1
Q
• When working with equations with logarithmic expressions, you can use the fact that a logarithm is an exponent to untangle the log pieces and simplify the equation.
A
• When working with equations with logarithmic expressions, you can use the fact that a logarithm is an exponent to untangle the log pieces and simplify the equation.
Pre-Calculus
flashcards
Decks in class (343)
# Cards
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The Top Ten List of Mistakes (1.1.1)1
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Concepts of Inequality (1.2.1)11
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Inequalities and Interval Notation (1.2.2)1
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Properties of Absolute Value (1.3.1)1
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Evaluating Absolute Value Expressions (1.3.2)2
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An Introduction to Exponents (1.4.1)1
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Evaluating Exponential Expressions (1.4.2)1
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Applying the Rules of Exponents (1.4.3)4
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Evaluating Expressions with Negative Exponents (1.4.4)3
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Converting between Decimal and Scientific Notation (1.5.1)5
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Converting Rational Exponents and Radicals (1.5.2)3
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Simplifying Radical Expressions (1.6.1)2
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Simplifying Radical Expressions with Variables (1.6.2)4
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Rationalizing Denominators (1.6.3)4
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Determining Components and Degree (1.7.1)4
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Adding, Subtracting, and Multiplying Polynomials (1.7.2)4
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Multiplying Big Products (1.7.3)3
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Using Special Products (1.7.4)4
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Factoring Using the Greatest Common Factor (1.8.1)2
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Factoring by Grouping (1.8.2)2
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Factoring Trinomials Completely (1.8.3)4
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Factoring Trinomials: The Grouping Method (1.8.4)3
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Factoring Perfect Square Trinomials (1.9.1)1
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Factoring the Difference of Two Squares (1.9.2)3
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Factoring the Sums and Differences of Cubes (1.9.3)2
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Factoring by Any Method (1.9.4)2
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Rational Expressions and Domain (1.10.1)4
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Working with Fractions (1.10.2)4
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Writing Rational Expressions in Lowest Terms (1.10.3)3
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Multiplying and Dividing Rational Expressions (1.11.1)5
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Adding and Subtracting Rational Expressions (1.11.2)5
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Rewriting Complex Fractions (1.11.3)2
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Introducing and Writing Complex Numbers (1.12.1)3
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Rewriting Powers of i (1.12.2)5
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Adding and Subtracting Complex Numbers (1.12.3)3
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Multiplying Complex Numbers (1.12.4)3
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Dividing Complex Numbers (1.12.5)4
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An Introduction to Solving Equations (2.1.1)3
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Solving a Linear Equation (2.1.2)2
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Solving a Linear Equation with Rationals (2.1.3)3
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Solving a Linear Equation That Has Restrictions (2.1.4)3
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An Introduction to Solving Word Problems (2.2.1)4
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Solving for Perimeter (2.2.2)4
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Solving a Linear Geometry Problem (2.2.3)3
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Solving for Consecutive Numbers (2.2.4)7
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Solving to Find the Average (2.2.5)3
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Solving for Constant Velocity (2.3.1)2
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Solving a Problem about Work (2.3.2)6
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Solving a Mixture Problem (2.3.3)6
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Solving an Investment Problem (2.3.4)2
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Solving Business Problems (2.3.5)5
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Solving Quadratics by Factoring (2.4.1)4
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Solving Quadratics by Completing the Square (2.4.2)2
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Completing the Square: Another Example (2.4.3)2
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Proving the Quadratic Formula (2.5.1)3
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Using the Quadratic Formula (2.5.2)5
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Predicting the Type of Solutions Using the Discriminant (2.5.3)5
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Solving for a Squared Variable (2.6.1)3
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Finding Real Number Restrictions (2.6.2)7
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Solving Fancy Quadratics (2.6.3)5
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An Introduction to Word Problems with Quadratics (2.7.1)1
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Solving a Quadratic Geometry Problem (2.7.2)5
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Solving with the Pythagorean Theorem (2.7.3)1
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The Pythagorean Theorem: Another Example (2.7.4)1
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Solving a Motion Problem (2.8.1)3
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Solving a Projectile Problem (2.8.2)1
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Solving Other Problems (2.8.3)2
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Determining Extraneous Roots (2.9.1)5
