Preface 

xi  
To the Student 

xix  
Index of Applications 

xxi  


1  (50) 


3  (6) 

To use inequality symbols with integers 


3  (2) 

To use opposites and absolute value 


5  (4) 

Addition and Subtraction of Integers 


9  (8) 


9  (1) 


10  (2) 

To solve application problems 


12  (5) 

Multiplication and Division of Integers 


17  (6) 


17  (1) 


18  (2) 

To solve application problems 


20  (3) 

Operations with Rational Numbers 


23  (14) 

To write a rational number in simplest form and as a decimal 


23  (2) 

To convert between percents, fractions, and decimals 


25  (1) 

To add or subtract rational numbers 


26  (2) 

To multiply or divide rational numbers 


28  (2) 

To solve application problems 


30  (7) 

Exponents and the Order of Operations Agreement 


37  (14) 

To evaluate exponential expressions 


37  (1) 

To use the Order of Operations Agreement to simplify expressions 


38  (5) 

Focus on Problem Solving: Inductive Reasoning 


43  (1) 

Projects and Group Activities: The +/ Key on a Calculator 


44  (1) 


44  (1) 


45  (1) 


45  (2) 


47  (2) 


49  (2) 


51  (34) 

Evaluating Variable Expressions 


53  (4) 

To evaluate a variable expression 


53  (4) 

Simplifying Variable Expressions 


57  (10) 

To simplify a variable expression using the Properties of Addition 


57  (2) 

To simplify a variable expression using the Properties of Multiplication 


59  (1) 

To simplify a variable expression using the Distributive Property 


60  (2) 

To simplify variable expressions 


62  (5) 

Translating Verbal Expressions into Variable Expressions 


67  (18) 

To translate a verbal expression into a variable expression, given the variable 


67  (1) 

To translate a verbal expression into a variable expression and then simplify 


68  (2) 

To translate application problems 


70  (5) 

Focus on Problem Solving: From Concrete to Abstract 


75  (1) 

Projects and Group Activities: Prime and Composite Numbers 


76  (1) 

Investigation into Operations with Even and Odd Integers 


77  (1) 


78  (1) 


79  (2) 


81  (2) 


83  (2) 


85  (76) 

Introduction to Equations 


87  (12) 

To determine whether a given number is a solution of an equation 


87  (1) 

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


88  (1) 

To solve an equation of the form ax = b 


89  (2) 

To solve application problems using the basic percent equation 


91  (8) 

General EquationsPart I 


99  (10) 

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


99  (1) 

To solve application problems using formulas 


100  (9) 

General EquationsPart II 


109  (8) 

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


109  (1) 

To solve an equation containing parentheses 


110  (2) 

To solve application problems using formulas 


112  (5) 

Translating Sentences into Equations 


117  (8) 

To solve integer problems 


117  (2) 

To translate a sentence into an equation and solve 


119  (6) 


125  (14) 

To solve perimeter problems 


125  (2) 

To solve problems involving angles formed by intersecting lines 


127  (4) 

To solve problems involving the angles of a triangle 


131  (8) 

Mixture and Uniform Motion Problems 


139  (22) 

To solve value mixture problems 


139  (2) 

To solve percent mixture problems 


141  (2) 

To solve uniform motion problems 


143  (8) 

Focus on Problem Solving: Trial and Error Approach to Problem Solving 


151  (1) 

Projects and Group Activities: Nielsen Ratings 


152  (1) 


153  (2) 


155  (2) 


157  (2) 


159  (2) 


161  (42) 

Addition and Subtraction of Polynomials 


163  (4) 


163  (1) 


164  (3) 

Multiplication of Monomials 


167  (4) 


167  (1) 

To simplify powers of monomials 


168  (3) 

Multiplication of Polynomials 


171  (8) 

To multiply a polynomial by a monomial 


171  (1) 

To multiply two polynomials 


171  (1) 

To multiply two binomials 


172  (1) 

