Study Skills: Your Brain Can Learn Mathematics
Chapter R: Prealgebra Review
R.1 Fractions
R.2 Decimals and Percents
1. The Real Number System
1.1 Exponents, Order of Operations, and Inequality
Study Skills: Homework: How, Why, and When
1.2 Variables, Expressions, and Equations
Study Skills: Taking Lecture Notes
1.3 Real Numbers and the Number Line
Study Skills: Using Study Cards
1.4 Adding Real Numbers
1.5 Subtracting Real Numbers
1.6 Multiplying and Dividing Real Numbers
Summary Exercises on Operations with Real Numbers
1.7 Properties of Real Numbers
1.8 Simplifying Expressions
Study Skills: Reviewing a Chapter
Study Skills: Preparing for Tests
2. Equations, Inequalities, and Applications
2.1 The Addition Property of Equality
2.2 The Multiplication Property of Equality
2.3 More on Solving Linear Equations
Study Skills: Using Study Cards Revisited
2.4 An Introduction to Applications of Linear Equations
2.5 Formulas and Additional Applications from Geometry
2.6 Ratio, Proportion, and Percent
Summary Exercises on Solving Applied Problems
2.7 Solving Linear Inequalities
Study Skills: Managing Your Time
Study Skills: Tips for Taking Math Tests
3. Graphs of Linear Equations and Inequalities; Functions
3.1 Reading Graphs; Linear Equations in Two Variables
3.2 Graphing Linear Equations in Two Variables
3.3 Slope of a Line
3.4 Equations of Lines
Summary Exercises on Linear Equations and Graphs
3.5 Graphing Linear Inequalities in Two Variables
3.6 Introduction to Functions
Study Skills: Analyzing Your Test Results
4. Systems of Linear Equations and Inequalities
4.1 Solving Systems of Linear Equations by Graphing
4.2 Solving Systems of Linear Equations by Substitution
4.3 Solving Systems of Linear Equations by Elimination
Summary Exercises of Solving Systems of Linear Equations
4.4 Applications of Linear Systems
4.5 Solving Systems of Linear Inequalities
5. Exponents and Polynomials
5.1 Adding and Subtracting Polynomials
5.2 The Product Rule and Power Rules for Exponents
5.3 Multiplying Polynomials
5.4 Special Products
5.5 Integer Exponents and the Quotient Rule
Summary Exercises on the Rules for Exponents
5.6 Dividing a Polynomial by a Monomial
5.7 Dividing a Polynomial by a Polynomial
5.8 An Application of Exponents: Scientific Notation
6. Factoring and Applications
6.1 Factors; The Greatest Common Factor
6.2 Factoring Trinomials
6.3 Factoring Trinomials by Grouping
6.4 Factoring Trinomials Using FOIL
6.5 Special Factoring Techniques
6.6 A General Approach to Factoring
6.7 Solving Quadratic Equations by Factoring
6.8 Applications of Quadratic Equations
Study Skills: Preparing for Your Math Final Exam
7. Rational Expressions and Functions
7.1 Rational Expressions and Functions; Multiplying and Dividing
Study Skills: Making a Mind Map
7.2 Adding and Subtracting Rational Expressions
7.3 Complex Functions
7.4 Equations with Rational Expressions and Graphs
Summary Exercises on Rational Expressions and Equations
7.5 Applications of Rational Expressions
7.6 Variation
8. Equations, Inequalities, and Systems Revisited
8.1 Review of Solving Linear Equations and Inequalities
8.2 Set Operations and Compound Inequalities
8.3 Absolute Value Equations and Inequalities
Summary Exercises on Solving Linear and Absolute Value Equations and Inequalities
8.4 Review of Systems of Linear Equations in Two Variables
8.5 Systems of Linear Equations in Three Variables; Applications
8.6 Solving Systems of Linear Equations by Matrix Methods
9. Roots, Radicals, and Root Functions
9.1 Radical Expressions and Graphs
9.2 Rational Exponents
9.3 Simplifying Radical Expressions
9.4 Adding and Subtracting Radical Expressions
9.5 Multiplying and Dividing Radical Expressions
Summary Exercises on Operations with Radicals and Rational Exponents
9.6 Solving Equations with Radicals
9.7 Complex Numbers
10. Quadratic Equations, Inequalities, and Functions
10.1 Solving Quadratic Equations by the Square Root Property
10.2 Solving Quadratic Equations by Completing the Square
10.3 Solving Quadratic Equations by the Quadratic Formula
10.4 Equations Quadratic in Form
Summary Exercises on Solving Quadratic Equations
10.5 Formulas and Further Applications
10.6 Graphs of Quadratic Functions
10.7 More about Parabolas and Their Applications
10.8 Polynomial and Rational Inequalities
11. Inverse, Exponential, and Logarithmic Functions
11.1 Inverse Functions
11.2 Exponential Functions
11.3 Logarithmic Functions
11.4 Properties of Logarithms
11.5 Common and Natural Logarithms
11.6 Exponential and Logarithmic Equations; Further Applications
12. Nonlinear Functions, Conic Sections, and Nonlinear Systems
12.1 Additional Graphs of Functions; Operations and Composition
12.2 The Circle and the Ellipse
12.3 The Hyperbola and Other Functions Defined by Radicals
12.4 Nonlinear Systems of Equations
12.5 Second-Degree Inequalities and Systems of Inequalities
Appendix A. Review of Exponents, Polynomials, and Factoring
Appendix B. Strategies for Problem Solving
Appendix C. Synthetic Division
