| |
| |
| |
| Review | |
| |
| |
| |
| Sets of Numbers | |
| |
| |
| |
| Identify sets | |
| |
| |
| |
| Classify real numbers | |
| |
| |
| |
| Plot real numbers on a number line | |
| |
| |
| |
| Use inequality symbols to order real numbers | |
| |
| |
| |
| Compute the absolute value of a real number | |
| |
| |
| |
| Order of Operations and Properties of Real Numbers | |
| |
| |
| |
| Perform operations on real numbers | |
| |
| |
| |
| Simplify numeric expressions containing exponents and radicals | |
| |
| |
| |
| Identify and use the properties of real numbers | |
| |
| |
| |
| Use order of operations to evaluate numeric expressions | |
| |
| |
| |
| Algebraic Expressions | |
| |
| |
| |
| Evaluate algebraic expressions | |
| |
| |
| |
| Simplify algebraic expressions | |
| |
| |
| |
| Write verbal descriptions as algebraic expressions | |
| |
| |
| |
| Equations and Inequalities in One Variable | |
| |
| |
| |
| Linear Equations in One Variable | |
| |
| |
| |
| Determine if a given value is a solution to an equation | |
| |
| |
| |
| Solve linear equations in one variable | |
| |
| |
| |
| Identify equations that are contradictions and those that are identities | |
| |
| |
| |
| Use linear equations to solve application problems | |
| |
| |
| |
| Linear Inequalities in One Variable | |
| |
| |
| |
| Determine if a given value is a solution to an inequality | |
| |
| |
| |
| Graph the solution set of an inequality on a number line | |
| |
| |
| |
| Use interval notation to express the solution set of an inequality | |
| |
| |
| |
| Solve linear inequalities in one variable | |
| |
| |
| |
| Use linear inequalities to solve application problems | |
| |
| |
| |
| Compound Inequalities; Absolute Value Equations and Inequalities | |
| |
| |
| |
| Find the union and intersection of two sets | |
| |
| |
| |
| Solve compound linear inequalities in one variable | |
| |
| |
| |
| Solve absolute value equations | |
| |
| |
| |
| Solve absolute value inequalities | |
| |
| |
| |
| Formulas and Problem Solving | |
| |
| |
| |
| Solve a formula for a given variable | |
| |
| |
| |
| Use formulas to solve application problems | |
| |
| |
| |
| Graphs and Functions | |
| |
| |
| |
| The Rectangular Coordinate System and Graphing | |
| |
| |
| |
| Plot ordered pairs in the rectangular coordinate system | |
| |
| |
| |
| Determine if an ordered pair is a solution to an equation | |
| |
| |
| |
| Find unknown coordinates | |
| |
| |
| |
| Graph equations by plotting points | |
| |
| |
| |
| Find x- and y-intercepts | |
| |
| |
| |
| Relations and Functions | |
| |
| |
| |
| Identify independent and dependent variables | |
| |
| |
| |
| Find the domain and range of a relation | |
| |
| |
| |
| Determine if relations are functions | |
| |
| |
| |
| Determine if graphs are functions | |
| |
| |
| |
| Solve application problems involving relations and functions | |
| |
| |
| |
| Function Notation and Applications | |
| |
| |
| |
| Express equations of functions using function notation | |
| |
| |
| |
| Evaluate functions | |
| |
| |
| |
| Graph simple functions by plotting points | |
| |
| |
| |
| Interpret graphs of functions | |
| |
| |
| |
| Solve application problems involving functions | |
| |
| |
| |
| Graphs of Linear Functions | |
| |
| |
| |
| Graph linear functions by plotting points | |
| |
| |
| |
| Graph linear functions by using intercepts | |
| |
| |
| |
| Graph vertical and horizontal lines | |
| |
| |
| |
| Linear Equations in Two Variables | |
| |
| |
| |
| Find the slope of a line | |
| |
| |
| |
| Graph a line using the slope and a point | |
| |
| |
| |
| Determine the relationship between two lines | |
| |
| |
| |
| Write the equation of a line from given information | |
| |
| |
| |
| Write equations of parallel and perpendicular lines | |
| |
| |
| |
| Use linear models to solve application problems; direct variation | |
| |
| |
| |