To multiply binomials that have special products 


173  (1) 

To solve application problems 


174  (5) 

Integer Exponents and Scientific Notation 


179  (10) 


179  (5) 

To write a number in scientific notation 


184  (5) 


189  (14) 

To divide a polynomial by a monomial 


189  (1) 


189  (4) 

Focus on Problem Solving: Dimensional Analysis 


193  (2) 

Projects and Group Activities: Pascal's Triangle 


195  (1) 


195  (2) 


197  (2) 


199  (2) 


201  (2) 


203  (50) 


205  (6) 

To factor a monomial from a polynomial 


205  (2) 


207  (4) 

Factoring Polynomials of the Form x2 + bx + c 


211  (8) 

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


211  (2) 


213  (6) 

Factoring Polynomials of the Form ax2 + bx + c 


219  (8) 

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


219  (2) 

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


221  (6) 


227  (8) 

To factor the difference of two squares and perfectsquare trinomials 


227  (2) 


229  (6) 


235  (18) 

To solve equations by factoring 


235  (2) 

To solve application problems 


237  (6) 

Focus on Problem Solving: Making a Table 


243  (1) 

Projects and Group Activities: Evaluating Polynomials Using a Calculator 


244  (1) 

Search the World Wide Web 


245  (1) 


246  (1) 


247  (2) 


249  (2) 


251  (2) 


253  (60) 

Multiplication and Division of Rational Expressions 


255  (8) 

To simplify a rational expression 


255  (1) 

To multiply rational expressions 


256  (2) 

To divide rational expressions 


258  (5) 

Expressing Fractions in Terms of the Least Common Multiple (LCM) 


263  (4) 

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


263  (1) 

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


264  (3) 

Addition and Subtraction of Rational Expressions 


267  (8) 

To add or subtract rational expressions with the same denominators 


267  (1) 

To add or subtract rational expressions with different denominators 


268  (7) 


275  (4) 

To simplify a complex fraction 


275  (4) 

Solving Equations Containing Fractions 


279  (4) 

To solve an equation containing fractions 


279  (4) 


283  (8) 


283  (1) 

To solve application problems 


284  (1) 

To solve problems involving similar triangles 


284  (7) 


291  (4) 

To solve a literal equation for one of the variables 


291  (4) 


295  (18) 


295  (2) 

To solve uniform motion problems 


297  (6) 

Focus on Problem Solving: Negations and If... then Sentences 


303  (1) 

Projects and Group Activities: Intensity of Illumination 


304  (2) 


306  (1) 


307  (2) 


309  (2) 


311  (2) 

Linear Equations in Two Variables 


313  (52) 

The Rectangular Coordinate System 


315  (12) 

To graph points in a rectangular coordinate system 


315  (2) 

To determine orderedpair solutions of an equation in two variables 


317  (2) 

To determine whether a set of ordered pairs is a function 


319  (3) 

To evaluate a function written in functional notation 


322  (5) 

Linear Equation in Two Variables 


327  (10) 

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


327  (2) 

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


329  (3) 

To solve application problems 


332  (5) 

Intercepts and Slopes of Straight Lines 


337  (10) 

To find the x and yintercepts of a straight line 


337  (1) 

To find the slope of a straight line 


338  (3) 

To graph a line using the slope and the yintercept 


341  (6) 

Equations of Straight Lines 


347  (18) 

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


347  (1) 

To find the equation of a line given two points 


348  (2) 

To solve application problems 


350  (5) 

Focus on Problem Solving: Counterexamples 


355  (1) 

Projects and Group Activities: Graphing Linear Equations with a Graphing Utility 


356  (1) 


357  (1) 


358  (1) 


359  (2) 


361  (2) 


363  (2) 

Systems of Linear Equations 


365  (42) 

Solving Systems of Linear Equations by Graphing 


367  (8) 

To solve a system of linear equations by graphing 


367  (8) 

