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Introduction | |

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About This Book | |

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Conventions Used in This Book | |

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Foolish Assumptions | |

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How This Book Is Organized | |

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Icons Used in This Book | |

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Where to Go from Here | |

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Homing in on Basic Solutions | |

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Going Beyond Beginning Algebra | |

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Outlining Algebra Properties | |

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Keeping order with the commutative property | |

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Maintaining group harmony with the associative property | |

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Distributing a wealth of values | |

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Checking out an algebraic ID | |

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Singing along in-verses | |

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Ordering Your Operations | |

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Equipping Yourself with the Multiplication Property of Zero | |

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Expounding on Exponential Rules | |

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Multiplying and dividing exponents | |

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Getting to the roots of exponents | |

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Raising or lowering the roof with exponents | |

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Making nice with negative exponents | |

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Implementing Factoring Techniques | |

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Factoring two terms | |

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Taking on three terms | |

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Factoring four or more terms by grouping | |

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Toeing the Straight Line: Linear Equations | |

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Linear Equations: Handling the First Degree | |

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Tackling basic linear equations | |

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Clearing out fractions | |

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Isolating different unknowns | |

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Linear Inequalities: Algebraic Relationship Therapy | |

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Solving basic inequalities | |

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Introducing interval notation | |

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Compounding inequality issues | |

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Absolute Value: Keeping Everything in Line | |

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Solving absolute-value equations | |

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Seeing through absolute-value inequality | |

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Cracking Quadratic Equations | |

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Solving Simple Quadratics with the Square Root Rule | |

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Finding simple square-root solutions | |

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Dealing with radical square-root solutions | |

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Dismantling Quadratic Equations into Factors | |

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Factoring binomials | |

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Factoring trinomials | |

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Factoring by grouping | |

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Resorting to the Quadratic Formula | |

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Finding rational solutions | |

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Straightening out irrational solutions | |

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Formulating huge quadratic results | |

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Completing the Square: Warming Up for Conics | |

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Squaring up to solve a quadratic equation | |

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Completing the square twice over | |

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Getting Promoted to High-Powered Quadratics (without the Raise) | |

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Handling the sum or difference of cubes | |

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Tackling quadratic-like trinomials | |

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Solving Quadratic Inequalities | |

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Keeping it strictly quadratic | |

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Signing up for fractions | |

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Increasing the number of factors | |

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Rooting Out the Rational, Radical, and Negative | |

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Acting Rationally with Fraction-Filled Equations | |

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Solving rational equations by tuning in your LCD | |

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Solving rational equations with proportions | |

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Ridding Yourself of a Radical | |

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Squaring both sides of a radical equation | |

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Calming two radicals | |

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Changing Negative Attitudes about Exponents | |

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Flipping negative exponents out of the picture | |

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Factoring out negatives to solve equations | |

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Fooling Around with Fractional Exponents | |

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Combining terms with fractional exponents | |

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Factoring fractional exponents | |

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Solving equations by working with fractional exponents | |

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Graphing Your Way to the Good Life | |

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Coordinating Your Graphing Efforts | |

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Identifying the parts of the coordinate plane | |

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Plotting from dot to dot | |

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Streamlining the Graphing Process with Intercepts and Symmetry | |

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Finding x- and y-intercepts | |

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Reflecting on a graph's symmetry | |

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Graphing Lines | |

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Finding the slope of a line | |

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Facing two types of equations for lines | |

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Identifying parallel and perpendicular lines | |

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Looking at 10 Basic Forms | |

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Lines and quadratics | |

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Cubics and quartics | |

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Radicals and rationals | |

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Exponential and logarithmic curves | |

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Absolute values and circles | |

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Solving Problems with a Graphing Calculator | |

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Entering equations into graphing calculators correctly | |

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Looking through the graphing window | |

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Facing Off with Functions | |

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Formulating Function Facts | |

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Defining Functions | |

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Introducing function notation | |

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Evaluating functions | |

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Homing In on Domain and Range | |

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Determining a function's domain | |

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Describing a function's range | |

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Betting on Even or Odd Functions | |

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Recognizing even and odd functions | |

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Applying even and odd functions to graphs | |

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Facing One-to-One Confrontations | |

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Defining one-to-one functions | |

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Eliminating one-to-one violators | |

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Going to Pieces with Piecewise Functions | |