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Solving an Equation Containing a Radical (2.9.2)5
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Solving an Equation with Two Radicals (2.9.3)3
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Solving an Equation with Rational Exponents (2.9.4)5
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An Introduction to Variation (2.10.1)7
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Direct Proportion (2.10.2)6
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Inverse Proportion (2.10.3)4
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An Introduction to Solving Inequalities (2.11.1)7
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Solving Compound Inequalities (2.11.2)6
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More on Compound Inequalities (2.11.3)2
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Solving Word Problems Involving Inequalities (2.11.4)2
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Solving Quadratic Inequalities (2.12.1)4
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Solving Quadratic Inequalities: Another Example (2.12.2)4
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Solving Rational Inequalities (2.13.1)7
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Solving Rational Inequalities (2.13.2)3
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Determining the Domains of Expressions with Radicals (2.13.3)4
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Matching Number Lines with Absolute Values (2.14.1)5
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Solving Absolute Value Equations (2.14.2)6
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Solving Equations with Two Absolute Value Expressions (2.14.3)6
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Solving Absolute Value Inequalities (2.14.4)6
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Solving Absolute Value Inequalities: More Examples (2.14.5)4
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Using the Cartesian System (3.1.1)7
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Thinking Visually (3.1.2)10
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Finding the Distance between Two Points (3.2.1)3
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Finding the Second Endpoint of a Segment (3.2.2)2
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Collinearity and Distance (3.3.1)7
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Triangles (3.3.2)5
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Finding the Center-Radius Form of the Equation of a Circle (3.4.1)6
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Finding the Center and Radius of a Circle (3.4.2)3
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Decoding the Circle Formula (3.4.3)4
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Solving Word Problems Involving Circles (3.4.4)2
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Graphing Equations by Locating Points (3.5.1)5
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Finding the x- and y- Intercepts of an Equation (3.5.2)5
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Functions and the Vertical Line Test (3.6.1)3
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Identifying Functions (3.6.2)3
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Function Notation and Finding Function Values (3.6.3)4
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Determining Intervals Over Which a Function is Increasing (3.7.1)9
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Evaluating Piecewise-Defined Functions for Given Values (3.7.2)4
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Solving Word Problems Involving Functions (3.7.3)5
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Finding the Domain and Range of a Function (3.8.1)4
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Domain and Range: One Explicit Example (3.8.2)5
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Satisfying the Domain of a Function (3.8.3)4
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An Introduction to Slope (3.9.1)3
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Finding the Slope of a Line Given Two Points (3.9.2)4
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Interpreting Slope from a Graph (3.9.3)6
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Graphing a Line Using Point and Slope (3.9.4)4
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Writing an Equation in Slope-Intercept Form (3.10.1)6
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Writing an Equation Given Two Points (3.10.2)6
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Writing an Equation in Point-Slope Form (3.10.3)2
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Matching a Slope-Intercept Equation with Its Graph (3.10.4)4
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Slope for Parallel and Perpendicular Lines (3.10.5)8
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Constructing Linear Function Models of Data (3.11.1)4
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Linear Cost and Revenue Functions (3.11.2)2
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Graphing Some Important Functions (3.12.1)3
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Graphing Piecewise-Defined Functions (3.12.2)2
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Matching Equations with Their Graphs (3.12.3)8
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The Greatest Integer Function (3.13.1)3
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Graphing the Greatest Integer Function (3.13.2)3
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Deconstructing the Graph of a Quadratic Function (3.14.1)3
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Nice-Looking Parabolas (3.14.2)6
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Using the Discriminant to Graph Parabolas (3.14.3)3
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Maximum Height in the Real World (3.14.4)2
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Finding the Vertex by Completing the Square (3.15.1)3
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Using the Vertex to Write the Quadratic Equation (3.15.2)3
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Finding the Maximum or Minimum of a Quadratic (3.15.3)4
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Graphing Parabolas (3.15.4)8
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Shifting Curves along Axes (3.16.1)6
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Shifting or Translating Curves along Axes (3.16.2)4
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Stretching a Graph (3.16.3)2
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Graphing Quadratics Using Patterns (3.16.4)2
