Preface 

ix  
Index of Applications 

xviii  


1  (48) 


3  (7) 


3  (2) 

Opposites and absolute value 


5  (5) 


10  (12) 


10  (1) 


11  (1) 


12  (2) 


14  (1) 


15  (7) 


22  (12) 

Write rational numbers as decimals 


22  (1) 

Convert among percents, fractions, and decimals 


23  (2) 

Add and subtract rational numbers 


25  (2) 

Multiply and divide rational numbers 


27  (7) 

Exponents and the Order of Operations Agreement 


34  (15) 


34  (1) 

The Order of Operations Agreement 


35  (5) 

Focus on Problem Solving: Inductive Reasoning 


40  (1) 

Projects and Group Activities: Calculators 


41  (1) 


42  (1) 


42  (1) 


42  (2) 


44  (3) 


47  (2) 


49  (36) 

Evaluating Variable Expressions 


51  (6) 

Evaluate variable expressions 


51  (6) 

Simplifying Variable Expressions 


57  (10) 

The Properties of the Real Numbers 


57  (2) 

Simplify variable expressions using the Properties of Addition 


59  (2) 

Simplify variable expressions using the Properties of Multiplication 


61  (1) 

Simplify variable expression using the Distributive Property 


62  (1) 

Simplify general variable expressions 


62  (5) 

Translating Verbal Expressions into Variable Expressions 


67  (18) 

Translate a verbal expression into a variable expression given the variable 


67  (2) 

Translate a verbal expression into a variable expression by assigning the variable 


69  (1) 

Translate a verbal expression into a variable expression and then simplify the resulting expression 


69  (1) 

Translate application problems 


70  (7) 

Focus on Problem Solving: From Concrete to Abstract 


77  (2) 

Projects And Group Activities: Investigation into Operations with Even and Odd Integers 


79  (1) 

Applications of Patterns in Mathematics 


79  (1) 


80  (1) 


81  (2) 


83  (1) 

Cumulative Review Exercises 


84  (1) 

Solving Equations and Inequalities 


85  (48) 

Introduction to Equations 


87  (14) 

Determine Whether a given number is a solution of an equation 


87  (1) 

Solve equations of the form x + a = b 


89  (1) 

Solve equations of the form ax = b 


90  (2) 

Application problems: the basic percent equation 


92  (9) 


101  (14) 

Solve equations of the form ax + b = c 


101  (3) 

Solve equations of the form ax + b = cx + d 


104  (1) 

Solve equations containing parentheses 


105  (1) 


106  (9) 


115  (18) 

Solve inequalities using the Addition Property of Inequalities 


115  (2) 

Solve inequalities using the Multiplication Property of Inequalities 


117  (2) 

Solve general inequalities 


119  (6) 

Focus on Problem Solving: Graphing Data 


125  (1) 

Project and Group Activities: Measurements as Approximations 


126  (1) 


127  (1) 


128  (2) 


130  (1) 

Cumulative Review Exercises 


131  (2) 

Solving Equations and inequalities: Applications 


133  (74) 

Translating Sentences into Equations 


135  (6) 

Translate a sentence into an equation and solve 


135  (1) 


135  (6) 

Integer, Coin, and Stamp Problems 


141  (8) 

Consecutive integer problems 


141  (2) 


143  (6) 


149  (14) 


149  (2) 

Problems involving angles formed by intersecting lines 


151  (4) 

Problems involving the angles of a triangle 


155  (8) 

Markup and Discount Problems 


163  (6) 


163  (2) 


165  (4) 


169  (6) 


169  (6) 


175  (9) 


175  (2) 


177  (7) 


184  (6) 


184  (6) 


190  (17) 

Applications of inequalities 


190  (5) 

Focus on Problem Solving: TrialandError Approach to Problem Solving 


195  (1) 


196  (1) 

Projects and Group Activities: Nielsen Ratings 


197  (1) 

Changes in Percent Concentration 


198  (1) 


199  (2) 


201  (3) 


204  (1) 

Cumulative Review Exercises 


205  (2) 

Linear Equations and Inequalities 


207  (68) 

The Rectangular Coordinate System 


209  (7) 

Graph points in a rectangular coordinate system 


209  (2) 


211  (5) 


216  (14) 

Determine solutions of linear equations in two variables 


216  (2) 

Graph equations of the form y = mx + b 


218  (2) 

Graph equations of the form Ax + By = C 


220  (10) 


230  (9) 

Find the slope of a straight line 


230  (4) 

Graph a line using the slope and yintercept 


234  (5) 

Equations of Straight Lines 


239  (5) 

Find the equation of a line using the equation y = mx + b 


239  (1) 

Find the equation of a line using the pointslope formula 


240  (4) 


244  (12) 

Introduction to functions 


244  (3) 

Graphs of linear functions 


247  (9) 

Graphing Linear Inequalities 


256  (19) 

Graph inequalities in two variable 


256  (5) 

Focus on Problem Solving: Counterexamples 


261  (1) 

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


262  (1) 


263  (1) 


264  (2) 


266  (3) 


269  (3) 

Cumulative Review Exercises 


272  (3) 

Systems of Linear Equations 


275  (38) 

Solving Systems of Linear Equations by Graphing 


277  (6) 

Solve systems of linear equations by graphing 


277  (6) 

Solving Systems of Linear Equations by the Substitution Method 


283  (5) 

Solve systems of linear equations by the substitution method 


283  (5) 

Solving Systems of Linear Equations by the Addition Method 


288  (5) 

Solve systems of linear equations by the addition method 


288  (5) 

Application Problems in Two Variables 


293  (20) 

