Chapter R. Review
R.1 Sets of Numbers
1 Identify sets
2 Classify real numbers
3 Plot real numbers on a number line
4 Use inequality symbols to order real numbers
5 Compute the absolute value of a real number
R.2 Order of Operations and Properties of Real Numbers
1 Perform operations on real numbers
2 Simplify numeric expressions containing exponents and radicals
3 Identify and use the properties of real numbers
4 Use order of operations to evaluate numeric expressions
R.3 Algebraic Expressions
1 Evaluate algebraic expressions
2 Simplify algebraic expressions
3 Write verbal descriptions as algebraic expressions
Chapter 1. Equations and Inequalities in One Variable
1.1 Linear Equations in One Variable
1 Determine if a given value is a solution to an equation
2 Solve linear equations in one variable
3 Identify equations that are contradictions and those that are identities
4 Use linear equations to solve application problems
1.2 Linear Inequalities in One Variable
1 Determine if a given value is a solution to an inequality
2 Graph the solution set of an inequality on a number line
3 Use interval notation to express the solution set of an inequality
4 Solve linear inequalities in one variable
5 Use linear inequalities to solve application problems
1.3 Compound Inequalities; Absolute Value Equations and Inequalities
1 Find the union and intersection of two sets
2 Solve compound linear inequalities in one variable
3 Solve absolute value equations
4 Solve absolute value inequalities
1.4 Formulas and Problem Solving
1 Solve a formula for a given variable
2 Use formulas to solve application problems
Chapter 2. Graphs and Functions
2.1 The Rectangular Coordinate System and Graphing
1 Plot ordered pairs in the rectangular coordinate system
2 Determine if an ordered pair is a solution to an equation
3 Find unknown coordinates
4 Graph equations by plotting points
5 Find x- and y-intercepts
2.2 Relations and Functions
1 Identify independent and dependent variables
2 Find the domain and range of a relation
3 Determine if relations are functions
4 Determine if graphs are functions
5 Solve application problems involving relations and functions
2.3. Function Notation and Applications
1 Express equations of functions using function notation
2 Evaluate functions
3 Graph simple functions by plotting points
4 Interpret graphs of functions
5 Solve application problems involving functions
2.4 Graphs of Linear Functions
1 Graph linear functions by plotting points
2 Graph linear functions by using intercepts
3 Graph vertical and horizontal lines
2.5 Linear Equations in Two Variables
1 Find the slope of a line
2 Graph a line using the slope and a point
3 Determine the relationship between two lines
4 Write the equation of a line from given information
5 Write equations of parallel and perpendicular lines
6 Use linear models to solve application problems; direct variation
2.6 Linear Inequalities in Two Variables
1 Determine if an ordered pair is a solution to a linear inequality in two variables
2 Graph a linear inequality in two variables
Chapter 3. Systems of Linear Equations and Inequalities
3.1 Systems of Linear Equations in Two Variables
1 Determine if an ordered pair is a solution to a system of linear equations in two variables
2 Solve systems of linear equations in two variables by graphing
3 Solve systems of linear equations in two variables by substitution
4 Solve systems of linear equations in two variables by elimination
5 Solve inconsistent and dependent systems
6 Use systems of linear equations in two variables to solve application problems
3.2 Systems of Linear Equations in Three Variables
1 Determine if an ordered triple is a solution to a system of linear equations in three variables
2 Solve systems of linear equations in three variables
3 Use systems of linear equations in three variables to solve application problems
3.3 More Problem Solving with Systems of Linear Equations
1 Use systems of linear equations to solve uniform motion problems
2 Use systems of linear equations to solve geometry problems
3 Use systems of linear equations to solve mixture problems
3.4 Systems of Linear Inequalities in Two Variables
1 Determine if an ordered pair is a solution to a system of linear inequalities in two variables
2 Graph systems of linear inequalities in two variables
Chapter 4. Polynomial Expressions and Functions
4.1 Rules for Exponents
1 Simplify exponential expressions using the product rule
2 Simplify exponential expressions using the quotient rule
3 Use the zero-power rule
4 Use the negative-power rule
5 Use the power-to-power rule
6 Use the product-to-power and quotient-to-power rules
7 Simplify exponential expressions using a combination of rules
8 Use rules for exponents with scientific notation
4.2 Introduction to Polynomial Functions
1 Find the coefficient and degree of a monomial
2 Find the leading coefficient and degree of a polynomial