Solving Systems of Linear Equations by the Substitution Method 


375  (10) 

To solve a system of linear equations by the substitution method 


375  (4) 

To solve investment problems 


379  (6) 

Solving Systems of Equations by the Addition Method 


385  (6) 

To solve a system of linear equations by the addition method 


385  (6) 

Application Problems in Two Variables 


391  (16) 

To solve rateofwind orcurrent problems 


391  (1) 

To solve application problems using two variables 


392  (5) 

Focus on Problem Solving: Using a Tale and Searching for a Pattern 


397  (1) 

Projects and Group Activities: Find a Pattern 


398  (1) 

Solving a System of Equations with a Scientific Calculator 


398  (1) 

Solving a System of Equations with a Graphing Calculator 


399  (1) 


400  (1) 


401  (2) 


403  (2) 


405  (2) 


407  (34) 


409  (6) 

To write a set using the roster method 


409  (1) 

To write a set using setbuilder notation 


410  (1) 

To graph an inequality on the number line 


411  (4) 

The Addition and Multiplication Properties of Inequalities 


415  (8) 

To solve an inequality using the Addition Property of Inequalities 


415  (1) 

To solve an inequality using the Multiplication Property of Inequalities 


416  (2) 

To solve application problems 


418  (5) 


423  (4) 

To solve general inequalities 


423  (1) 

To solve application problems 


424  (3) 

Graphing Linear Inequalities 


427  (14) 

To graph an inequality in two variables 


427  (4) 

Focus on Problem Solving: Graphing Data 


431  (1) 

Projects and Group Activities: Mean and Standard Deviation 


432  (2) 


434  (1) 


435  (2) 


437  (2) 


439  (2) 


441  (34) 

Introduction to Radical Expressions 


443  (6) 

To simplify numerical radical expressions 


443  (2) 

To simplify variable radical expressions 


445  (4) 

Addition and Subtraction of Radical Expressions 


449  (4) 

To add and subtract radical expressions 


449  (4) 

Multiplication and Division of Radical Expressions 


453  (6) 

To multiply radical expressions 


453  (1) 

To divide radical expressions 


454  (5) 

Solving Equations Containing Radical Expressions 


459  (16) 

To solve an equation containing a radical expression 


459  (2) 

To solve application problems 


461  (4) 

Focus on Problem Solving: Deductive Reasoning 


465  (1) 

Projects and Group Activities: Measurements as Approximations 


466  (1) 


467  (1) 


468  (1) 


469  (2) 


471  (2) 


473  (2) 


475  (36) 

Solving Quadratic Equations by Factoring or by Taking Square Roots 


477  (6) 

To solve a quadratic equation by factoring 


477  (2) 

To solve a quadratic equation by taking square roots 


479  (4) 

Solving Quadratic Equations by Completing the Square 


483  (6) 

To solve a quadratic equation by completing the square 


483  (6) 

Solving Quadratic Equations by Using the Quadratic Formula 


489  (4) 

To solve a quadratic equation by using the quadratic formula 


489  (4) 

Graphing Quadratic Equations in Two Variables 


493  (4) 

To graph a quadratic equation of the form y = ax2 + bx + c 


493  (4) 


497  (14) 

To solve application problems 


497  (4) 

Focus on Problem Solving: Algebraic Manipulation and Graphing Techniques 


501  (1) 

Projects and Group Activities: Graphical Solutions of Quadratic Equations 


502  (1) 

Properties of Polynomials 


502  (1) 


503  (1) 

Geometric Construction of Completing the Square 


503  (1) 


504  (1) 


505  (2) 


507  (2) 


509  (2) 
Final Exam 

511  (4) 
Appendix 


Guidelines for Using Graphing Calculators 


515  (8) 

Table of Symbols and Table of Measurement Abbreviations 


523  
Solutions to ``You Try It'' 

S1  
Answers to OddNumbered Exercises 

A1  
Glossary 

G1  
Index 

I1  