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the Graph of a Circle
Writing an Ellipse’s Equation in Standard Form
Identifying the Center, the Foci, and Axis Endpoints
Sketching the Graphs of Ellipses
Writing the Equation of a Hyperbola in Standard Form
Finding the Center, Foci, and Asymptotes of Hyperbolas
Sketching the Graphs of Hyperbolas
Chapter 11: Systems of Linear Equations
The Problems You’ll Work On
What to Watch Out For
Solving Systems of Two Linear Equations
Performing Row Operations on Linear Equations
Solving Systems of Equations with Row Echelon Form
Using Reduced Row Echelon Form to Solve Systems
Solving Systems of Linear Equations
Decomposing Fractions Using Systems of Equations
Chapter 12: Systems of Nonlinear Equations and Inequalities
The Problems You’ll Work On
What to Watch Out For
Determining Intersections of Parabolas and Lines
Finding Where Two Parabolas Meet
Solving for Intersections of Conics
Finding the Intersections of Exponential Functions
Using Graphing to Solve Systems of Inequalities
Chapter 13: Working with Complex Numbers
The Problems You’ll Work On
What to Watch Out For
Rewriting Powers of i as i, –i, 1, or –1
Operating on and Simplifying Complex Expressions
Multiplying and Simplifying Complex Numbers
Using Conjugates to Divide Complex Numbers
Solving for Complex Solutions in Quadratic Equations
Chapter 14: Matrices
The Problems You’ll Work On
What to Watch Out For
Determining the Dimension and Type of Matrix
Adding and Subtracting Matrices
Performing Scalar Multiplication on Matrices
Multiplying Matrices
Determining Inverses of Square Matrices
Dividing Matrices Using Inverses
Using Matrices to Solve Systems of Equations
Chapter 15: Sequences and Series
The Problems You’ll Work On
What to Watch Out For
Writing Terms of a Sequence Given a Rule
Finding a General Term for an Arithmetic Sequence
Writing a General Term for a Geometric Sequence
Recognizing Patterns in Sequences
Creating Recursively Defined Sequences
Writing More Terms of Special Sequences
Finding the Sum of the Terms in a Series
Summing Arithmetic Series
Determining the Sum of a Geometric Series
Computing the Sum of a Special Series
Using a Special Formula for the Sum of an Infinite Series
Chapter 16: Sets
The Problems You’ll Work On
What to Watch Out For
Creating the Elements of a Set from a Description
Performing Set Operations
Operating on Sets of Special Numbers
Using Venn Diagrams to Solve Problems Involving Sets
Enlisting Venn Diagrams to Solve Applications
Chapter 17: Counting Techniques and Probability
The Problems You’ll Work On
What to Watch Out For
Solving Problems Using the Multiplication Property
Counting How Many Using Permutations
Incorporating Combinations in Counting Problems
Performing a Binomial Expansion
Solving Probability Problems Using Counting Techniques
6 Part