| Linear Inequalities in Two Variables | |
| |
| |
| |
| Determine if an ordered pair is a solution to a linear inequality in two variables | |
| |
| |
| |
| Graph a linear inequality in two variables | |
| |
| |
| |
| Systems of Linear Equations and Inequalities | |
| |
| |
| |
| Systems of Linear Equations in Two Variables | |
| |
| |
| |
| Determine if an ordered pair is a solution to a system of linear equations in two variables | |
| |
| |
| |
| Solve systems of linear equations in two variables by graphing | |
| |
| |
| |
| Solve systems of linear equations in two variables by substitution | |
| |
| |
| |
| Solve systems of linear equations in two variables by elimination | |
| |
| |
| |
| Solve inconsistent and dependent systems | |
| |
| |
| |
| Use systems of linear equations in two variables to solve application problems | |
| |
| |
| |
| Systems of Linear Equations in Three Variables | |
| |
| |
| |
| Determine if an ordered triple is a solution to a system of linear equations in three variables | |
| |
| |
| |
| Solve systems of linear equations in three variables | |
| |
| |
| |
| Use systems of linear equations in three variables to solve application problems | |
| |
| |
| |
| More Problem Solving with Systems of Linear Equations | |
| |
| |
| |
| Use systems of linear equations to solve uniform motion problems | |
| |
| |
| |
| Use systems of linear equations to solve geometry problems | |
| |
| |
| |
| Use systems of linear equations to solve mixture problems | |
| |
| |
| |
| Systems of Linear Inequalities in Two Variables | |
| |
| |
| |
| Determine if an ordered pair is a solution to a system of linear inequalities in two variables | |
| |
| |
| |
| Graph systems of linear inequalities in two variables | |
| |
| |
| |
| Polynomial Expressions and Functions | |
| |
| |
| |
| Rules for Exponents | |
| |
| |
| |
| Simplify exponential expressions using the product rule | |
| |
| |
| |
| Simplify exponential expressions using the quotient rule | |
| |
| |
| |
| Use the zero-power rule | |
| |
| |
| |
| Use the negative-power rule | |
| |
| |
| |
| Use the power-to-power rule | |
| |
| |
| |
| Use the product-to-power and quotient-to-power rules | |
| |
| |
| |
| Simplify exponential expressions using a combination of rules | |
| |
| |
| |
| Use rules for exponents with scientific notation | |
| |
| |
| |
| Introduction to Polynomial Functions | |
| |
| |
| |
| Find the coefficient and degree of a monomial | |
| |
| |
| |
| Find the leading coefficient and degree of a polynomial | |
| |
| |
| |
| Evaluate a polynomial function for a given value | |
| |
| |
| |
| Add polynomials | |
| |
| |
| |
| Subtract polynomials | |
| |
| |
| |
| Add and subtract polynomial functions | |
| |
| |
| |
| Multiplying Polynomials | |
| |
| |
| |
| Multiply monomials | |
| |
| |
| |
| Multiply a polynomial by a monomial | |
| |
| |
| |
| Multiply two binomials | |
| |
| |
| |
| Multiply two binomials using special product rules | |
| |
| |
| |
| Multiply two or more polynomials | |
| |
| |
| |
| Multiply polynomial functions | |
| |
| |
| |
| Dividing Polynomials | |
| |
| |
| |
| Divide a polynomial by a monomial | |
| |
| |
| |
| Divide polynomials using long division | |
| |
| |
| |
| Divide polynomials using synthetic division | |
| |
| |
| |
| Divide polynomial functions | |
| |
| |
| |
| Use the Remainder and Factor theorems | |
| |
| |
| |
| Factoring | |
| |
| |
| |
| Greatest Common Factor and Factoring by Grouping | |
| |
| |
| |
| Factor out the greatest common factor from a polynomial | |
| |
| |
| |
| Factor by grouping | |
| |
| |
| |
| Factoring Trinomials | |
| |
| |
| |
| Factor trinomials of the form x2+ bx + c | |
| |
| |
| |
| Factor trinomials of the form ax2+ bx + c using trial-and-error | |
| |
| |
| |
| Factor trinomials of the form ax2+ bx + c using the ac method | |
| |
| |
| |
| Factor trinomials using substitution | |
| |
| |
| |