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Doing piecework | |

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Applying piecewise functions | |

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Composing Yourself and Functions | |

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Performing compositions | |

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Simplifying the difference quotient | |

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Singing Along with Inverse Functions | |

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Determining if functions are inverses | |

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Solving for the inverse of a function | |

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Sketching and Interpreting Quadratic Functions | |

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Interpreting the Standard Form of Quadratics | |

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Starting with "a" in the standard form | |

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Following up with "b" and "c" | |

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Investigating Intercepts in Quadratics | |

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Finding the one and only y-intercept | |

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Finding the x-intercepts | |

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Going to the Extreme: Finding the Vertex | |

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Lining Up along the Axis of Symmetry | |

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Sketching a Graph from the Available Information | |

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Applying Quadratics to the Real World | |

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Selling candles | |

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Shooting basketballs | |

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Launching a water balloon | |

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Staying Ahead of the Curves: Polynomials | |

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Taking a Look at the Standard Polynomial Form | |

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Exploring Polynomial Intercepts and Turning Points | |

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Interpreting relative value and absolute value | |

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Counting intercepts and turning points | |

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Solving for polynomial intercepts | |

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Determining Positive and Negative Intervals | |

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Using a sign-line | |

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Interpreting the rule | |

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Finding the Roots of a Polynomial | |

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Factoring for polynomial roots | |

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Saving your sanity: The Rational Root Theorem | |

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Letting Descartes make a ruling on signs | |

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Synthesizing Root Findings | |

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Using synthetic division to test for roots | |

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Synthetically dividing by a binomial | |

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Wringing out the Remainder (Theorem) | |

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Relying on Reason: Rational Functions | |

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Exploring Rational Functions | |

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Sizing up domain | |

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Introducing intercepts | |

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Adding Asymptotes to the Rational Pot | |

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Determining the equations of vertical asymptotes | |

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Determining the equations of horizontal asymptotes | |

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Graphing vertical and horizontal asymptotes | |

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Crunching the numbers and graphing oblique asymptotes | |

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Accounting for Removable Discontinuities | |

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Removal by factoring | |

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Evaluating the removal restrictions | |

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Showing removable discontinuities on a graph | |

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Pushing the Limits of Rational Functions | |

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Evaluating limits at discontinuities | |

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Going to infinity | |

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Catching rational limits at infinity | |

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Putting It All Together: Sketching Rational Graphs from Clues | |

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Exposing Exponential and Logarithmic Functions | |

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Evaluating Exponential Expressions | |

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Exponential Functions: It's All About the Base, Baby | |

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Observing the trends in bases | |

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Meeting the most frequently used bases: 10 and e | |

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Solving Exponential Equations | |

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Making bases match | |

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Recognizing and using quadratic patterns | |

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Showing an "Interest" in Exponential Functions | |

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Applying the compound interest formula | |

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Looking at continuous compounding | |

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Logging On to Logarithmic Functions | |

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Meeting the properties of logarithms | |

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Putting your logs to work | |

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Solving Logarithmic Equations | |

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Setting log equal to log | |

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Rewriting log equations as exponentials | |

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Graphing Exponential and Logarithmic Functions | |

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Expounding on the exponential | |

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Not seeing the logs for the trees | |

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Conquering Conics and Systems of Equations | |

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Cutting Up Conic Sections | |

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Cutting Up a Cone | |

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Opening Every Which Way with Parabolas | |

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Looking at parabolas with vertices at the origin | |

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Observing the general form of parabola equations | |

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Sketching the graphs of parabolas | |

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Converting parabolic equations to the standard form | |

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Going Round and Round in Conic Circles | |

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Standardizing the circle | |

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Specializing in circles | |

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Preparing Your Eyes for Solar Ellipses | |

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Raising the standards of an ellipse | |

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Sketching an elliptical path | |

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Feeling Hyper about Hyperbolas | |

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Including the asymptotes | |

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Graphing hyperbolas | |

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Identifying Conics from Their Equations, Standard or Not | |

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Solving Systems of Linear Equations | |

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Looking at the Standard Linear-Systems Form and Its Possible Solutions | |

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Graphing Solutions of Linear Systems | |

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Pinpointing the intersection | |

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Toeing the same line twice | |

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Dealing with parallel lines | |

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Eliminating Systems of Two Linear Equations with Addition | |

