Pre-Calculus All-in-One For Dummies: Book + Chapter Quizzes Online [1 ed.] 1394201249, 9781394201242

Table of contents :
Title Page
Copyright Page
Table of Contents
Introduction
About This Book
Foolish Assumptions
Icons Used in This Book
Beyond the Book
Where to Go from Here
Unit 1: Getting Started with Pre-Calculus
Chapter 1: Preparing for Pre-Calculus
Recapping Pre-Calculus: An Overview
Checking in on Number Basics and Processes
Understanding the multitude of number types: Terms to know
Looking at the fundamental operations you can perform on numbers
Knowing the properties of numbers: Truths to remember
Looking at Visual Statements: When Math Follows Form with Function
Using basic terms and concepts
Graphing linear equalities and inequalities
Gathering information from graphs
Getting Yourself a Graphing Calculator
Practice Questions Answers and Explanations
Whaddya Know? Chapter 1 Quiz
Answers to Chapter 1 Quiz
Chapter 2: Operating with Real Numbers
Describing Numbers on the Number Line
Solving Inequalities
Recapping inequality how-tos
Solving equations and inequalities involving absolute value
Expressing solutions for inequalities with interval notation
Working with Radicals and Exponents
Defining and relating radicals and exponents
Rewriting radicals as exponents (or, creating rational exponents)
Getting a radical out of a denominator: Rationalizing
Practice Questions Answers and Explanations
Whaddya Know? Chapter 2 Quiz
Answers to Chapter 2 Quiz
Chapter 3: Cementing the Building Blocks of Pre-Calculus Functions
Identifying Special Function Types and Their Graphs
Even and odd functions
One-to-one functions
Dealing with Parent Functions and Their Graphs
Linear functions
Quadratic functions
Square-root functions
Absolute-value functions
Cubic functions
Cube-root functions
Setting the Stage for Rational Functions
Searching for vertical asymptotes and holes
Searching for horizontal asymptotes
Seeking out oblique asymptotes
Locating the x- and y-intercepts
Putting the Results to Work: Graphing Rational Functions
Practice Questions Answers and Explanations
Whaddya Know? Chapter 3 Quiz
Answers to Chapter 3 Quiz
Chapter 4: Operating on Functions
Transforming the Parent Graphs
Stretching and flattening
Graphing translations
Seeing reflections
Combining various transformations (a transformation in itself!)
Transforming functions point by point
Sharpen Your Scalpel: Operating on Functions
Adding and subtracting
Multiplying and dividing
Breaking down a composition of functions
Adjusting the domain and range of combined functions (if applicable)
Turning Inside Out with Inverse Functions
Graphing an inverse
Inverting a function to find its inverse
Verifying an inverse
Practice Questions Answers and Explanations
Whaddya Know? Chapter 4 Quiz
Answers to Chapter 4 Quiz
Unit 2: Getting the Grip on Graphing
Chapter 5: Graphing Polynomial Functions
Understanding Degrees and Roots
Factoring a Polynomial Expression
Always the first step: Looking for a GCF
Unwrapping the box containing a trinomial
Recognizing and factoring special polynomials
Grouping to factor four or more terms
Finding the Roots of a Factored Equation
Cracking a Quadratic Equation When It Won’t Factor
Using the quadratic formula
Completing the square
Solving Polynomial Equations with a Degree Higher Than Two
Counting a polynomial’s total roots
Tallying the real roots: Descartes’s rule of signs
Accounting for imaginary roots: The fundamental theorem of algebra
Guessing and checking the real roots
Put It in Reverse: Using Solutions to Find Factors
Graphing Polynomials
Graphing when all the roots are real numbers
Graphing when roots are imaginary numbers: Combining all techniques
Practice Questions Answers and Explanations
Whaddya Know? Chapter 5 Quiz
Answers to Chapter 5 Quiz
Chapter 6: Exponential and Logarithmic Functions
Exploring Exponential Functions
Searching the ins and outs of exponential functions
Graphing and transforming exponential functions
Logarithms: The Inverse of Exponential Functions
Getting a better handle on logarithms
Managing the properties and identities of logs
Changing a log’s base
Calculating a number when you know its log: Inverse logs
Graphing logs
Base Jumping to Simplify and Solve Equations
Stepping through the process of solving exponential equations
Solving logarithmic equations
Growing Exponentially: Word Problems in the Kitchen
Practice Questions Answers and Explanations
Whaddya Know? Chapter 6 Quiz
Answers to Chapter 6 Quiz
Chapter 7: Piece-Wise and Greatest-Integer Functions
Looking at Functions with More Than One Rule: Piece-Wise Functions
Graphing piece-wise functions
