Preface 

xiii  
AIM for Success 

xxv  


1  (86) 


2  (1) 

Section 1.1 Introduction to Whole Numbers 


3  (16) 

Objective A Order relations between whole numbers 


3  (1) 


4  (2) 


6  (2) 

Objective D Applications and statistical graphs 


8  (11) 

Section 1.2 Addition and Subtraction of Whole Numbers 


19  (22) 

Objective A Addition of whole numbers 


19  (6) 

Objective B Subtraction of whole numbers 


25  (4) 

Objective C Applications and formulas 


29  (12) 

Section 1.3 Multiplication and Division of Whole Numbers 


41  (26) 

Objective A Multiplication of whole numbers 


41  (5) 


46  (2) 

Objective C Division of whole numbers 


48  (5) 

Objective D Factors and prime factorization 


53  (2) 

Objective E Applications and formulas 


55  (12) 

Section 1.4 Solving Equations with Whole Numbers 


67  (6) 

Objective A Solving equations 


67  (2) 

Objective B Applications and formulas 


69  (4) 

Section 1.5 The Order of Operations Agreement 


73  (14) 

Objective A The Order of Operations Agreement 


73  (4) 


77  (1) 



Projects and Group Activities 


78  (1) 



Applications of Patterns in Mathematics 



Salary Calculator Subtraction Squares 




79  (4) 


83  (2) 


85  (2) 


87  (64) 


88  (1) 

Section 2.1 Introduction to Integers 


89  (12) 

Objective A Integers and the number line 


89  (2) 


91  (1) 

Objective C Absolute value 


92  (1) 


93  (8) 

Section 2.2 Addition and Subtraction of Integers 


101  (16) 

Objective A Addition of integers 


101  (4) 

Objective B Subtraction of integers 


105  (4) 

Objective C Applications and formulas 


109  (8) 

Section 2.3 Multiplication and Division of Integers 


117  (12) 

Objective A Multiplication of integers 


117  (2) 

Objective B Division of integers 


119  (3) 


122  (7) 

Section 2.4 Solving Equations with Integers 


129  (6) 

Objective A Solving equations 


129  (2) 

Objective B Applications and formulas 


131  (4) 

Section 2.5 The Order of Operations Agreement 


135  (4) 

Objective A The Order of Operations Agreement 


135  (4) 


139  (12) 



Projects and Group Activities 


140  (3) 



Multiplication of Integers 








143  (2) 


145  (2) 


147  (2) 

Cumulative Review Exercises 


149  (2) 


151  (86) 


152  (1) 

Section 3.1 Least Common Multiple and Greatest Common Factor 


153  (6) 

Objective A Least common multiple (LCM) 


153  (1) 

Objective B Greatest common factor (GCF) 


154  (1) 


155  (4) 

Section 3.2 Introduction to Fractions 


159  (14) 

Objective A Proper fractions, improper fractions, and mixed numbers 


159  (3) 

Objective B Equivalent fractions 


162  (2) 

Objective C Order relations between two fractions 


164  (2) 


166  (7) 

Section 3.3 Addition and Subtraction of Fractions 


173  (18) 

Objective A Addition of fractions 


173  (5) 

Objective B Subtraction of fractions 


178  (3) 

Objective C Applications and formulas 


181  (10) 

Section 3.4 Multiplication and Division of Fractions 


191  (18) 

Objective A Multiplication of fractions 


191  (5) 

Objective B Division of fractions 


196  (3) 

Objective C Applications and formulas 


199  (10) 

Section 3.5 Solving Equations with Fractions 


209  (6) 

Objective A Solving equations 


209  (2) 


211  (4) 

Section 3.6 Exponents, Complex Fractions, and the Order of Operations Agreement 


215  (22) 


215  (1) 

Objective B Complex fractions 


216  (3) 

Objective C The Order of Operations Agreement 


219  (6) 


225  (1) 



Projects and Group Activities 


226  (2) 







Puzzle from the Middle Ages 



Using Patterns in Experimentation 




228  (3) 


231  (2) 


233  (2) 

Cumulative Review Exercises 


235  (2) 

Decimals and Real Numbers 


237  (76) 


238  (1) 

Section 4.1 Introduction to Decimals 


239  (10) 


239  (2) 

Objective B Order relations between decimals 


241  (1) 


242  (2) 


244  (5) 

Section 4.2 Operations on Decimals 


249  (28) 

Objective A Addition and subtraction of decimals 


249  (3) 

