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Review | |

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Sets of Numbers | |

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Identify sets | |

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Classify real numbers | |

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Plot real numbers on a number line | |

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Use inequality symbols to order real numbers | |

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Compute the absolute value of a real number | |

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Order of Operations and Properties of Real Numbers | |

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Perform operations on real numbers | |

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Simplify numeric expressions containing exponents and radicals | |

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Identify and use the properties of real numbers | |

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Use order of operations to evaluate numeric expressions | |

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Algebraic Expressions | |

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Evaluate algebraic expressions | |

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Simplify algebraic expressions | |

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Write verbal descriptions as algebraic expressions | |

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Equations and Inequalities in One Variable | |

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Linear Equations in One Variable | |

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Determine if a given value is a solution to an equation | |

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Solve linear equations in one variable | |

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Identify equations that are contradictions and those that are identities | |

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Use linear equations to solve application problems | |

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Linear Inequalities in One Variable | |

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Determine if a given value is a solution to an inequality | |

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Graph the solution set of an inequality on a number line | |

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Use interval notation to express the solution set of an inequality | |

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Solve linear inequalities in one variable | |

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Use linear inequalities to solve application problems | |

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Compound Inequalities; Absolute Value Equations and Inequalities | |

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Find the union and intersection of two sets | |

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Solve compound linear inequalities in one variable | |

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Solve absolute value equations | |

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Solve absolute value inequalities | |

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Formulas and Problem Solving | |

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Solve a formula for a given variable | |

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Use formulas to solve application problems | |

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Graphs and Functions | |

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The Rectangular Coordinate System and Graphing | |

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Plot ordered pairs in the rectangular coordinate system | |

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Determine if an ordered pair is a solution to an equation | |

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Find unknown coordinates | |

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Graph equations by plotting points | |

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Find x- and y-intercepts | |

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Relations and Functions | |

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Identify independent and dependent variables | |

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Find the domain and range of a relation | |

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Determine if relations are functions | |

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Determine if graphs are functions | |

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Solve application problems involving relations and functions | |

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Function Notation and Applications | |

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Express equations of functions using function notation | |

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Evaluate functions | |

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Graph simple functions by plotting points | |

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Interpret graphs of functions | |

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Solve application problems involving functions | |

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Graphs of Linear Functions | |

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Graph linear functions by plotting points | |

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Graph linear functions by using intercepts | |

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Graph vertical and horizontal lines | |

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Linear Equations in Two Variables | |

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Find the slope of a line | |

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Graph a line using the slope and a point | |

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Determine the relationship between two lines | |

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Write the equation of a line from given information | |

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Write equations of parallel and perpendicular lines | |

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Use linear models to solve application problems; direct variation | |

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Linear Inequalities in Two Variables | |

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Determine if an ordered pair is a solution to a linear inequality in two variables | |

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Graph a linear inequality in two variables | |

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Systems of Linear Equations and Inequalities | |

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Systems of Linear Equations in Two Variables | |

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Determine if an ordered pair is a solution to a system of linear equations in two variables | |

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Solve systems of linear equations in two variables by graphing | |

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Solve systems of linear equations in two variables by substitution | |

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Solve systems of linear equations in two variables by elimination | |

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Solve inconsistent and dependent systems | |

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Use systems of linear equations in two variables to solve application problems | |

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Systems of Linear Equations in Three Variables | |

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Determine if an ordered triple is a solution to a system of linear equations in three variables | |

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Solve systems of linear equations in three variables | |

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Use systems of linear equations in three variables to solve application problems | |

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More Problem Solving with Systems of Linear Equations | |

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Use systems of linear equations to solve uniform motion problems | |

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Use systems of linear equations to solve geometry problems | |

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Use systems of linear equations to solve mixture problems | |

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Systems of Linear Inequalities in Two Variables | |

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Determine if an ordered pair is a solution to a system of linear inequalities in two variables | |

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Graph systems of linear inequalities in two variables | |

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Polynomial Expressions and Functions | |

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Rules for Exponents | |

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Simplify exponential expressions using the product rule | |

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Simplify exponential expressions using the quotient rule | |

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Use the zero-power rule | |

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Use the negative-power rule | |

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Use the power-to-power rule | |

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Use the product-to-power and quotient-to-power rules | |

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Simplify exponential expressions using a combination of rules | |

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Use rules for exponents with scientific notation | |

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Introduction to Polynomial Functions | |

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Find the coefficient and degree of a monomial | |

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Find the leading coefficient and degree of a polynomial | |

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Evaluate a polynomial function for a given value | |

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Add polynomials | |

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Subtract polynomials | |

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Add and subtract polynomial functions | |

