Preface 

xiii  
To the Student 

xxi  
Index of Applications 

xxiii  

Real Numbers and Variable Expressions 


1  (70) 


3  (14) 

To use inequality symbols with integers 


3  (1) 

To find the additive inverse and absolute value of a number 


4  (1) 

To add of subtract integers 


5  (2) 

To multiply or divide integers 


7  (3) 

To solve application problems 


10  (7) 

Rational and Irrational Numbers 


17  (16) 

To Write a rational number as a decimal 


17  (1) 

To convert among percents, fractions, and decimals 


18  (1) 

To add or subtract rational numbers 


19  (1) 

To multiply or divide rational numbers 


20  (2) 

To evaluate exponential expressions 


22  (2) 

To simplify numerical radical expressions 


24  (2) 

To solve application problems 


26  (7) 

The Order of Operations Agreement 


33  (4) 

To use the Order of Operations Agreement to simplify expressions 


33  (4) 


37  (18) 

To evaluate a variable expression 


37  (1) 

To simplify a variable expression using the Properties of Addition 


38  (2) 

To simplify a variable expression using the Properties of Multiplication 


40  (2) 

To simplify a variable expression using the Distributive Property 


42  (2) 

To translate a verbal expression into a variable expression 


44  (11) 


55  (16) 

To write a set using the roster method 


55  (1) 

To write a set using setbuilder notation 


56  (1) 

To graph an inequality on the number line 


57  (4) 


61  (1) 

Projects and Group Activities 


62  (2) 


64  (3) 


67  (2) 


69  (2) 

FirstDegree Equations and Inequalities 


71  (72) 

Introduction to Equations 


73  (12) 

To determine whether a given number is solution of an equation 


73  (1) 

To solve an equation of the form x + a = b 


74  (1) 

To solve an equation of the form ax = b 


75  (2) 

To solve application problems using the basic percent equation 


77  (8) 


85  (12) 

To solve an equation of the form ax + b = c 


85  (1) 

To solve an equation of the form ax + b = cx + d 


86  (1) 

To solve an equation containing parentheses 


87  (2) 

To translate a sentence into an equation and solve 


89  (8) 

Mixture, Investment, and Motion Problems 


97  (16) 

To solve value mixture problems 


97  (2) 

To solve percent mixture problems 


99  (2) 

To solve investment problems 


101  (2) 

To solve uniform motion problems 


103  (10) 

Inequalities in One Variable 


113  (12) 

To solve an inequality in one variable 


113  (3) 

To solve a compound inequality 


116  (2) 

To solve application problems 


118  (7) 

Absolute Value Equations and Inequalities 


125  (18) 

To solve an absolute value equation 


125  (1) 

To solve an absolute value inequality 


126  (2) 

To solve application problems 


128  (5) 


133  (1) 

Projects and Group Activities 


134  (2) 


136  (1) 


137  (2) 


139  (2) 


141  (2) 


143  (56) 


145  (16) 

To solve problems involving lines and angles 


145  (5) 

To solve problems involving angles formed by intersecting lines 


150  (3) 

To solve problems involving the angles of a triangle 


153  (8) 


161  (18) 

To solve problems involving the perimeter of geometric figures 


161  (5) 

To solve problems involving the area of geometric figures 


166  (13) 


179  (20) 

To solve problems involving the volume of a solid 


179  (3) 

To solve problems involving the surface area of a solid 


182  (7) 


189  (1) 

Projects and Group Activities 


190  (1) 


191  (2) 


193  (2) 


195  (2) 


197  (2) 

Linear Equations and Inequalities in Two Variables 


199  (64) 

The Rectangular Coordinate System 


201  (12) 

To graph points in a rectangular coordinate system 


201  (2) 

To determine orderedpair solutions of an equation in two variables 


203  (2) 

To determine whether a set of ordered pairs is a function 


205  (3) 

To evaluate a function written in functional notation 


208  (5) 

Linear Equations in Two Variables 


213  (12) 

To graph an equation of the form y = mx + b 


213  (2) 

To graph an equation of the form Ax + By = C 


215  (5) 

To solve application problems 


220  (5) 


225  (10) 

To find the slope of a straight line 


225  (4) 

To graph a line using the slope and the yintercept 


229  (6) 

Euqations of Straight Lines 


235  (8) 

To find the equation of a line given a point and the slope 


235  (1) 

To find the equation of a line given two points 


236  (2) 

To solve application problems 


238  (5) 

Parallel and Perpendicular Lines 


243  (6) 

