Skip to content
- Solve Radical Equations
- Solve Equations Quadratic in Form
- Solve Equations by Factoring
1.5 Solving Inequalities
- Use Interval Notation
- Use Properties of Inequalities
- Solve Inequalities
- Solve Combined Inequalities
1.6 Equations and Inequalities Involving Absolute Value
- Solve Equations Involving Absolute Value
- Solve Inequalities Involving Absolute Value
1.7 Problem Solving: Interest, Mixture, Uniform Motion, Constant Rate Job Applications
- Translate Verbal Descriptions into Mathematical Expressions
- Solve Interest Problems
- Solve Mixture Problems
- Solve Uniform Motion Problems
- Solve Constant Rate Job Problems
2. Graphs
2.1 The Distance and Midpoint Formulas
- Use the Distance Formula
- Use the Midpoint Formula
2.2 Graphs of Equations in Two Variables; Intercepts; Symmetry
- Graph Equations by Plotting Points
- Find Intercepts from a Graph
- Find Intercepts from an Equation
- Test an Equation for Symmetry with Respect to the x-Axis, y-Axis, and the Origin
- Know How to Graph Key Equations
2.3 Lines
- Calculate and Interpret the Slope of a Line
- Graph Lines Given a Point and the Slope
- Find the Equation of a Vertical Line
- Use the Point-Slope Form of a Line
- Identify Horizontal Lines
- Use the Slope-Intercept Form of a Line
- Find an Equation of a Line Given Two Points
- Graph Lines Written in General Form Using Intercepts
- Find Equations of Parallel Lines
- Find Equations of Perpendicular Lines
2.4 Circles
- Write the Standard Form of the Equation of a Circle
- Graph a Circle
- Work with the General Form of the Equation of a Circle
2.5 Variation
- Construct a Model Using Direct Variation
- Construct a Model Using Inverse Variation
- Construct a Model Using Joint Variation
3. Functions and Their Graphs
3.1 Functions
- Describe a Relation
- Determine Whether a Relation Represents a Function
- Use Function Notation
- Find the Value of a Function
- Find the Difference Quotient of a Function
- Find the Domain of a Function Defined by an Equation
- Form the Sum, Difference, Product, and Quotient of Two Functions
3.2 The Graph of a Function
- Identify the Graph of a Function
- Obtain Information from or about the Graph of a Function
3.3 Properties of Functions
- Identify Even and Odd Functions from a Graph
- Identify Even and Odd Functions from an Equation
- Use a Graph to Determine Where a Function Is Increasing, Decreasing, or Constant
- Use a Graph to Locate Local Maxima and Local Minima
- Use a Graph to Locate the Absolute Maximum and the Absolute Minimum
- Use a Graphing Utility to Approximate Local Maxima and Local Minima
- Determine Where a Function Is Increasing or Decreasing
- Find the Average Rate of Change of a Function
3.4 Library of Functions; Piecewise-defined Functions
- Graph the Functions Listed in the Library of Functions
- Analyze a Piecewise-defined Function
3.5 Graphing Techniques: Transformations (Page 254)
- Graph Functions Using Vertical and Horizontal Shifts
- Graph Functions Using Compressions and Stretches
- Graph Functions Using Reflections about the x-Axis and the y-Axis
3.6 Mathematical Models: Building Functions
- Build and Analyze Functions
4. Linear and Quadratic Functions
4.1 Properties of Linear Functions and Linear Models
- Graph Linear Functions
- Use Average Rate of Change to Identify Linear Functions
- Determine Whether a Linear Function Is Increasing, Decreasing, or Constant
- Build Linear Models from Verbal Descriptions
4.2 Building Linear Models from Data
- Draw and Interpret Scatter Plots
- Distinguish Between Linear and Nonlinear Relations
- Use a Graphing Utility to Find the Line of Best Fit
4.3 Quadratic Functions and Their Properties
- Graph a Quadratic Function Using Transformations
- Identify the Vertex and Axis of Symmetry of a Parabola
- Graph a Quadratic Function Using Its Vertex, Axis, and Intercepts
