Subtracting Polynomial Expressions and Functions
7.2 Multiplying Polynomial Expressions and Functions
7.3 Powers of Polynomials; Product of Binomial Conjugates
7.4 Properties of Exponents
7.5 Dividing Polynomials: Long Division and Synthetic Division
Taking It to the Lab: Climate Change Lab (continued from Chapter 6) • Projectile Lab
Factoring Polynomials and Solving Polynomial Equations
8.1 Factoring Trinomials of the Form x2 + bx + c and Differences of Two Squares
8.2 Factoring Out the GCF; Factoring by Grouping
8.3 Factoring Trinomials of the Form ax2 + bx + c
8.4 Sums and Differences of Cubes; A Factoring Strategy
8.5 Using Factoring to Solve Polynomial Equations
8.6 Using Factoring to Make Predictions with Quadratic Models
Quadratic Functions
9.1 Graphing Quadratic Functions in Vertex Form
9.2 Graphing Quadratic Functions in Standard Form
9.3 Simplifying Radical Expressions
9.4 Using the Square Root Property to Solve Quadratic Equations
9.5 Solving Quadratic Equations by Completing the Square
9.6 Using the Quadratic Formula to Solve Quadratic Equations
9.7 Solving Systems of Linear Equations in Three Variables; Finding Quadratic Functions
9.8 Finding Quadratic Models
9.9 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 Choice
Exponential Functions
10.1 Integer Exponents
10.2 Rational Exponents
10.3 Graphing Exponential Functions
10.4 Finding Equations of Exponential Functions
10.5 Using Exponential Functions to Model Data
Taking It to the Lab: Stringed Instrument Lab • Cooling Water Lab • Exponential Lab: Topic of Your Choice
Logarithmic Functions
11.1 Composite Functions
11.2 Inverse Functions
11.3 Logarithmic Functions
11.4 Properties of Logarithms
11.5 Using the Power Property with Exponential Models to Make Predictions
11.6 More Properties of Logarithms
11.7 Natural Logarithms
Taking It to the Lab: China and India Populations Lab • Folding Paper Lab • Exponential/Logarithmic Lab:
Topic of Your Choice
Rational Functions
12.1 Finding the Domains of Rational Functions and Simplifying Rational Expressions
12.2 Multiplying and Dividing Rational Expressions; Converting Units
12.3 Adding and Subtracting Rational Expressions
12.4 Simplifying Complex Rational Expressions
12.5 Solving Rational Equations
12.6 Modeling with Rational Functions
12.7 Proportions; Similar Triangles
12.8 Variation
Taking It to the Lab: Climate Change Lab (continued from Chapter 9) • Illumination Lab • Boyle's Law Lab • Estimating 5 Lab
Radical Functions
13.1 Simplifying Radical Expressions
13.2 Adding, Subtracting, and Multiplying Radical Expressions
13.3 Rationalizing Denominators and Simplifying Quotients of Radical Expressions
13.4 Graphing and Combining Square Root Functions
13.5 Solving Radical Equations
13.6 Modeling with Square Root Functions
Taking It to the Lab: Pendulum Lab
Sequences and Series
14.1 Arithmetic Sequences
14.2 Geometric Sequences
14.3 Arithmetic Series
14.4 Geometric Series
Taking It to the Lab: Bouncing Ball Lab • Stacked Cups Lab
Additional Topics
15.1 Absolute Value: Equations and Inequalities
15.2 Performing Operations with Complex Numbers
15.3 Pythagorean Theorem, Distance Formula, and Circles
15.4 Ellipses and Hyperbolas
15.5 Solving Nonlinear Systems of Equations
APPENDICES
A. Using a TI-83 or TI-84 Graphing Calculator
B. Using StatCrunch
