Pre-calculus all-in-one
Book - 2024
The easy way to understand and retain all the concepts taught in pre-calculus classes Pre-Calculus All-in-One For Dummies is a great resource if you want to do you best in Pre-Calculus. Packed with lessons, examples, and practice problems in the book, plus extra chapter quizzes online, it gives you absolutely everything you need to succeed in pre-calc. Unlike your textbook, this book presents the essential topics clearly and concisely, so you can really understand the stuff you learn in class, score high on your tests (including the AP Pre-Calculus exam!), and get ready to confidently move ahead to upper-level math courses. And if you need a refresher before launching into calculus, look no further--this book has your back. Review what you ...learned in algebra and geometry, then dig into pre-calculus Master logarithms, exponentials, conic sections, linear equations, and beyond Get easy-to-understand explanations that match the methods your teacher uses Learn clever shortcuts, test-taking tips, and other hacks to make your life easier Pre-Calculus All-in-One For Dummies is the must-have resource for students who need to review for exams or just want a little (or a lot of!) extra help understanding what's happening in class.
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- handbooks
Handbooks and manuals
Guides et manuels - Published
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Hoboken, NJ :
For Dummies
[2024]
- Language
- English
- Main Author
- Item Description
- Includes index.
- Physical Description
- xvi, 597 pages : illustrations (black & white) ; 26 cm
- ISBN
- 9781394201242
- 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
- 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