1. Functions, Graphs, and Models; Linear Functions
INTEGRATED REVIEW TOPICS:
1. Write sets of numbers using descriptions or elements
2. Identify sets of real numbers as being integers, rational numbers, and/or irrational numbers
3. Graph numbers on a number line
4. Work with set operations
5. Find absolute values
6. Calculate with real numbers
7. Use properties of real numbers
8. Express inequalities as intervals and graph inequalities
9. Identify the coefficients of terms and constants in algebraic expressions
10. Combine like terms
11. Removing parentheses
12. Evaluate algebraic expressions
13. Plot points on a coordinate system
14. Use subscripts to represent fixed points
1.1 Functions and Models
1.2 Graphs of Functions
1.3 Linear Functions
1.4 Equations of Lines
2. Linear Models, Equations, and Inequalities
INTEGRATED REVIEW TOPICS:
1. Rounding and significant digits
2. Write fractions in lowest terms
3. Multiply and divide fractions
4. Add and subtract fractions
5. Identify expressions and equations
6. Solve basic linear equations using the addition or multiplication property
7. Use the multiplication or division properties of equations to solve linear equations
8. Solve more linear equations
9. Determine if a linear equation is a conditional equation, and identity, or a contradiction
10. Evaluate formulas for given values
11. Use properties of inequalities to solve linear inequalities
2.1 Algebraic and Graphical Solution of Linear Equations
2.2 Fitting Lines to Data Points: Modeling Linear Functions
2.3 Systems of Linear Equations in Two Variables
2.4 Solutions of Linear Inequalities
3. Quadratic, Piecewise-Defined, and Power Functions
INTEGRATED REVIEW TOPICS:
1. Use the properties of exponents with integers
2. Understand terminology related to polynomials
3. Add and subtract monomials and polynomials
4. Multiply monomials and polynomials
5. Factor out common factors
6. Factor by grouping
7. Factor polynomials
8. Factor trinomials
9. Radicals
10. Simplify radicals
11. Multiply and divide radicals
12. Add and subtract radicals
13. Convert between exponential and radical form
3.1 Quadratic Functions; Parabolas
3.2 Solving Quadratic Equations
3.3 Piecewise-Defined Functions and Power Functions
3.4 Quadratic and Power Models
4. Additional Topics with Functions
INTEGRATED REVIEW TOPICS:
1. Write rational expressions in lowest terms
2. Multiply and divide rational expressions
3. Add and subtract rational expressions with the same denominator
4. Find the least common denominator
5. Add and subtract rational expressions with the unlike denominators
6. Simplify complex fractions
7. Work with the complex number i
8. Add and subtract complex numbers
9. Multiply and divide complex numbers
4.1 Transformations of Graphs and Symmetry
4.2 Combining Functions; Composite Functions
4.3 One-to-One and Inverse Functions
4.4 Additional Equations and Inequalities
5. Exponential and Logarithmic Functions
INTEGRATED REVIEW TOPICS:
1. Use properties of exponents with real numbers
2. Simplify exponential expressions
3. Convert between standard notation and scientific notation
4. Simplify expressions involving scientific notation
5. Simplify expressions involving rational exponents
6. Divide polynomials
5.1 Exponential Functions
5.2 Logarithmic Functions; Properties of Logarithms
5.3 Exponential and Logarithmic Equations
5.4 Exponential and Logarithmic Models
5.5 Exponential Functions and Investing
5.6 Annuities; Loan Repayment
5.7 Logistic and Gompertz Functions
6. Higher-Degree Polynomial and Rational Functions
6.1 Higher-Degree Polynomial Functions
6.2 Modeling with Cubic and Quartic Functions
6.3 Solution of Polynomial Equations
6.4 Polynomial Equations Continued; Fundamental Theorem of Algebra
6.5 Rational Functions and Rational Equations
6.6 Polynomial and Rational Inequalities
7. Systems of Equations and Matrices
7.1 Systems of Linear Equations in Three Variables
7.2 Matrix Solution of Systems of Linear Equations
7.3 Matrix Operations
7.4 Inverse Matrices; Matrix Equations
7.5 Systems of/onlinear Equations
8. Special Topics: Systems of Inequalities and Linear Programming; Sequences and Series; Preparing for Calculus
8.1 Systems of Inequalities
8.2 Linear Programming: Graphical Methods
8.3 Sequences and Discrete Functions
8.4 Series
8.5 Preparing for Calculus
Appendix A: Basic Calculator Guide
Appendix B: Basic Guide to Excel 2003 and Excel 2010
Answers to Selected Exercises
Index