| Special-Case Factoring; A General Factoring Strategy | |
| |
| |
| |
| Factor the difference of two squares | |
| |
| |
| |
| Factor perfect square trinomials | |
| |
| |
| |
| Factor the sum or difference of two cubes | |
| |
| |
| |
| Factor polynomials completely | |
| |
| |
| |
| Polynomial Equations and Models | |
| |
| |
| |
| Solve polynomial equations by factoring | |
| |
| |
| |
| Find the zeros of a polynomial function | |
| |
| |
| |
| Use polynomial equations and models to solve application problems | |
| |
| |
| |
| Rational Expressions, Equations, and Functions | |
| |
| |
| |
| Introduction to Rational Expressions and Functions | |
| |
| |
| |
| Find the domain of a rational function | |
| |
| |
| |
| Evaluate rational functions | |
| |
| |
| |
| Simplify rational expressions | |
| |
| |
| |
| Multiplying and Dividing Rational Expressions | |
| |
| |
| |
| Multiply rational expressions | |
| |
| |
| |
| Divide rational expressions | |
| |
| |
| |
| Adding and Subtracting Rational Expressions | |
| |
| |
| |
| Add and subtract rational expressions with common denominators | |
| |
| |
| |
| Find the least common denominator of rational expressions | |
| |
| |
| |
| Add and subtract rational expressions with unlike denominators | |
| |
| |
| |
| Complex Rational Expressions | |
| |
| |
| |
| Simplify complex rational expressions by first simplifying the numerator and denominator | |
| |
| |
| |
| Simplify complex rational expressions by multiplying by a common denominator | |
| |
| |
| |
| Rational Equations and Models | |
| |
| |
| |
| Identify rational equations | |
| |
| |
| |
| Solve rational equations | |
| |
| |
| |
| Find the zeros of a rational function | |
| |
| |
| |
| Use rational equations to solve application problems | |
| |
| |
| |
| Variation | |
| |
| |
| |
| Solve application problems involving direct variation | |
| |
| |
| |
| Solve application problems involving inverse variation | |
| |
| |
| |
| Solve application problems involving combined variation | |
| |
| |
| |
| Radicals and Rational Exponents | |
| |
| |
| |
| Radical Expressions | |
| |
| |
| |
| Find square roots of perfect squares | |
| |
| |
| |
| Approximate square roots | |
| |
| |
| |
| Simplify radical expressions of the formv(a2) | |
| |
| |
| |
| Find cube roots | |
| |
| |
| |
| Find and approximatenth roots | |
| |
| |
| |
| Radical Functions | |
| |
| |
| |
| Evaluate radical functions | |
| |
| |
| |
| Find the domain of a radical function | |
| |
| |
| |
| Graph functions that contain square roots or cube roots | |
| |
| |
| |
| Rational Exponents and Simplifying Radical Expressions | |
| |
| |
| |
| Use the definition for rational exponents of the forma1/n | |
| |
| |
| |
| Use the definition for rational exponents of the form am/n | |
| |
| |
| |
| Simplify exponential expressions involving rational exponents | |
| |
| |
| |
| Use rational exponents to simplify radical expressions | |
| |
| |
| |
| Simplify radical expressions using the product rule | |
| |
| |
| |
| Simplify radical expressions using the quotient rule | |
| |
| |
| |
| Operations with Radicals | |
| |
| |
| |
| Add and subtract radical expressions | |
| |
| |
| |
| Multiply radical expressions | |
| |
| |
| |
| Rationalize denominators of radical expressions | |
| |
| |
| |
| Radical Equations and Models | |
| |
| |
| |
| Solve equations involving one radical expression | |
| |
| |
| |
| Solve equations involving two radical expressions | |
| |
| |
| |
| Use radical equations and models to solve application problems | |
| |
| |
| |
| Complex Numbers | |
| |
| |
| |
| Simplify powers of i | |
| |
| |
| |
| Add and subtract complex numbers | |
| |
| |
| |
| Multiply complex numbers | |
| |
| |
| |
| Divide complex numbers | |
| |
| |
| |
| Simplify radicals with negative radicands | |
| |
| |
| |
| Quadratic Equations and Functions; Circles | |
| |
| |
| |
| Solving Quadratic Equations | |