Using piece-wise functions in real-world applications
Grappling with the Greatest-Integer Function
Observing the greatest-integer function
Making use of the greatest-integer function
Practice Questions Answers and Explanations
Whaddya Know? Chapter 7 Quiz
Answers to Chapter 7 Quiz
Unit 3: The Essentials of Trigonometry
Chapter 8: Circling In on Angles
Introducing Radians and Relating to Degrees
Trig Ratios: Taking Right Triangles a Step Further
Following the sine
Looking for a cosine
Going out on a tangent
Discovering the flip side: Reciprocal trig functions
Working in reverse: Inverse trig functions
Defining ranges of inverse trig functions
Understanding How Trig Ratios Work on the Coordinate Plane
Digesting Special Triangle Ratios
The 45er: Isosceles right triangle
The 30–60–90 right triangle
Triangles and the Unit Circle: Working Together for the Common Good
Placing the major angles correctly
Retrieving trig-function values on the unit circle
Practice Questions Answers and Explanations
Whaddya Know? Chapter 8 Quiz
Answers to Chapter 8 Quiz
Chapter 9: Homing In on the Friendliest Angles
Building on the Unit Circle
Familiarizing yourself with the most common angles
Finding the reference angle to solve for functions of angles
Relating reference angles to their parents
Drawing uncommon angles
Solving Equations Using Inverse Functions
Measuring Arcs: When the Circle Is Put in Motion
Practice Questions Answers and Explanations
Whaddya Know? Chapter 9 Quiz
Answers to Chapter 9 Quiz
Chapter 10: Picturing Basic Trig Functions and Reciprocal Functions
Drafting the Sine and Cosine Parent Graphs
Sketching sine
Looking at cosine
Graphing Tangent and Cotangent Parent Graphs
Tackling tangent
Clarifying cotangent
Putting Secant and Cosecant in Parent Graphs Pictures
Graphing secant
Checking out cosecant
Practice Questions Answers and Explanations
Whaddya Know? Chapter 10 Quiz
Answers to Chapter 10 Quiz
Chapter 11: Graphing and Transforming Trig Functions
Transforming Trig Graphs
Messing with sine and cosine graphs
Tweaking tangent and cotangent graphs
Transforming the graphs of secant and cosecant
Practice Questions Answers and Explanations
Whaddya Know? Chapter 11 Quiz
Answers to Chapter 11 Quiz
Unit 4: Identities and Special Triangles
Chapter 12: Identifying with Trig Identities: The Basics
Keeping the End in Mind: A Quick Primer on Identities
Lining Up the Means to the End: Basic Trig Identities
Reciprocal and ratio identities
Pythagorean identities
Even/odd identities
Co-function identities
Periodicity identities
Tackling Difficult Trig Proofs: Some Techniques to Know
Dealing with demanding denominators
Going solo on each side
Practice Questions Answers and Explanations
Whaddya Know? Chapter 12 Quiz
Answers to Chapter 12 Quiz
Chapter 13: Advancing with Advanced Identities
Finding Trig Functions of Sums and Differences
Searching out the sine of a  b 
Calculating the cosine of a  b 
Taming the tangent of a  b 
Doubling an Angle and Finding Its Trig Value
Finding the sine of a doubled angle
Calculating cosines for two
Squaring your cares away
Having twice the fun with tangents
Taking Trig Functions of Common Angles Divided in Two
A Glimpse of Calculus: Traveling from Products to Sums and Back
Expressing products as sums (or differences)
Transporting from sums (or differences) to products
Eliminating Exponents with Power-Reducing Formulas
Practice Questions Answers and Explanations
Whaddya Know? Chapter 13 Quiz
Answers to Chapter 13 Quiz
Chapter 14: Getting the Slant on Oblique Triangles
Solving a Triangle with the Law of Sines
When you know two angle measures
When you know two consecutive side lengths
Conquering a Triangle with the Law of Cosines
SSS: Finding angles using only sides
SAS: Tagging the angle in the middle (and the two sides)
Filling in the Triangle by Calculating Area
Finding area with two sides and an included angle (for SAS scenarios)
Using Heron’s Formula (for SSS scenarios)
Making Triangles Work for You
Practice Questions Answers and Explanations
Whaddya Know? Chapter 14 Quiz
Answers to Chapter 14 Quiz
Unit 5: Analytic Geometry
Chapter 15: Coordinating with Complex Numbers
Understanding Real versus Imaginary
Combining Real and Imaginary: The Complex Number System
Simplifying expressions when complex numbers are created
Performing operations with complex numbers
Graphing Complex Numbers
Grasping the usefulness of complex numbers
Solving quadratic equations with complex answers
Analyzing the graphs of quadratics
Keeping pace with polynomials
Practice Questions Answers and Explanations
Whaddya Know? Chapter 15 Quiz
Answers to Chapter 15 Quiz