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Determining Symmetry (3.17.1)6
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Reflections (3.17.2)2
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Reflecting Specific Functions (3.17.3)4
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Using Operations on Functions (3.18.1)4
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Composite Functions (3.18.2)5
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Components of Composite Functions (3.18.3)4
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Finding Functions That Form a Given Composite (3.18.4)4
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Finding the Difference Quotient of a Function (3.18.5)2
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Using Long Division with Polynomials (4.1.1)4
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Long Division: Another Example (4.1.2)4
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Using Synthetic Division with Polynomials (4.2.1)4
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More Synthetic Division (4.2.2)3
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The Remainder Theorem (4.3.1)4
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More on the Remainder Theorem (4.3.2)4
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The Factor Theorem and Its Uses (4.4.1)3
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Factoring a Polynomial Given a Zero (4.4.2)2
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Presenting the Rational Zero Theorem (4.5.1)4
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Considering Possible Solutions (4.5.2)2
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Finding Polynomials Given Zeros, Degree, and One Point (4.6.1)3
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Finding all Zeros and Multiplicities of a Polynomial (4.6.2)3
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Finding the Real Zeros for a Polynomial (4.6.3)3
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Using Descartes' Rule of Signs (4.6.4)3
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Finding the Zeros of a Polynomial from Start to Finish (4.6.5)4
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Matching Graphs to Polynomial Functions (4.7.1)4
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Sketching the Graphs of Basic Polynomial Functions (4.7.2)4
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Understanding Rational Functions (4.8.1)2
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Basic Rational Functions (4.8.2)2
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Vertical Asymptotes (4.9.1)2
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Horizontal Asymptotes (4.9.2)2
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Graphing Rational Functions (4.9.3)2
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Graphing Rational Functions: More Examples (4.9.4)2
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Oblique Asymptotes (4.9.5)3
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Oblique Asymptotes: Another Example (4.9.6)2
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Understanding Inverse Functions (5.1.1)4
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The Horizontal Line Test (5.1.2)2
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Are Two Functions Inverses of Each Other? (5.1.3)3
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Graphing the Inverse (5.1.4)3
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Finding the Inverse of a Function (5.2.1)1
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Finding the Inverse of a Function with Higher Powers (5.2.2)1
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An Introduction to Exponential Functions (5.3.1)1
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Graphing Exponential Functions: Useful Patterns (5.3.2)3
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Graphing Exponential Functions: More Examples (5.3.3)3
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Using Properties of Exponents to Solve Exponential Equations (5.4.1)3
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Finding Present Value and Future Value (5.4.2)3
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Finding an Interest Rate to Match Given Goals (5.4.3)3
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e (5.5.1)2
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Applying Exponential Functions (5.5.2)3
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An Introduction to Logarithmic Functions (5.6.1)3
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Converting between Exponential and Logarithmic Functions (5.6.2)2
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Finding the Value of a Logarithmic Function (5.7.1)2
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Solving for x in Logarithmic Equations (5.7.2)2
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Graphing Logarithmic Functions (5.7.3)1
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Matching Logarithmic Functions with Their Graphs (5.7.4)1
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Properties of Logarithms (5.8.1)3
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Expanding a Logarithmic Expression Using Properties (5.8.2)2
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Combining Logarithmic Expressions (5.8.3)4
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Evaluating Logarithmic Functions Using a Calculator (5.9.1)2
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Using the Change of Base Formula (5.9.2)3
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The Richter Scale (5.10.1)1
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The Distance Modulus Formula (5.10.2)3
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Solving Exponential Equations (5.11.1)1
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Solving Logarithmic Equations (5.11.2)2
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Solving Equations with Logarithmic Exponents (5.11.3)1
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Compound Interest (5.12.1)1
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Predicting Change (5.12.2)1
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An Introduction to Exponential Growth and Decay (5.13.1)2
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Half-Life (5.13.2)1
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Newton's Law of Cooling (5.13.3)2
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Continuously Compounded Interest (5.13.4)2
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Finding the Quadrant in Which an Angle Lies (6.1.1)7
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Finding Coterminal Angles (6.1.2)2
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Finding the Complement and Supplement of an Angle (6.1.3)2