| |
| |
| |
| Solve quadratic equations using factoring | |
| |
| |
| |
| Solve quadratic equations using the square root property | |
| |
| |
| |
| Solve quadratic equations by completing the square | |
| |
| |
| |
| Solve quadratic equations using the quadratic formula | |
| |
| |
| |
| Use the discriminant to determine the number and type of solutions to a quadratic equation | |
| |
| |
| |
| Solve equations that are quadratic in form | |
| |
| |
| |
| Quadratic Functions and Their Graphs | |
| |
| |
| |
| Identify the characteristics of a quadratic function from its graph | |
| |
| |
| |
| Graph quadratic functions by using translations | |
| |
| |
| |
| Graph quadratic functions of the form f(x) = a(x-h)2+ k | |
| |
| |
| |
| Find the vertex of a parabola by completing the square | |
| |
| |
| |
| Graph quadratic functions of the form f(x) = ax2+ bx + c by completing the square | |
| |
| |
| |
| Find the vertex of a parabola by using the vertex formula | |
| |
| |
| |
| Graph quadratic functions of the form f(x) = ax2+ bx + c by using the vertex formula | |
| |
| |
| |
| Applications and Modeling of Quadratic Functions | |
| |
| |
| |
| Solve applications involving unknown numbers | |
| |
| |
| |
| Solve applications involving projectile motion | |
| |
| |
| |
| Solve applications involving geometric formulas | |
| |
| |
| |
| Solve applications involving distance, rate, and time | |
| |
| |
| |
| Solve applications involving work | |
| |
| |
| |
| Maximize quadratic functions to solve application problems | |
| |
| |
| |
| Minimize quadratic functions to solve application problems | |
| |
| |
| |
| Circles | |
| |
| |
| |
| Find the distance between two points | |
| |
| |
| |
| Find the midpoint of a line segment | |
| |
| |
| |
| Write the standard form of an equation of a circle | |
| |
| |
| |
| Sketch the graph of a circle | |
| |
| |
| |
| Find the center and radius of a circle | |
| |
| |
| |
| Polynomial and Rational Inequalities | |
| |
| |
| |
| Solve polynomial inequalities | |
| |
| |
| |
| Solve rational inequalities | |
| |
| |
| |
| Exponential and Logarithmic Functions and Equations | |
| |
| |
| |
| Transformations of Functions | |
| |
| |
| |
| Use vertical shifts to graph functions | |
| |
| |
| |
| Use horizontal shifts to graph functions | |
| |
| |
| |
| Use reflections to graph functions | |
| |
| |
| |
| Use vertical stretches and compressions to graph functions | |
| |
| |
| |
| Use horizontal stretches and compressions to graph functions | |
| |
| |
| |
| Use a combination of transformations to graph functions | |
| |
| |
| |
| Composite and Inverse Functions | |
| |
| |
| |
| Form and evaluate composite functions | |
| |
| |
| |
| Determine the domain of composite functions | |
| |
| |
| |
| Determine if a function is one-to-one using the horizontal line test | |
| |
| |
| |
| Verify inverse functions | |
| |
| |
| |
| Sketch the graphs of inverse functions | |
| |
| |
| |
| Find the inverse of a one-to-one function | |
| |
| |
| |
| Exponential Functions | |
| |
| |
| |
| Use the characteristics of exponential functions | |
| |
| |
| |
| Sketch the graph of exponential functions using transformations | |
| |
| |
| |
| Solve exponential equations by relating the bases | |
| |
| |
| |
| Solve applications of exponential functions | |
| |
| |
| |
| The Natural Exponential Function | |
| |
| |
| |
| Use the characteristics of the natural exponential function | |
| |
| |
| |
| Sketch the graph of natural exponential functions using transformations | |
| |
| |
| |
| Solve natural exponential equations by relating the bases | |
| |
| |
| |
| Solve applications of natural exponential functions | |
| |
| |
| |
| Logarithmic Functions | |
| |
| |
| |
| Use the definition of a logarithmic function | |
| |
| |
| |
| Evaluate logarithmic expressions | |
| |
| |
| |
| Use the properties of logarithms | |
| |
| |
| |