- Find a Quadratic Function Given Its Vertex and One Other Point
- Find the Maximum or Minimum Value of a Quadratic Function
4.4 Building Quadratic Models from Verbal Descriptions and from Data
- Build Quadratic Models from Verbal Descriptions
- Build Quadratic Models from Data
4.5 Inequalities Involving Quadratic Functions
- Solve Inequalities Involving a Quadratic Function
5. Polynomial and Rational Functions
5.1 Polynomial Functions
- Identify Polynomial Functions and Their Degree
- Graph Polynomial Functions Using Transformations
- Identify the Real Zeros of a Polynomial Function and Their Multiplicity
5.2 Graphing Polynomial Functions; Models
- Graph a Polynomial Function
- Graph a Polynomial Function Using a Graphing Utility
- Build Cubic Models from Data
5.3 Properties of Rational Functions
- Find the Domain of a Rational Function
- Find the Vertical Asymptotes of a Rational Function
- Find a Horizontal or an Oblique Asymptote of a Rational Function
5.4 The Graph of a Rational Function
- Graph a Rational Function
- Solve Applied Problems Involving Rational Functions
5.5 Polynomial and Rational Inequalities
- Solve Polynomial Inequalities
- Solve Rational Inequalities
5.6 The Real Zeros of a Polynomial Function
- Use the Remainder and Factor Theorems
- Use Descartes’ Rule of Signs to Determine the Number of Positive and Negative Real Zeros
- Use the Rational Zeros Theorem to List the Potential Rational Zeros
- Find the Real Zeros of a Polynomial Function
- Solve Polynomial Equations
- Use the Theorem for Bounds on Zeros
- Use the Intermediate Value Theorem
5.7 Complex Zeros; Fundamental Theorem of Algebra
- Use the Conjugate Pairs Theorem
- Find a Polynomial Function with Specified Zeros
- Find the Complex Zeros of a Polynomial Function
6. Exponential and Logarithmic Functions
6.1 Composite Functions
- Form a Composite Function
- Find the Domain of a Composite Function
6.2 One-to-One Functions; Inverse Functions
- Determine Whether a Function Is One-to-One
- Obtain the Graph of the Inverse Function from the Graph of a One-to-One Function
- Verify an Inverse Function
- Find the Inverse of a Function Defined by an Equation
6.3 Exponential Functions
- Evaluate Exponential Functions
- Graph Exponential Functions
- Define the Number ee
- Solve Exponential Equations
6.4 Logarithmic Functions
- Change Exponential Statements to Logarithmic Statements and Vice Versa
- Evaluate Logarithmic Expressions
- Determine the Domain of a Logarithmic Function
- Graph Logarithmic Functions
- Solve Logarithmic Equations
6.5 Properties of Logarithms
- Work with the Properties of Logarithms
- Write a Logarithmic Expression as a Sum or Difference of Logarithms
- Write a Logarithmic Expression as a Single Logarithm
- Evaluate Logarithms Whose Base Is Neither 10 Nor ee
6.6 Logarithmic and Exponential Equations
- Solve Logarithmic Equations
- Solve Exponential Equations
- Solve Logarithmic and Exponential Equations Using a Graphing Utility
6.7 Financial Models
- Determine the Future Value of a Lump Sum of Money
- Calculate Effective Rates of Return
- Determine the Present Value of a Lump Sum of Money
- Determine the Rate of Interest or the Time Required to Double a Lump Sum of Money
6.8 Exponential Growth and Decay Models; Newton’s Law; Logistic Growth and Decay Models
- Model Populations That Obey the Law of Uninhibited Growth
- Model Populations That Obey the Law of Uninhibited Decay
- Use Newton’s Law of Cooling
- Use Logistic Models
6.9 Building Exponential, Logarithmic, and Logistic Models from Data
- Build an Exponential Model from Data
- Build a Logarithmic Model from Data
- Build a Logistic Model from Data
7. Analytic Geometry
7.1 Conics
- Know the Names of the Conics
7.2 The Parabola
- Analyze Parabolas with Vertex at the Origin