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Converting between Degrees and Radians (6.1.4)2
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Using the Arc Length Formula (6.1.5)1
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An Introduction to the Trigonometric Functions (6.2.1)3
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Evaluating Trigonometric Functions for an Angle in a Right Triangle (6.2.2)2
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Finding an Angle Given the Value of a Trigonometric Function (6.2.3)1
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Using Trigonometric Functions to Find Unknown Sides of Right Triangles (6.2.4)1
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Finding the Height of a Building (6.2.5)2
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Evaluating Trigonometric Functions for an Angle in the Coordinate Plane (6.3.1)2
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Evaluating Trigonometric Functions Using the Reference Angle (6.3.2)2
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Finding the Value of Trigonometric Functions Given Information about the Values of Other Trigonometric Functions (6.3.3)1
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Trigonometric Functions of Important Angles (6.3.4)1
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An Introduction to the Graphs of Sine and Cosine Functions (6.4.1)3
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Graphing Sine or Cosine Functions with Different Coefficients (6.4.2)3
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Finding Maximum and Minimum Values and Zeros of Sine and Cosine (6.4.3)2
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Solving Word Problems Involving Sine or Cosine Functions (6.4.4)1
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Graphing Sine and Cosine Functions with Phase Shifts (6.5.1)1
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Fancy Graphing: Changes in Period, Amplitude, Vertical Shift, and Phase Shift (6.5.2)1
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Graphing the Tangent, Secant, Cosecant, and Cotangent Functions (6.6.1)1
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Fancy Graphing: Tangent, Secant, Cosecant, and Cotangent (6.6.2)1
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Identifying a Trigonometric Function from its Graph (6.6.3)1
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An Introduction to Inverse Trigonometric Functions (6.7.1)2
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Evaluating Inverse Trigonometric Functions (6.7.2)1
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Solving an Equation Involving an Inverse Trigonometric Function (6.7.3)1
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Evaluating the Composition of a Trigonometric Function and Its Inverse (6.7.4)2
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Applying Trigonometric Functions: Is He Speeding? (6.7.5)5
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Fundamental Trigonometric Identities (7.1.1)2
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Finding All Function Values (7.1.2)2
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Simplifying a Trigonometric Expression Using Trigonometric Identities (7.2.1)3
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Simplifying Trigonometric Expressions Involving Fractions (7.2.2)3
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Simplifying Products of Binomials Involving Trigonometric Functions (7.2.3)3
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Factoring Trigonometric Expressions (7.2.4)3
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Determining Whether a Trigonometric Function Is Odd, Even, or Neither (7.2.5)2
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Proving an Identity (7.3.1)2
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Proving an Identity: Other Examples (7.3.2)2
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Solving Trigonometric Equations (7.4.1)1
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Solving Trigonometric Equations by Factoring (7.4.2)2
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Solving Trigonometric Equations with Coefficients in the Argument (7.4.3)1
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Solving Trigonometric Equations Using the Quadratic Formula (7.4.4)3
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Solving Word Problems Involving Trigonometric Equations (7.4.5)2
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Identities for Sums and Differences of Angles (7.5.1)1
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Using Sum and Difference Identities (7.5.2)2
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Using Sum and Difference Identities to Simplify an Expression (7.5.3)2
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Confirming a Double-Angle Identity (7.6.1)2
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Using Double-Angle Identities (7.6.2)2
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Solving Word Problems Involving Multiple-Angle Identities (7.6.3)5
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Using a Cofunction Identity (7.7.1)1
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Using a Power-Reducing Identity (7.7.2)2
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Using Half-Angle Identities to Solve a Trigonometric Equation (7.7.3)1
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The Law of Sines (8.1.1)2
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Solving a Triangle Given Two Sides and One Angle (8.1.2)2
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Solving a Triangle (SAS): Another Example (8.1.3)2
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The Law of Sines: An Application (8.1.4)1
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The Law of Cosines (8.2.1)3
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The Law of Cosines (SSS) (8.2.2)3
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The Law of Cosines (SAS): An Application (8.2.3)3
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Heron's Formula (8.2.4)2
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An Introduction to Vectors (8.3.1)1
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Finding the Magnitude and Direction of a Vector (8.3.2)2
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Vector Addition and Scalar Multiplication (8.3.3)3
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Finding the Components of a Vector (8.4.1)1
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Finding a Unit Vector (8.4.2)2
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Solving Word Problems Involving Velocity or Forces (8.4.3)2