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Multiplying Polynomials | |

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Multiply monomials | |

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Multiply a polynomial by a monomial | |

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Multiply two binomials | |

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Multiply two binomials using special product rules | |

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Multiply two or more polynomials | |

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Multiply polynomial functions | |

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Dividing Polynomials | |

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Divide a polynomial by a monomial | |

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Divide polynomials using long division | |

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Divide polynomials using synthetic division | |

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Divide polynomial functions | |

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Use the Remainder and Factor theorems | |

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Factoring | |

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Greatest Common Factor and Factoring by Grouping | |

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Factor out the greatest common factor from a polynomial | |

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Factor by grouping | |

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Factoring Trinomials | |

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Factor trinomials of the form x2+ bx + c | |

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Factor trinomials of the form ax2+ bx + c using trial-and-error | |

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Factor trinomials of the form ax2+ bx + c using the ac method | |

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Factor trinomials using substitution | |

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Special-Case Factoring; A General Factoring Strategy | |

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Factor the difference of two squares | |

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Factor perfect square trinomials | |

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Factor the sum or difference of two cubes | |

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Factor polynomials completely | |

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Polynomial Equations and Models | |

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Solve polynomial equations by factoring | |

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Find the zeros of a polynomial function | |

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Use polynomial equations and models to solve application problems | |

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Rational Expressions, Equations, and Functions | |

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Introduction to Rational Expressions and Functions | |

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Find the domain of a rational function | |

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Evaluate rational functions | |

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Simplify rational expressions | |

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Multiplying and Dividing Rational Expressions | |

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Multiply rational expressions | |

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Divide rational expressions | |

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Adding and Subtracting Rational Expressions | |

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Add and subtract rational expressions with common denominators | |

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Find the least common denominator of rational expressions | |

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Add and subtract rational expressions with unlike denominators | |

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Complex Rational Expressions | |

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Simplify complex rational expressions by first simplifying the numerator and denominator | |

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Simplify complex rational expressions by multiplying by a common denominator | |

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Rational Equations and Models | |

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Identify rational equations | |

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Solve rational equations | |

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Find the zeros of a rational function | |

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Use rational equations to solve application problems | |

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Variation | |

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Solve application problems involving direct variation | |

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Solve application problems involving inverse variation | |

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Solve application problems involving combined variation | |

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Radicals and Rational Exponents | |

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Radical Expressions | |

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Find square roots of perfect squares | |

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Approximate square roots | |

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Simplify radical expressions of the formv(a2) | |

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Find cube roots | |

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Find and approximatenth roots | |

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Radical Functions | |

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Evaluate radical functions | |

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Find the domain of a radical function | |

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Graph functions that contain square roots or cube roots | |

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Rational Exponents and Simplifying Radical Expressions | |

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Use the definition for rational exponents of the forma1/n | |

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Use the definition for rational exponents of the form am/n | |

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Simplify exponential expressions involving rational exponents | |

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Use rational exponents to simplify radical expressions | |

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Simplify radical expressions using the product rule | |

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Simplify radical expressions using the quotient rule | |

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Operations with Radicals | |

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Add and subtract radical expressions | |

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Multiply radical expressions | |

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Rationalize denominators of radical expressions | |

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Radical Equations and Models | |

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Solve equations involving one radical expression | |

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Solve equations involving two radical expressions | |

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Use radical equations and models to solve application problems | |

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Complex Numbers | |

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Simplify powers of i | |

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Add and subtract complex numbers | |

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Multiply complex numbers | |

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Divide complex numbers | |

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Simplify radicals with negative radicands | |

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Quadratic Equations and Functions; Circles | |

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Solving Quadratic Equations | |

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Solve quadratic equations using factoring | |

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Solve quadratic equations using the square root property | |

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Solve quadratic equations by completing the square | |

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Solve quadratic equations using the quadratic formula | |

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Use the discriminant to determine the number and type of solutions to a quadratic equation | |

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Solve equations that are quadratic in form | |

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Quadratic Functions and Their Graphs | |

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Identify the characteristics of a quadratic function from its graph | |

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Graph quadratic functions by using translations | |

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Graph quadratic functions of the form f(x) = a(x-h)2+ k | |

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Find the vertex of a parabola by completing the square | |

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Graph quadratic functions of the form f(x) = ax2+ bx + c by completing the square | |

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Find the vertex of a parabola by using the vertex formula | |

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Graph quadratic functions of the form f(x) = ax2+ bx + c by using the vertex formula | |

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Applications and Modeling of Quadratic Functions | |

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Solve applications involving unknown numbers | |

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Solve applications involving projectile motion | |

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Solve applications involving geometric formulas | |

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Solve applications involving distance, rate, and time | |

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Solve applications involving work | |