3 Evaluate a polynomial function for a given value
4 Add polynomials
5 Subtract polynomials
6 Add and subtract polynomial functions
4.3 Multiplying Polynomials
1 Multiply monomials
2 Multiply a polynomial by a monomial
3 Multiply two binomials
4 Multiply two binomials using special product rules
5 Multiply two or more polynomials
6 Multiply polynomial functions
4.4 Dividing Polynomials
1 Divide a polynomial by a monomial
2 Divide polynomials using long division
3 Divide polynomials using synthetic division
4 Divide polynomial functions
5 Use the Remainder and Factor theorems
Chapter 5. Factoring
5.1 Greatest Common Factor and Factoring by Grouping
1 Factor out the greatest common factor from a polynomial
2 Factor by grouping
5.2 Factoring Trinomials
1 Factor trinomials of the form x2 + bx + c
2 Factor trinomials of the form ax2 + bx + c using trial-and-error
3 Factor trinomials of the form ax2 + bx + c using the ac method
4 Factor trinomials using substitution
5.3 Special-Case Factoring; A General Factoring Strategy
1 Factor the difference of two squares
2 Factor perfect square trinomials
3 Factor the sum or difference of two cubes
4 Factor polynomials completely
5.4 Polynomial Equations and Models
1 Solve polynomial equations by factoring
2 Find the zeros of a polynomial function
3 Use polynomial equations and models to solve application problems
Chapter 6. Rational Expressions, Equations, and Functions
6.1 Introduction to Rational Expressions and Functions
1 Find the domain of a rational function
2 Evaluate rational functions
3 Simplify rational expressions
6.2 Multiplying and Dividing Rational Expressions
1 Multiply rational expressions
2 Divide rational expressions
6.3 Adding and Subtracting Rational Expressions
1 Add and subtract rational expressions with common denominators
2 Find the least common denominator of rational expressions
3 Add and subtract rational expressions with unlike denominators
6.4 Complex Rational Expressions
1 Simplify complex rational expressions by first simplifying the numerator and denominator
2 Simplify complex rational expressions by multiplying by a common denominator
6.5 Rational Equations and Models
1 Identify rational equations
2 Solv e rational equations
3 Find the zeros of a rational function
4 Us e rational equations to solve application problems
6.6 Variation
1 Solve application problems involving direct variation
2 Solve application problems involving inverse variation
2 Solve application problems involving combined variation
Chapter 7. Radicals and Rational Exponents
7.1 Radical Expressions
1 Find square roots of perfect squares
2 Approximate square roots
3 Simplify radical expressions of the form √(a2)
4 Find cube roots
5 Find and approximate nth roots
7.2 Radical Functions
1 Evaluate radical functions
2 Find the domain of a radical function
3 Graph functions that contain square roots or cube roots
7.3 Rational Exponents and Simplifying Radical Expressions
1 Use the definition for rational exponents of the form a1/n
2 Use the definition for rational exponents of the form am/n
3. Simplify exponential expressions involving rational exponents
4 Use rational exponents to simplify radical expressions
5 Simplify radical expressions using the product rule
6 Simplify radical expressions using the quotient rule
7.4 Operations with Radicals
1 Add and subtract radical expressions
2 Multiply radical expressions
3 Rationalize denominators of radical expressions
7.5 Radical Equations and Models
1 Solve equations involving one radical expression
2 Solve equations involving two radical expressions
3 Use radical equations and models to solve application problems
7.6 Complex Numbers
1 Simplify powers of i
2 Add and subtract complex numbers
3 Multiply complex numbers
4 Divide complex numbers
5 Simplify radicals with negative radicands
Chapter 8. Quadratic Equations and Functions; Circles
8.1 Solving Quadratic Equations
1 Solve quadratic equations using factoring
2 Solve quadratic equations using the square root property
3 Solve quadratic equations by completing the square
4 Solve quadratic equations using the quadratic formula
5 Use the discriminant to determine the number and type of solutions to a quadratic equation
6 Solve equations that are quadratic in form
8.2 Quadratic Functions and Their Graphs
1 Identify the characteristics of a quadratic function from its graph
2 Graph quadratic functions by using translations
3 Graph quadratic functions of the form f(x) = a(x-h)2 + k
4 Find the vertex of a parabola by completing the square
5 Graph quadratic functions of the form f(x) = ax2 + bx + c by completing the square
6 Find the vertex of a parabola by using the vertex formula
7 Graph quadratic functions of the form f(x) = ax2 + bx + c by using the vertex formula
8.3 Applications and Modeling of Quadratic Functions
1 Solve applications involving unknown numbers
2 Solve applications involving projectile motion