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Graphing a Complex Number and Finding Its Absolute Value (8.5.1)3
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Expressing a Complex Number in Trigonometric or Polar Form (8.5.2)2
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Multiplying and Dividing Complex Numbers in Trigonometric or Polar Form (8.5.3)2
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Using DeMoivre's Theorem to Raise a Complex Number to a Power (8.6.1)2
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Roots of Complex Numbers (8.6.2)3
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More Roots of Complex Numbers (8.6.3)2
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Roots of Unity (8.6.4)2
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An Introduction to Polar Coordinates (8.7.1)2
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Converting between Polar and Rectangular Coordinates (8.7.2)2
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Converting between Polar and Rectangular Equations (8.7.3)1
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Graphing Simple Polar Equations (8.7.4)2
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Graphing Special Polar Equations (8.7.5)1
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An Introduction to Linear Systems (9.1.1)2
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Solving a System by Substitution (9.1.2)2
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Solving a System by Elimination (9.1.3)2
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An Introduction to Linear Systems in Three Variables (9.2.1)2
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Solving Linear Systems in Three Variables (9.2.2)4
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Solving Inconsistent Systems (9.2.3)2
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Solving Dependent Systems (9.2.4)3
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Solving Systems with Two Equations (9.2.5)2
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Investments (9.3.1)1
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Solving with Partial Fractions (9.3.2)2
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Solving Nonlinear Systems Using Elimination (9.4.1)2
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Solving Nonlinear Systems by Substitution (9.4.2)1
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An Introduction to Matrices (9.5.1)4
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The Arithmetic of Matrices (9.5.2)2
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Multiplying Matrices by a Scalar (9.5.3)3
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Multiplying Matrices (9.5.4)4
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Using the Gauss-Jordan Method (9.6.1)3
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Using Gauss-Jordan: Another Example (9.6.2)2
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Evaluating 2x2 Determinants (9.7.1)7
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Evaluating nxn Determinants (9.7.2)4
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Finding a Determinant using Expanding by Cofactors (9.7.3)3
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Applying Determinants (9.7.4)2
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Using Cramer's Rule (9.8.1)3
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Using Cramer's Rule in a 3x3 Matrix (9.8.2)2
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An Introduction to Inverses (9.9.1)4
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Inverses: 2x2 Matrices (9.9.2)4
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Another Look at 2x2 Inverses (9.9.3)4
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Inverses: 3x3 Matrices (9.9.4)5
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Solving a System of Equations with Inverses (9.9.5)3
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An Introduction to Graphing Linear Inequalities (9.10.1)2
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Graphing Linear and Nonlinear Inequalities (9.10.2)1
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Graphing the Solution Set of a System of Inequalities (9.10.3)1
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Solving for Maxima-Minima (9.11.1)2
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Applying Linear Programming (9.11.2)1
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An Introduction to Conic Sections (10.1.1)1
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An Introduction to Parabolas (10.1.2)1
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Determining Information about a Parabola from Its Equation (10.1.3)2
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Writing an Equation for a Parabola (10.1.4)3
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An Introduction to Ellipses (10.2.1)4
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Finding the Equation for an Ellipse (10.2.2)2
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Applying Ellipses: Satellites (10.2.3)1
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An Introduction to Hyperbolas (10.3.1)5
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Finding the Equation for a Hyperbola (10.3.2)3
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Applying Hyperbolas: Navigation (10.3.3)4
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Identifying a Conic (10.4.1)4
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Name that Conic (10.4.2)4
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Rotation of Axes (10.4.3)3
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Rotating Conics (10.4.4)4
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Using the Binomial Theorem (10.5.1)3
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Binomial Coefficients (10.5.2)2
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Finding a Term of a Binomial Expression (10.5.3)1
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Understanding Sequence Problems (10.6.1)3
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Solving Problems Involving Arithmetic Sequences (10.6.2)2
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Solving Problems Involving Geometric Sequences (10.6.3)1
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Proving Formulas Using Mathematical Induction (10.7.1)1
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Examples of Induction (10.7.2)1
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Solving Problems Involving Permutations (10.8.1)3
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Solving Problems Involving Combinations (10.8.2)2
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Independent Events (10.8.3)2
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Inclusive and Exclusive Events (10.8.4)3