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Maximize quadratic functions to solve application problems | |

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Minimize quadratic functions to solve application problems | |

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Circles | |

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Find the distance between two points | |

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Find the midpoint of a line segment | |

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Write the standard form of an equation of a circle | |

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Sketch the graph of a circle | |

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Find the center and radius of a circle | |

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Polynomial and Rational Inequalities | |

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Solve polynomial inequalities | |

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Solve rational inequalities | |

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Exponential and Logarithmic Functions and Equations | |

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Transformations of Functions | |

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Use vertical shifts to graph functions | |

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Use horizontal shifts to graph functions | |

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Use reflections to graph functions | |

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Use vertical stretches and compressions to graph functions | |

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Use horizontal stretches and compressions to graph functions | |

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Use a combination of transformations to graph functions | |

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Composite and Inverse Functions | |

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Form and evaluate composite functions | |

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Determine the domain of composite functions | |

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Determine if a function is one-to-one using the horizontal line test | |

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Verify inverse functions | |

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Sketch the graphs of inverse functions | |

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Find the inverse of a one-to-one function | |

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Exponential Functions | |

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Use the characteristics of exponential functions | |

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Sketch the graph of exponential functions using transformations | |

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Solve exponential equations by relating the bases | |

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Solve applications of exponential functions | |

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The Natural Exponential Function | |

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Use the characteristics of the natural exponential function | |

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Sketch the graph of natural exponential functions using transformations | |

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Solve natural exponential equations by relating the bases | |

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Solve applications of natural exponential functions | |

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Logarithmic Functions | |

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Use the definition of a logarithmic function | |

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Evaluate logarithmic expressions | |

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Use the properties of logarithms | |

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Use the common and natural logarithms | |

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Use the characteristics of logarithmic functions | |

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Sketch the graph of logarithmic functions using transformations | |

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Find the domain of logarithmic functions | |

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Properties of Logarithms | |

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Use the product rule, quotient rule, and power rule for logarithms | |

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Expand and condense logarithmic expressions | |

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Solve logarithmic equations by using the logarithm property of equality | |

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Use the change-of-base formula | |

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Exponential and Logarithmic Equations | |

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Solve exponential equations | |

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Solve logarithmic equations | |

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Applications of Exponential and Logarithmic Functions | |

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Solve compound interest applications | |

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Solve exponential growth and decay applications | |

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Solve logistic growth applications | |

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Use Newton's Law of Cooling | |

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Conic Sections | |

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Introduction to Conic Sections | |

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The Parabola | |

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Work With the Equation of a Parabola with a Vertical Axis of Symmetry | |

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Work With the Equation of a Parabola with a Horizontal Axis of Symmetry | |

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Find the Equation of a Parabola Given Information about the Graph | |

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Complete the Square to Find the Equation of a Parabola in Standard Form | |

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Solve Applications Involving Parabolas | |

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The Ellipse | |

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Sketch the Graph of an Ellipse | |

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Find the Equation of an Ellipse Given Information about the Graph | |

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Complete the Square to Find the Equation of an Ellipse in Standard Form | |

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Solve Applications Involving Ellipses | |

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The Hyperbola | |

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Sketch the Graph of a Hyperbola | |

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Find the Equation of a Hyperbola in Standard Form | |

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Complete the Square to Find the Equation of a Hyperbola in Standard Form | |

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Solve Applications Involving Hyperbolas | |

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Sequences and Series | |

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Introduction to Sequences and Series | |

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Write the terms of a sequence | |

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Write the terms of a recursive sequence | |

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Write the general term for a given sequence | |

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Compute partial sums of a series | |

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Determine the sum of a finite series written in summation notation | |

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Write a series using summation notation | |

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Arithmetic Sequences and Series | |

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Determine if a sequence is arithmetic | |

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Find the general term or specific term of an arithmetic sequence | |

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Compute the nth partial sum of an arithmetic series | |

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Solve applications of arithmetic sequences and series | |

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Geometric Sequences and Series | |

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Write the terms of a geometric sequence | |

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Determine if a sequence is geometric | |

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Find the general term or specific term of a geometric sequence | |

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Compute the nth partial sum of a geometric series | |

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Determine if an infinite geometric series converges or diverges | |

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Solve applications of geometric sequences and series | |

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The Binomial Theorem | |

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Expand binomials raised to a power using Pascal's Triangle | |

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Evaluate binomial coefficients | |

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Expand binomials raised to a power using the Binomial Theorem | |

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Find a particular term or a particular coefficient of a binomial expansion | |

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Basic Math Review - Fractions, Decimals, Proportions, Percents | |

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Fractions | |

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Decimals | |

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Proportions | |

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Percents | |