3 Solve applications involving geometric formulas
4 Solve applications involving distance, rate, and time
5 Solve applications involving work
6 Maximize quadratic functions to solve application problems
7 Minimize quadratic functions to solve application problems
8.4 Circles
1 Find the distance between two points
2 Find the midpoint of a line segment
3 Write the standard form of an equation of a circle
4 Sketch the graph of a circle
5 Find the center and radius of a circle
8.5 Polynomial and Rational Inequalities
1 Solve polynomial inequalities
2 Solve rational inequalities
Chapter 9. Exponential and Logarithmic Functions and Equations
9.1 Transformations of Functions
1 Use vertical shifts to graph functions
2 Use horizontal shifts to graph functions
3 Use reflections to graph functions
4 Use vertical stretches and compressions to graph functions
5 Use horizontal stretches and compressions to graph functions
6 Use a combination of transformations to graph functions
9.2 Composite and Inverse Functions
1 Form and evaluate composite functions
2 Determine the domain of composite functions
3 Determine if a function is one-to-one using the horizontal line test
4 Verify inverse functions
5 Sketch the graphs of inverse functions
6 Find the inverse of a one-to-one function
9.3 Exponential Functions
1 Use the characteristics of exponential functions
2 Sketch the graph of exponential functions using transformations
3 Solve exponential equations by relating the bases
4 Solve applications of exponential functions
9.4 The Natural Exponential Function
1 Use the characteristics of the natural exponential function
2 Sketch the graph of natural exponential functions using transformations
3 Solve natural exponential equations by relating the bases
4 Solve applications of natural exponential functions
9.5 Logarithmic Functions
1 Use the definition of a logarithmic function
2 Evaluate logarithmic expressions
3 Use the properties of logarithms
4 Use the common and natural logarithms
5 Use the characteristics of logarithmic functions
6 Sketch the graph of logarithmic functions using transformations
7 Find the domain of logarithmic functions
9.6 Properties of Logarithms
1 Use the product rule, quotient rule, and power rule for logarithms
2 Expand and condense logarithmic expressions
3 Solve logarithmic equations by using the logarithm property of equality
4 Use the change-of-base formula
9.7 Exponential and Logarithmic Equations
1 Solve exponential equations
2 Solve logarithmic equations
9.8 Applications of Exponential and Logarithmic Functions
1 Solve compound interest applications
2 Solve exponential growth and decay applications
3 Solve logistic growth applications
4 Use Newton’s Law of Cooling
Appendix A. Conic Sections
Introduction to Conic Sections
A.1 The Parabola
1 Work With the Equation of a Parabola with a Vertical Axis of Symmetry
2 Work With the Equation of a Parabola with a Horizontal Axis of Symmetry
3 Find the Equation of a Parabola Given Information about the Graph
4 Complete the Square to Find the Equation of a Parabola in Standard Form
5 Solve Applications Involving Parabolas
A.2 The Ellipse
1 Sketch the Graph of an Ellipse
2 Find the Equation of an Ellipse Given Information about the Graph
3 Complete the Square to Find the Equation of an Ellipse in Standard Form
4 Solve Applications Involving Ellipses
A.3 The Hyperbola
1 Sketch the Graph of a Hyperbola
2 Find the Equation of a Hyperbola in Standard Form
3 Complete the Square to Find the Equation of a Hyperbola in Standard Form
4 Solve Applications Involving Hyperbolas
Appendix B Sequences and Series
B.1 Introduction to Sequences and Series
1 Write the terms of a sequence
2 Write the terms of a recursive sequence
3 Write the general term for a given sequence
4 Compute partial sums of a series
5 Determine the sum of a finite series written in summation notation
6 Write a series using summation notation
B.2 Arithmetic Sequences and Series
1 Determine if a sequence is arithmetic
2 Find the general term or specific term of an arithmetic sequence
3 Compute the nth partial sum of an arithmetic series
4 Solve applications of arithmetic sequences and series
B.3 Geometric Sequences and Series
1 Write the terms of a geometric sequence
2 Determin e if a sequence is geometric
2 Find the general term or specific term of a geometric sequence
3 Comput e the nth partial sum of a geometric series
5 Determine if an infinite geometric series converges or diverges
4 Solve applications of geometric sequences and series
B.4 The Binomial Theorem
1 Expand binomials raised to a power using Pascal’s Triangle
2 Evaluate binomial coefficients
3 Expand binomials raised to a power using the Binomial Theorem
4 Find a particular term or a particular coefficient of a binomial expansion
Appendix C Basic Math Review - Fractions, Decimals, Proportions, Percents
C.1 Fractions
C.2 Decimals
C.3 Proportions
C.4 Percents