- Analyze Parabolas with Vertex at (h,k)(h, k)
- Solve Applied Problems Involving Parabolas
7.3 The Ellipse
- Analyze Ellipses with Center at the Origin
- Analyze Ellipses with Center at (h,k)(h, k)
- Solve Applied Problems Involving Ellipses
7.4 The Hyperbola
- Analyze Hyperbolas with Center at the Origin
- Find the Asymptotes of a Hyperbola
- Analyze Hyperbolas with Center at (h,k)(h, k)
- Solve Applied Problems Involving Hyperbolas
8. Systems of Equations and Inequalities
8.1 Systems of Linear Equations: Substitution and Elimination
- Solve Systems of Equations by Substitution
- Solve Systems of Equations by Elimination
- Identify Inconsistent Systems of Equations Containing Two Variables
- Express the Solution of a System of Dependent Equations Containing Two Variables
- Solve Systems of Three Equations Containing Three Variables
- Identify Inconsistent Systems of Equations Containing Three Variables
- Express the Solution of a System of Dependent Equations Containing Three Variables
8.2 Systems of Linear Equations: Matrices
- Write the Augmented Matrix of a System of Linear Equations
- Write the System of Equations from the Augmented Matrix
- Perform Row Operations on a Matrix
- Solve a System of Linear Equations Using Matrices
8.3 Systems of Linear Equations: Determinants
- Evaluate 2×2 Determinants
- Use Cramer’s Rule to Solve a System of Two Equations Containing Two Variables
- Evaluate 3×3 Determinants
- Use Cramer’s Rule to Solve a System of Three Equations Containing Three Variables
- Know Properties of Determinants
8.4 Matrix Algebra
- Find the Sum and Difference of Two Matrices
- Find Scalar Multiples of a Matrix
- Find the Product of Two Matrices
- Find the Inverse of a Matrix
- Solve a System of Linear Equations Using an Inverse Matrix
8.5 Partial Fraction Decomposition
- Decompose PQ\frac{P}{Q} Where QQ Has Only Nonrepeated Linear Factors
- Decompose PQ\frac{P}{Q} Where QQ Has Repeated Linear Factors
- Decompose PQ\frac{P}{Q} Where QQ Has a Nonrepeated Irreducible Quadratic Factor
- Decompose PQ\frac{P}{Q} Where QQ Has a Repeated Irreducible Quadratic Factor
8.6 Systems of Nonlinear Equations
- Solve a System of Nonlinear Equations Using Substitution
- Solve a System of Nonlinear Equations Using Elimination
8.7 Systems of Inequalities
- Graph an Inequality
- Graph a System of Inequalities
8.8 Linear Programming
- Set Up a Linear Programming Problem
- Solve a Linear Programming Problem
9. Sequences; Induction; the Binomial Theorem
9.1 Sequences
- List the First Several Terms of a Sequence
- List the Terms of a Sequence Defined by a Recursive Formula
- Use Summation Notation
- Find the Sum of a Sequence
9.2 Arithmetic Sequences
- Determine Whether a Sequence Is Arithmetic
- Find a Formula for an Arithmetic Sequence
- Find the Sum of an Arithmetic Sequence
9.3 Geometric Sequences; Geometric Series
- Determine Whether a Sequence Is Geometric
- Find a Formula for a Geometric Sequence
- Find the Sum of a Geometric Sequence
- Determine Whether a Geometric Series Converges or Diverges
- Solve Annuity Problems
9.4 Mathematical Induction
- Prove Statements Using Mathematical Induction
9.5 The Binomial Theorem
- Evaluate (nj)\binom{n}{j}
- Use the Binomial Theorem
10. Counting and Probability
10.1 Counting
- Find All the Subsets of a Set
- Count the Number of Elements in a Set
- Solve Counting Problems Using the Multiplication Principle
10.2 Permutations and Combinations
- Solve Counting Problems Using Permutations Involving nn Distinct Objects
- Solve Counting Problems Using Combinations
- Solve Counting Problems Using Permutations Involving nn Nondistinct Objects
10.3 Probability
- Construct Probability Models
- Compute Probabilities of Equally Likely Outcomes
- Find Probabilities of the Union of Two Events
- Use the Complement Rule to Find Probabilities