Pre-Calculus For Dummies
3rd Edition
Published on 25. October 2018
416 pages
978-1-119-50879-3 (ISBN)
Description
Get ahead in pre-calculus
Pre-calculus courses have become increasingly popular with 35 percent of students in the U.S. taking the course in middle or high school. Often, completion of such a course is a prerequisite for calculus and other upper level mathematics courses.
Pre-Calculus For Dummies is an invaluable resource for students enrolled in pre-calculus courses. By presenting the essential topics in a clear and concise manner, the book helps students improve their understanding of pre-calculus and become prepared for upper level math courses.
* Provides fundamental information in an approachable manner
* Includes fresh example problems
* Practical explanations mirror today's teaching methods
* Offers relevant cultural references
Whether used as a classroom aid or as a refresher in preparation for an introductory calculus course, this book is one you'll want to have on hand to perform your very best.
Pre-calculus courses have become increasingly popular with 35 percent of students in the U.S. taking the course in middle or high school. Often, completion of such a course is a prerequisite for calculus and other upper level mathematics courses.
Pre-Calculus For Dummies is an invaluable resource for students enrolled in pre-calculus courses. By presenting the essential topics in a clear and concise manner, the book helps students improve their understanding of pre-calculus and become prepared for upper level math courses.
* Provides fundamental information in an approachable manner
* Includes fresh example problems
* Practical explanations mirror today's teaching methods
* Offers relevant cultural references
Whether used as a classroom aid or as a refresher in preparation for an introductory calculus course, this book is one you'll want to have on hand to perform your very best.
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Additional editions
Mary Jane Sterling
Pre-Calculus For Dummies
Book
12/2018
3rd Edition
Wiley
€24.00
Shipment within 15-20 days
Content
- Intro
- 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
- Part 1 Getting Started with Pre-Calculus
- Chapter 1 Pre-Pre-Calculus
- Pre-Calculus: An Overview
- All the Number Basics (No, Not How to Count Them!)
- The multitude of number types: Terms to know
- The fundamental operations you can perform on numbers
- The properties of numbers: Truths to remember
- Visual Statements: When Math Follows Form with Function
- Basic terms and concepts
- Graphing linear equalities and inequalities
- Gathering information from graphs
- Get Yourself a Graphing Calculator
- Chapter 2 Playing with Real Numbers
- Solving Inequalities
- Recapping inequality how-tos
- Solving equations and inequalities when absolute value is involved
- Expressing solutions for inequalities with interval notation
- Variations on Dividing and Multiplying: 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
- Chapter 3 The Building Blocks of Pre-Calculus Functions
- Qualities of 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
- Graphing Functions That Have More Than One Rule: Piece-Wise Functions
- Setting the Stage for Rational Functions
- Step 1: Search for vertical asymptotes
- Step 2: Look for horizontal asymptotes
- Step 3: Seek out oblique asymptotes
- Step 4: Locate the x- and y-intercepts
- Putting the Results to Work: Graphing Rational Functions
- Graphing f(x)=3x-1/x2+4x-21
- Graphing g(x)=6x+12/4-3x
- Graphing h(x)=x2-9/x+2
- Chapter 4 Operating on Functions
- Transforming the Parent Graphs
- Stretching and flattening
- Translations
- 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
- Chapter 5 Digging Out and Using Roots to Graph 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 Unfactorable Polynomials 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
- Listing the possibilities with the rational root theorem
- Testing roots by dividing polynomials
- Put It in Reverse: Using Solutions to Find Factors
- Graphing Polynomials
- When all the roots are real numbers
- When roots are imaginary numbers: Combining all techniques
- 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 exponential equation solving
- Solving logarithmic equations
- Growing Exponentially: Word Problems in the Kitchen
- Part 2 The Essentials of Trigonometry
- Chapter 7 Circling in on Angles
- Introducing Radians: Circles Weren't Always Measured in Degrees
- Trig Ratios: Taking Right Triangles a Step Further
- Making a sine
- Looking for a cosine
- Going on a tangent
- Discovering the flip side: Reciprocal trig functions
- Working in reverse: Inverse trig functions
- Understanding How Trig Ratios Work on the Coordinate Plane
- Building the Unit Circle by Dissecting the Right Way
- Familiarizing yourself with the most common angles
- Drawing uncommon angles
- Digesting Special Triangle Ratios
- The 45er:45deg-45deg-90deg triangle
- The old 30-60:30deg-60deg-90deg triangle
- Triangles and the Unit Circle: Working Together for the Common Good
- Placing the major angles correctly, sans protractor
- Retrieving trig-function values on the unit circle
- Finding the reference angle to solve for angles on the unit circle
- Measuring Arcs: When the Circle Is Put in Motion
- Chapter 8 Simplifying the Graphing and Transformation of Trig Functions
- Drafting the Sine and Cosine Parent Graphs
- Sketching sine
- Looking at cosine
- Graphing Tangent and Cotangent
- Tackling tangent
- Clarifying cotangent
- Putting Secant and Cosecant in Pictures
- Graphing secant
- Checking out cosecant
- Transforming Trig Graphs
- Messing with sine and cosine graphs
- Tweaking tangent and cotangent graphs
- Transforming the graphs of secant and cosecant
- Chapter 9 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
- Chapter 10 Advanced Identities: Your Keys to Success
- 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
- Chapter 11 Taking Charge of Oblique Triangles with the Laws of Sines and Cosines
- 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)
- Part 3 Analytic Geometry and System Solving
- Chapter 12 Plane Thinking: Complex Numbers and Polar Coordinates
- Understanding Real versus Imaginary
- Combining Real and Imaginary: The Complex Number System
- Grasping the usefulness of complex numbers
- Performing operations with complex numbers
- Graphing Complex Numbers
- 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
- Chapter 13 Creating Conics by Slicing Cones
- Cone to Cone: Identifying the Four Conic Sections
- In picture (graph form)
- In print (equation 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 min and max of vertical parabolas
- The Fat and the Skinny on the Ellipse
- Labeling ellipses and expressing them with algebra
- Identifying the parts from the equation
- Pair Two Curves and What Do You Get? Hyperbolas
- Visualizing the two types of hyperbolas and their bits and pieces
- Graphing a hyperbola from an equation
- 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
- Chapter 14 Streamlining Systems, Managing Variables
- A Primer on Your System-Solving Options
- 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
- 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
- Chapter 15 Sequences, Series, and Expanding Binomials for the Real World
- Speaking Sequentially: Grasping the General Method
- Determining a sequence's terms
- Working in reverse: Forming an expression from terms
- Recursive sequences: One type of general sequence
- Difference between Terms: Arithmetic Sequences
- Using consecutive terms to find another
- Using any two terms
- Ratios and Consecutive Paired Terms: Geometric Sequences
- Identifying a particular term when given consecutive terms
- 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
- Expanding with the Binomial Theorem
- Breaking down the binomial theorem
- Expanding by using the binomial theorem
- Chapter 16 Onward to Calculus
- Scoping Out the Differences between Pre-Calculus and 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
- Part 4 The Part of Tens
- Chapter 17 Ten Polar Graphs
- Spiraling Outward
- Falling in Love with a Cardioid
- Cardioids and Lima Beans
- Leaning Lemniscates
- Lacing through Lemniscates
- Roses with Even Petals
- A Rose Is a Rose Is a Rose
- Limaçon or Escargot?
- Limaçon on the Side
- Bifolium or Rabbit Ears?
- Chapter 18 Ten Habits to Adjust before Calculus
- 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
- Index
- EULA