| Use the common and natural logarithms | |
| |
| |
| |
| Use the characteristics of logarithmic functions | |
| |
| |
| |
| Sketch the graph of logarithmic functions using transformations | |
| |
| |
| |
| Find the domain of logarithmic functions | |
| |
| |
| |
| Properties of Logarithms | |
| |
| |
| |
| Use the product rule, quotient rule, and power rule for logarithms | |
| |
| |
| |
| Expand and condense logarithmic expressions | |
| |
| |
| |
| Solve logarithmic equations by using the logarithm property of equality | |
| |
| |
| |
| Use the change-of-base formula | |
| |
| |
| |
| Exponential and Logarithmic Equations | |
| |
| |
| |
| Solve exponential equations | |
| |
| |
| |
| Solve logarithmic equations | |
| |
| |
| |
| Applications of Exponential and Logarithmic Functions | |
| |
| |
| |
| Solve compound interest applications | |
| |
| |
| |
| Solve exponential growth and decay applications | |
| |
| |
| |
| Solve logistic growth applications | |
| |
| |
| |
| Use Newton's Law of Cooling | |
| |
| |
| |
| Conic Sections | |
| |
| |
| Introduction to Conic Sections | |
| |
| |
| |
| The Parabola | |
| |
| |
| |
| Work With the Equation of a Parabola with a Vertical Axis of Symmetry | |
| |
| |
| |
| Work With the Equation of a Parabola with a Horizontal Axis of Symmetry | |
| |
| |
| |
| Find the Equation of a Parabola Given Information about the Graph | |
| |
| |
| |
| Complete the Square to Find the Equation of a Parabola in Standard Form | |
| |
| |
| |
| Solve Applications Involving Parabolas | |
| |
| |
| |
| The Ellipse | |
| |
| |
| |
| Sketch the Graph of an Ellipse | |
| |
| |
| |
| Find the Equation of an Ellipse Given Information about the Graph | |
| |
| |
| |
| Complete the Square to Find the Equation of an Ellipse in Standard Form | |
| |
| |
| |
| Solve Applications Involving Ellipses | |
| |
| |
| |
| The Hyperbola | |
| |
| |
| |
| Sketch the Graph of a Hyperbola | |
| |
| |
| |
| Find the Equation of a Hyperbola in Standard Form | |
| |
| |
| |
| Complete the Square to Find the Equation of a Hyperbola in Standard Form | |
| |
| |
| |
| Solve Applications Involving Hyperbolas | |
| |
| |
| |
| Sequences and Series | |
| |
| |
| |
| Introduction to Sequences and Series | |
| |
| |
| |
| Write the terms of a sequence | |
| |
| |
| |
| Write the terms of a recursive sequence | |
| |
| |
| |
| Write the general term for a given sequence | |
| |
| |
| |
| Compute partial sums of a series | |
| |
| |
| |
| Determine the sum of a finite series written in summation notation | |
| |
| |
| |
| Write a series using summation notation | |
| |
| |
| |
| Arithmetic Sequences and Series | |
| |
| |
| |
| Determine if a sequence is arithmetic | |
| |
| |
| |
| Find the general term or specific term of an arithmetic sequence | |
| |
| |
| |
| Compute the nth partial sum of an arithmetic series | |
| |
| |
| |
| Solve applications of arithmetic sequences and series | |
| |
| |
| |
| Geometric Sequences and Series | |
| |
| |
| |
| Write the terms of a geometric sequence | |
| |
| |
| |
| Determine if a sequence is geometric | |
| |
| |
| |
| Find the general term or specific term of a geometric sequence | |
| |
| |
| |
| Compute the nth partial sum of a geometric series | |
| |
| |
| |
| Determine if an infinite geometric series converges or diverges | |
| |
| |
| |
| Solve applications of geometric sequences and series | |
| |
| |
| |
| The Binomial Theorem | |
| |
| |
| |
| Expand binomials raised to a power using Pascal's Triangle | |
| |
| |
| |
| Evaluate binomial coefficients | |
| |
| |
| |
| Expand binomials raised to a power using the Binomial Theorem | |
| |
| |
| |
| Find a particular term or a particular coefficient of a binomial expansion | |
| |
| |
| |
| Basic Math Review - Fractions, Decimals, Proportions, Percents | |
| |
| |
| |
| Fractions | |
| |
| |
| |
| Decimals | |
| |
| |
| |
| Proportions | |
| |
| |
| |
| Percents | |