To find parallel and perpendicular lines 


243  (6) 

Graphing Linear Inequalities 


249  (14) 

To graph an inequality in two variables 


249  (4) 


253  (1) 

Projects and Group Activities 


254  (2) 


256  (1) 


257  (2) 


259  (2) 


261  (2) 

Systems of Linear Equations and Inequalities 


263  (56) 

Solving Systems of Linear Equations by Graphing 


265  (6) 

To solve a system of linear equations by graphing 


265  (6) 

Solving Systems of Linear Equations by the Substitution Method 


271  (6) 

To solve a system of linear equations by the substitution method 


271  (6) 

Solving Systems of Linear Equations by the Addition Method 


277  (12) 

To solve a system of linear equations in two variables by the addition method 


277  (3) 

To solve a system of three linear equations in three variables by the addition method 


280  (9) 

Solving Systems of Equations by Using Determinants 


289  (8) 

To evaluate a determinant 


289  (3) 

To solve a system of equations by using Cramer's Rule 


292  (5) 

Application Problems in Two Variables 


297  (8) 

To solve rateofwind of rateofcurrent problems 


297  (1) 

To solve application problems using two variables 


298  (7) 

Solving Systems of Linear Inequalities 


305  (14) 

To graph the solution set of a system of linear inequalities 


305  (4) 


309  (1) 

Projects and Group Activities 


309  (2) 


311  (2) 


313  (2) 


315  (2) 


317  (2) 


319  (50) 


321  (12) 


321  (2) 

To divide monomials and simplify expressions with negative exponents 


323  (4) 

To write a number using scientific notation 


327  (1) 

To solve application problems 


328  (5) 

Introduction to Polynomials 


333  (8) 

To evaluate polynomial functions 


333  (3) 

To add or subtract polynomials 


336  (5) 

Multiplication of Polynomials 


341  (8) 

To multiply a polynomial by a monomial 


341  (1) 

To multiply two polynomials 


341  (1) 

To multiply two binomials 


342  (1) 

To multiply binomials that have special products 


343  (1) 

To solve application problems 


344  (5) 


349  (20) 


349  (2) 

To divide polynomials using synthetic division 


351  (3) 

To evaluate a polynomial using synthetic division 


354  (5) 


359  (2) 

Projects and Group Activities 


361  (1) 


361  (2) 


363  (2) 


365  (2) 


367  (2) 


369  (52) 


371  (6) 

To factor a monomial from a polynomial 


371  (2) 


373  (4) 

Factoring Polynomials of the Form x2 + bx + c 


377  (8) 

To factor a trinomial of the form x2 + bx + c 


377  (2) 


379  (6) 

Factoring Polynomials of the Form ax2 + bx + c 


385  (8) 

To factor a trinomial of the form ax2 + bx + c by using trial factors 


385  (2) 

To factor a trinomial of the form ax2 + bx + c by grouping 


387  (6) 


393  (10) 

To factor the difference of two perfect squares or a perfectsquare trinomial 


393  (2) 

To factor the sum or the difference of two cubes 


395  (1) 

To factor a trinomial that is quadratic in form 


396  (1) 


397  (6) 


403  (18) 

To solve equations by factoring 


403  (2) 

To solve application problems 


405  (6) 


411  (2) 

Projects and Group Activities 


413  (1) 


414  (1) 


415  (2) 


417  (2) 


419  (2) 


421  (66) 

Multiplication and Division of Rational Expressions 


423  (8) 

To simplify a rational expression 


423  (1) 

To multiply rational expressions 


424  (2) 

To divide rational expressions 


426  (5) 

Addition and Subtraction of Rational Expressions 


431  (12) 

To find the least common multiple (LCM) of two or more polynomials 


431  (1) 

To express two fractions in terms of the LCM of their denominators 


432  (1) 

To add or subtract rational expressions with the same denominator 


433  (1) 

To add or subtract rational expressions with different denominators 


434  (9) 


443  (4) 

To simplify a complex fraction 


433  (14) 


447  (12) 

To solve rational equations 


447  (2) 


449  (1) 

To solve problems involving similar triangles 


450  (2) 

To solve application problems 


452  (7) 


459  (4) 

To solve a literal equation for one of the variables 


459  (4) 

Work and Uniform Motion Problems 


463  (8) 


463  (2) 

To solve uniform motion problems 


465  (6) 


471  (16) 

To solve variation problems 


471  (6) 


477  (1) 

Projects and Group Activities 


478  (2) 


480  (1) 