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Getting to an elimination point | |

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Recognizing solutions for parallel and coexisting lines | |

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Solving Systems of Two Linear Equations with Substitution | |

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Variable substituting made easy | |

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Identifying parallel and coexisting lines | |

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Using Cramer's Rule to Defeat Unwieldy Fractions | |

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Setting up the linear system for Cramer | |

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Applying Cramer's Rule to a linear system | |

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Raising Linear Systems to Three Linear Equations | |

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Solving three-equation systems with algebra | |

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Settling for a generalized solution for linear combinations | |

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Upping the Ante with Increased Equations | |

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Applying Linear Systems to Our 3-D World | |

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Using Systems to Decompose Fractions | |

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Solving Systems of Nonlinear Equations and Inequalities | |

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Crossing Parabolas with Lines | |

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Determining the point(s) where a line and parabola cross paths | |

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Dealing with a solution that's no solution | |

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Intertwining Parabolas and Circles | |

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Managing multiple intersections | |

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Sorting out the solutions | |

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Planning Your Attack on Other Systems of Equations | |

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Mixing polynomials and lines | |

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Crossing polynomials | |

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Navigating exponential intersections | |

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Rounding up rational functions | |

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Playing Fair with Inequalities | |

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Drawing and quartering inequalities | |

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Graphing areas with curves and lines | |

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Shifting into High Gear with Advanced Concepts | |

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Simplifying Complex Numbers in a Complex World | |

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Using Your Imagination to Simplify Powers of i | |

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Understanding the Complexity of Complex Numbers | |

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Operating on complex numbers | |

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Multiplying by the conjugate to perform division | |

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Simplifying radicals | |

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Solving Quadratic Equations with Complex Solutions | |

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Working Polynomials with Complex Solutions | |

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Identifying conjugate pairs | |

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Interpreting complex zeros | |

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Making Moves with Matrices | |

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Describing the Different Types of Matrices | |

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Row and column matrices | |

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Square matrices | |

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Zero matrices | |

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Identity matrices | |

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Performing Operations on Matrices | |

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Adding and subtracting matrices | |

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Multiplying matrices by scalars | |

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Multiplying two matrices | |

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Applying matrices and operations | |

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Defining Row Operations | |

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Finding Inverse Matrices | |

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Determining additive inverses | |

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Determining multiplicative inverses | |

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Dividing Matrices by Using Inverses | |

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Using Matrices to Find Solutions for Systems of Equations | |

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Making a List: Sequences and Series | |

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Understanding Sequence Terminology | |

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Using sequence notation | |

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No-fear factorials in sequences | |

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Alternating sequential patterns | |

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Looking for sequential patterns | |

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Taking Note of Arithmetic and Geometric Sequences | |

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Finding common ground: Arithmetic sequences | |

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Taking the multiplicative approach: Geometric sequences | |

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Recursively Defining Functions | |

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Making a Series of Moves | |

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Introducing summation notation | |

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Summing arithmetically | |

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Summing geometrically | |

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Applying Sums of Sequences to the Real World | |

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Cleaning up an amphitheater | |

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Negotiating your allowance | |

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Bouncing a ball | |

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Highlighting Special Formulas | |

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Everything You Wanted to Know about Sets | |

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Revealing Set Notation | |

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Listing elements with a roster | |

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Building sets from scratch | |

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Going for all (universal set) or nothing (empty set) | |

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Subbing in with subsets | |

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Operating on Sets | |

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Celebrating the union of two sets | |

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Looking both ways for set intersections | |

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Feeling complementary about sets | |

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Counting the elements in sets | |

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Drawing Venn You Feel Like It | |

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Applying the Venn diagram | |

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Using Venn diagrams with set operations | |

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Adding a set to a Venn diagram | |

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Focusing on Factorials | |

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Making factorial manageable | |

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Simplifying factorials | |

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How Do I Love Thee? Let Me Count Up the Ways | |

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Applying the multiplication principle to sets | |

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Arranging permutations of sets | |

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Mixing up sets with combinations | |

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Branching Out with Tree Diagrams | |

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Picturing a tree diagram for a permutation | |

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Drawing a tree diagram for a combination | |

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The Part of Tens | |

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Ten Multiplication Tricks | |

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Ten Special Types of Numbers | |

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Index | |