Rateofwind and watercurrent problems 


293  (2) 


295  (6) 

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


301  (1) 

Projects and Group Activities: Find a Pattern 


302  (1) 

Solving a system of Equations with a Scientific Calculator 


302  (1) 

Solving a System of Equations with a Graphing Calculator 


302  (3) 


305  (2) 


307  (2) 


309  (1) 

Cumulative Review Exercises 


310  (3) 


313  (40) 

Addition and Subtraction of Polynomials 


315  (4) 


315  (1) 


316  (3) 

Multiplication of Monomials 


319  (4) 


319  (1) 

Simplify powers of monomials 


320  (3) 

Multiplication of Polynomials 


323  (9) 

Multiply a polynomial by a monomial 


323  (1) 


324  (1) 


324  (1) 

Multiply binomials that have special products 


325  (2) 


327  (5) 


332  (21) 


332  (3) 


335  (2) 

Divide a polynomial by a monomial 


337  (1) 


338  (6) 

Focus on Problem Solving: Dimensional Analysis 


344  (2) 

Projects and Group Activities: Pascal's Triangle 


346  (1) 

Properties of Polynomials 


347  (1) 


347  (1) 


348  (2) 


350  (1) 

Cumulative Review Exercises 


351  (2) 


353  (46) 


355  (5) 

Factor a monomial from a polynomial 


355  (1) 


356  (4) 

Factoring Polynomials of the Form x2 + bx + c 


360  (6) 

Factor trinomials of the form x2 + bx + c 


360  (3) 


363  (3) 

Factoring Polynomials of the Form ax2 + bx + c 


366  (9) 

Factor trinomials of the form ax2 + bx + c using trial factors 


366  (4) 

Factor trinomials of the form ax2 + bx + c by grouping 


370  (5) 


375  (7) 

Factor the difference of two squares and perfectsquare trinomials 


375  (3) 


378  (4) 


382  (17) 

Solve equations by factoring 


382  (1) 


383  (6) 

Focus on Problem solving: Making a Table 


389  (1) 

The TrialandError Method 


389  (2) 

Projects and Group Activities: Prime and Composite Numbers 


391  (1) 

Search the World Wide Web 


392  (1) 


393  (1) 


394  (2) 


396  (1) 

Cumulative Review Exercises 


397  (2) 


399  (62) 

Multiplication and Division of Algebraic Fractions 


401  (7) 

Simplify algebraic fractions 


401  (1) 

Multiply algebraic fractions 


402  (2) 

Divide algebraic fractions 


404  (4) 

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


408  (5) 

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


408  (1) 

Express two fractions in terms of the LCM of their denominators 


409  (4) 

Addition and Subtraction of Algebraic Fractions 


413  (6) 

Add and subtract algebraic fractions with the same denominator 


413  (1) 

Add and subtract algebraic fractions with different denominators 


414  (5) 


419  (4) 

Simplify complex fractions 


419  (4) 

Equations Containing Fractions 


423  (14) 

Solve equations containing fractions 


423  (2) 


425  (1) 

Applications of proportions 


426  (1) 

Problems involving similar triangles 


427  (10) 


437  (4) 

Solve a literal equation for one of the variables 


437  (4) 


441  (20) 


441  (1) 


442  (7) 

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


449  (2) 


451  (1) 

Projects and Group Activities: Intensity of Illumination 


451  (2) 


453  (2) 


455  (2) 


457  (1) 

Cumulative Review Exercises 


458  (3) 


461  (40) 

Introduction to Radical Expressions 


463  (6) 

Simplify numerical radical expression 


463  (2) 

Simplify variable radical expressions 


465  (4) 

Addition and Subtraction of Radical Expressions 


469  (3) 

Add and subtract radical expressions 


469  (3) 

Multiplication and Division of Radical Expressions 


472  (6) 

Multiply radical expressions 


472  (2) 

Divide radical expressions 


474  (4) 

Solving Equations Containing Radical Expressions 


478  (23) 

Solve equations containing one or more radical expressions 


478  (3) 


481  (7) 

Focus on Problems Solving: Deductive Reasoning 


488  (1) 

Projects and Group Activities: Mean and Standard Deviation 


489  (3) 


492  (1) 

Expressway OnRamp Curves 


493  (1) 


493  (2) 


495  (2) 


497  (1) 

Cumulative Review Exercises 


498  (3) 


501  (44) 

Solving Quadratic Equations by Factoring or by Taking Square Roots 


503  (7) 

Solve quadratic equations by factoring 


503  (2) 

Solve quadratic equations by taking square roots 


505  (5) 

Solving Quadratic Equations by Completing the Square 


510  (6) 

Solve quadratic equations by completing the square 


510  (6) 

Solving Quadratic Equations by using the Quadratic Formula 


516  (5) 

Solve quadratic equations by using the quadratic formula 


516  (5) 

Graphing Quadratic Equations in Two Variables 


521  (6) 

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


521  (6) 


527  (18) 


527  (6) 

Focus on Problem Solving: Algebraic Manipulation and Graphing Techniques 


533  (1) 

Projects and Group Activities: Graphical Solutions of Quadratic Equations 


534  (1) 


535  (1) 

Geometric Construction of Completing the Square 


535  (1) 


536  (2) 


538  (3) 


541  (1) 

Cumulative Review Exercises 


542  (3) 
Final Exam 

545  (4) 
Appendix: Guidelines for Using Graphing Calculators 

549  
Solutions to Problems 

S1  
Answers to the OddNumbered Exercises 

A1  
Glossary 

G1  
Index 

I1  