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Mary Jane Sterling. Algebra II: 1001 Practice Problems For Dummies (+ Free Online Practice)
Algebra II: 1001 Practice Problems For Dummies® To view this book's Cheat Sheet, simply go to www.dummies.com and search for “Algebra II: 1001 Practice Problems For Dummies Cheat Sheet” in the Search box. Table of Contents
Guide
Pages
Introduction
What You’ll Find
How This Workbook Is Organized
Part 1: Questions
Part 2: Answers
Beyond the Book
Where to Go for Additional Help
The Questions
Reviewing Algebra Basics
The Problems You’ll Work On
What to Watch Out For
Multiplying Binomials and Trinomials
Using Pascal’s Triangle to Multiply Binomials
Solving Linear Equations
Solving Linear Equations for Variables
Solving Linear Inequalities
Making Radical Expressions Simpler
Working with Complex Expressions
Solving Quadratic Equations and Nonlinear Inequalities
The Problems You’ll Work On
What to Watch Out For
Applying the Square Root Rule on Quadratic Equations
Solving Quadratic Equations Using Factoring
Using the Quadratic Formula to Solve Equations
Recognizing and Solving Quadratic-Like Equations
Completing the Square to Solve Quadratic Equations
Combining Methods When Solving Quadratic Equations
Solving Quadratic Inequalities Using Number Lines
Solving Radical and Rational Equations
The Problems You’ll Work On
What to Watch Out For
Solving Rational Equations
Taking on Radical Equations Involving One Radical Term
Solving Radical Equations with Multiple Radical Terms
Graphs and Equations of Lines
The Problems You’ll Work On
What to Watch Out For
Sketching Lines Using a Point and Slope
Writing Equations of Lines Given Point and Slope
Writing Equations of Lines Given Two Points
Finding Equations of Parallel Lines
Writing Equations of Perpendicular Lines
Functions
The Problems You’ll Work On
What to Watch Out For
Determining a Function’s Domain and Range
Finding Inverses of Functions
Recognizing Even and Odd Functions
Performing the Composition Operation on Functions
Creating a Difference-Quotient and Simplifying
Evaluating Piecewise Functions for Particular Inputs
Quadratic Functions and Relations
The Problems You’ll Work On
What to Watch Out For
Determining the Vertex and Intercepts of a Parabola
Writing Equations of Parabolas in a Standard Form
Sketching Graphs of Parabolas
Using Quadratic Equations in Applications
Polynomial Functions and Equations
The Problems You’ll Work On
What to Watch Out For
Recognizing the Intercepts of Polynomials
Factoring by Grouping to Solve for Intercepts
Applying the Rational Root Theorem to Find Roots
Performing Synthetic Division to Factor Polynomials
Evaluating Polynomials for Input Values
Investigating End-Behavior of Polynomials
Sketching the Graphs of Polynomial Functions
Rational Functions
The Problems You’ll Work On
What to Watch Out For
Investigating the Domain of a Rational Function
Determining a Function’s Removable Discontinuity
Evaluating a Function When x Is Infinitely Large or Small
Determining a Function’s Infinite Limit
Writing Equations of Asymptotes
Adding Oblique Asymptotes to the Mix
Sketching the Graphs of Rational Functions
Exponential and Logarithmic Functions
The Problems You’ll Work On
What to Watch Out For
Evaluating Exponential Functions for Input
Evaluating Exponential Functions in Base e
Sketching the Graphs of Exponential Functions
Finding Values of Logarithmic Expressions for Given Input
Evaluating Natural Logarithms in Base e
Sketching the Graphs of Log Functions
Rewriting a Log Function as Its Exponential Inverse
Changing Exponential Functions to Logarithmic Inverses
Solving Exponential Equations
Solving Logarithmic Equations
Conic Sections
The Problems You’ll Work On
What to Watch Out For
Rewriting Equations of Parabolas in Standard Form
Determining a Vertex, Focus, Directrix, and Axis of Symmetry
Sketching the Graph of a Parabola
Rewriting a Circle’s Equation in Standard Form
Identifying the Center and Radius of a Circle
Sketching 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
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
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
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
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
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
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
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
The Answers
The Answers
Index. A
B
C
D
E
F
G
H
I
L
M
N
O
P
Q
R
S
T
U
V
W
About the Author
Dedication
Author’s Acknowledgments
WILEY END USER LICENSE AGREEMENT