Chapter 16: Warming Up to Polar Coordinates
Plotting around a Pole: Polar Coordinates
Wrapping your brain around the polar coordinate plane
Graphing polar coordinates with negative values
Changing to and from polar coordinates
Picturing polar equations
Circling around with two circles
Spiraling and planting roses
Practice Questions Answers and Explanations
Whaddya Know? Chapter 16 Quiz
Answers to Chapter 16 Quiz
Chapter 17: Relating Conics to Sliced Cones
Cone to Cone: Identifying the Four Conic Sections
Picturing the conics — graph form
Writing conic equations — printed form
Going Round and Round: Graphing Circles
Graphing circles at the origin
Graphing circles away from the origin
Writing in center–radius form
Riding the Ups and Downs with Parabolas
Labeling the parts
Understanding the characteristics of a standard parabola
Plotting the variations: Parabolas all over the plane
The vertex, axis of symmetry, focus, and directrix
Identifying the extremes of vertical parabolas
The Fat and the Skinny on the Ellipse
Labeling ellipses and expressing them with algebra
Identifying the parts from the equation
Join Two Curves and Get a Hyperbola
Visualizing the two types of hyperbolas and their bits and pieces
Finding the equations of asymptotes
Expressing Conics Outside the Realm of Cartesian Coordinates
Graphing conic sections in parametric form
The equations of conic sections on the polar coordinate plane
Practice Questions Answers and Explanations
Whaddya Know? Chapter 17 Quiz
Answers to Chapter 17 Quiz
Unit 6: Systems, Sequences, and Series
Chapter 18: Streamlining Systems of Equations
A Primer on Your System-Solving Options
Graphing Equations to Find Solutions
Common solutions of linear equations
Common solutions of a linear and a quadratic equation
Common solutions of two polynomials
Algebraic Solutions of Two-Equation Systems
Solving linear systems
Working nonlinear systems
Solving Systems with More Than Two Equations
Decomposing Partial Fractions
Surveying Systems of Inequalities
Practice Questions Answers and Explanations
Whaddya Know? Chapter 18 Quiz
Answers to Chapter 18 Quiz
Chapter 19: Making Matrices Work
Introducing Matrices: The Basics
Applying basic operations to matrices
Multiplying matrices by each other
Simplifying Matrices to Ease the Solving Process
Writing a system in matrix form
Reduced row-echelon form
Augmented form
Making Matrices Work for You
Using Gaussian elimination to solve systems
Multiplying a matrix by its inverse
Using determinants: Cramer’s Rule
Practice Questions Answers and Explanations
Whaddya Know? Chapter 19 Quiz
Answers to Chapter 19 Quiz
Chapter 20: Sequences and Series
Speaking Sequentially: Grasping the General Method
Determining a sequence’s terms
Working in reverse: Forming an expression from terms
Recognizing recursive formulas: A type of general sequence
Finding the Difference between Terms: Arithmetic Sequences
Using consecutive terms to find another
Using any two terms
Looking at Ratios and Consecutive Paired Terms: Geometric Sequences
Embracing some basic concepts
Going out of order: Dealing with nonconsecutive terms
Creating a Series: Summing Terms of a Sequence
Reviewing general summation notation
Summing an arithmetic sequence
Seeing how a geometric sequence adds up
Practice Questions Answers and Explanations
Whaddya Know? Chapter 20 Quiz
Answers to Chapter 20 Quiz
Chapter 21: Expanding Binomials for the Real World
Expanding with the Binomial Theorem
Concocting binomial coefficients
Breaking down the binomial theorem
Expanding by using the binomial theorem
Working Backwards
Practice Questions Answers and Explanations
Whaddya Know? Chapter 21 Quiz
Answers to Chapter 21 Quiz
Unit 7: Onward to Calculus
Chapter 22: Lining Up the Tools
Scoping Out the Changes: Pre-Calculus to Calculus
Understanding Your Limits
Finding the Limit of a Function
Graphically
Analytically
Algebraically
Operating on Limits: The Limit Laws
Calculating the Average Rate of Change
Exploring Continuity in Functions
Determining whether a function is continuous
Discontinuity in rational functions
Practice Questions Answers and Explanations
Whaddya Know? Chapter 22 Quiz
Answers to Chapter 22 Quiz
Chapter 23: Proceeding with Successful Procedures
Figure Out What the Problem Is Asking
Draw Pictures (the More the Better)
Plan Your Attack: Identify Your Targets
Write Down Any Formulas
Show Each Step of Your Work
Know When to Quit
Check Your Answers
Practice Plenty of Problems
Keep Track of the Order of Operations
Use Caution When Dealing with Fractions
Practice Questions Answers and Explanations
Whaddya Know? Chapter 23 Quiz
Answers to Chapter 23 Quiz
Index
EULA