481  (2) 


483  (2) 


485  (2) 

Rational Exponents and Radicals 


487  (48) 

Rational Exponents and Radical Expressions 


489  (10) 

To simplify expressions with rational exponents 


489  (2) 

To write exponential expressions as radical expressions and to write radical expressions as exponential expressions 


491  (2) 

To simplify radical expressions that are roots of perfect powers 


493  (6) 

Operations on Radical Expressions 


499  (10) 

To simplify radical expressions 


499  (1) 

To add or subtract radical expressions 


500  (1) 

To multiply radical expressions 


501  (1) 

To divide radical expressions 


502  (7) 


509  (8) 

To simplify a complex number 


509  (1) 

To add or subtract complex numbers 


510  (1) 

To multiply complex numbers 


511  (3) 

To divide complex numbers 


514  (3) 

Solving Equations Containing Radical Expressions 


517  (18) 

To solve a radical equation 


517  (2) 

To solve application problems 


519  (6) 


525  (1) 

Projects and Group Activities 


526  (1) 


527  (2) 


529  (2) 


531  (2) 


533  (2) 


535  (46) 

Solving Quadratic Equations by Factoring or by Taking Square Roots 


537  (8) 

To solve a quadratic equation by factoring 


537  (1) 

To write a quadratic equation given its solutions 


538  (1) 

To solve a quadratic equation by taking square roots 


539  (6) 

Solving Quadratic Equations by Completing the Square 


545  (6) 

To solve a quadratic equation by completing the square 


545  (6) 

Solving Quadratic Equations by Using the Quadratic Formula 


551  (6) 

To solve quadratic equation by using the quadratic formula 


551  (6) 

Solving Equations That are Reducible to Quadratic Equations 


557  (6) 

To solve an equation that is quadratic in form 


557  (1) 

To solve a radical equation that is reducible to a quadratic equation 


558  (2) 

To solve a fractional equation that is reducible to a quadratic equation 


560  (3) 

Applications of Quadratic Equations 


563  (4) 

To solve application problems 


563  (4) 

Quadratic Inequalities and Rational Inequalities 


567  (14) 

To solve a nonlinear inequality 


567  (4) 


571  (1) 

Projects and Group Activities 


572  (2) 


574  (1) 


575  (2) 


577  (2) 


579  (2) 


581  (60) 


583  (4) 

To graph a linear function 


583  (1) 

To solve application problems 


584  (3) 


587  (10) 

To graph a quadratic function 


587  (2) 

To find the xintercepts of a parabola 


589  (2) 

To find the minimum or maximum of a quadratic function 


591  (1) 

To solve application problems 


592  (5) 


597  (6) 


597  (6) 


603  (6) 

To perform operations on functions 


603  (2) 

To find the composition of two functions 


605  (4) 

OnetoOne and Inverse Functions 


609  (8) 

To determine whether a function is onetoone 


609  (1) 

To find the inverse of a function 


610  (7) 


617  (24) 


617  (4) 

To find the Equation of a circle and to graph a circle 


621  (2) 

To graph an ellipse with center at the origin 


623  (2) 

To graph a hyperbola with center at the origin 


625  (6) 


631  (1) 

Projects and Group Activities 


632  (1) 


633  (2) 


635  (2) 


637  (2) 


639  (2) 

Exponential and Logarithmic Functions 


641  (52) 


643  (8) 

To evaluate an exponential function 


643  (2) 

To graph an exponential function 


645  (6) 

Introduction to Logarithms 


651  (10) 

To write equivalent exponential and logarithmic equations 


651  (2) 

To use the Properties of Logarithms 


653  (3) 

To use the changeofbase formula 


656  (5) 

Graphs of Logarithmic Functions 


661  (4) 

To graph a logarithmic function 


661  (4) 

Solving Exponential and Logarithmic Equations 


665  (6) 

To solve an exponential equation 


665  (2) 

To solve a logarithmic equation 


667  (4) 

Applications of Exponential and Logarithmic Functions 


671  (22) 

To solve application problems 


671  (8) 


679  (1) 

Projects and Group Activities 


680  (2) 


682  (1) 


683  (2) 


685  (2) 


687  (2) 


689  (4) 
Appendix 

693  (1) 

Guidelines for Using Graphing Calculators 


693  (8) 

Table of Symbols and Table of Measurement Abbreviations 


701  
Solutions to ``You Try It'' 

S1  
Answers to OddNumbered Exercises 

A1  
Glossary 

G1  
Index 

I1  