**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 x ^{2} + bx + c *

* 2 Factor trinomials of the form ax ^{2} + bx + c using trial-and-error*

* 3 Factor trinomials of the form ax ^{2} + 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 * *√(a ^{2})*

* 4 Find cube roots*

* 5 Find and approximate *n*th 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 * *a ^{1/n} *

* 2 Use the definition for rational exponents of the form a ^{m/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) = ax ^{2} + 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) = ax ^{2} + 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