Objective B Multiplication of decimals 


252  (4) 

Objective C Division of decimals 


256  (4) 

Objective D Fractions and decimals 


260  (2) 

Objective E Applications and formulas 


262  (15) 

Section 4.3 Solving Equations with Decimals 


277  (4) 

Objective A Solving equations 


277  (1) 


278  (3) 

Section 4.4 Radical Expressions 


281  (10) 

Objective A Square roots of perfect squares 


281  (3) 

Objective B Square roots of whole numbers 


284  (2) 

Objective C Applications and formulas 


286  (5) 


291  (22) 

Objective A Real numbers and the real number line 


291  (3) 

Objective B Inequalities in one variable 


294  (2) 


296  (5) 


301  (1) 

From Concrete to Abstract 



Projects and Group Activities 


302  (2) 








304  (3) 


307  (2) 


309  (2) 

Cumulative Review Exercises 


311  (2) 


313  (62) 


314  (1) 

Section 5.1 Properties of Real Numbers 


315  (10) 

Objective A Application of the Properties of Real Numbers 


315  (3) 

Objective B The Distributive Property 


318  (7) 

Section 5.2 Variable Expressions in Simplest Form 


325  (8) 

Objective A Addition of like terms 


325  (2) 

Objective B General variable expressions 


327  (6) 

Section 5.3 Addition and Subtraction of Polynomials 


333  (8) 

Objective A Addition of polynomials 


333  (1) 

Objective B Subtraction of polynomials 


334  (2) 


336  (5) 

Section 5.4 Multiplication of Monomials 


341  (6) 

Objective A Multiplication of monomials 


341  (2) 

Objective B Powers of monomials 


343  (4) 

Section 5.5 Multiplication of Polynomials 


347  (4) 

Objective A Multiplication of a polynomial by a monomial 


347  (1) 

Objective B Multiplication of two binomials 


348  (3) 

Section 5.6 Division of Monomials 


351  (6) 

Objective A Division of monomials 


351  (3) 

Objective B Scientific notation 


354  (3) 

Section 5.7 Verbal Expressions and Variable Expressions 


357  (18) 

Objective A Translation of verbal expressions into variable expressions 


357  (2) 

Objective B Translation and simplification of verbal expressions 


359  (1) 


360  (5) 


365  (1) 



Projects and Group Activities 


366  (1) 

Multiplication of Polynomials 




366  (3) 


369  (2) 


371  (2) 

Cumulative Review Exercises 


373  (2) 


375  (60) 


376  (1) 

Section 6.1 Equations of the Form x + a = b and ax = b 


377  (8) 

Objective A Equations of the form x + a = b 


377  (3) 

Objective B Equations of the form ax = b 


380  (5) 

Section 6.2 Equations of the Form ax + b = c 


385  (6) 

Objective A Equations of the form ax + b = c 


385  (1) 


386  (5) 

Section 6.3 General FirstDegree Equations 


391  (8) 

Objective A Equations of the form ax + b = cx + d 


391  (1) 

Objective B Equations with parentheses 


392  (2) 


394  (5) 

Section 6.4 Translating Sentences into Equations 


399  (8) 

Objective A Translate a sentence into an equation and solve 


399  (2) 


401  (6) 

Section 6.5 The Rectangular Coordinate System 


407  (8) 

Objective A The rectangular coordinate system 


407  (2) 

Objective B Scatter diagrams 


409  (6) 

Section 6.6 Graphs of Straight Lines 


415  (20) 

Objective A Solutions of linear equations in two variables 


415  (1) 

Objective B Equations of the form y = mx + b 


416  (9) 


425  (1) 



Projects and Group Activities 


426  (1) 




427  (2) 


429  (2) 


431  (2) 

Cumulative Review Exercises 


433  (2) 

Measurement and Proportion 


435  (52) 


436  (1) 

Section 7.1 The Metric System of Measurement 


437  (8) 

Objective A The metric system 


437  (8) 

Section 7.2 Ratios and Rates 


445  (4) 

Objective A Ratios and rates 


445  (4) 

Section 7.3 The U.S. Customary System of Measurement 


449  (10) 

Objective A The U.S. Customary System of Measurement 


449  (2) 


451  (2) 

Objective C Conversion between the U.S. Customary System and the metric system 


453  (6) 


459  (8) 


459  (2) 


461  (6) 

Section 7.5 Direct and Inverse Variation 


467  (20) 

Objective A Direct variation 


467  (2) 

Objective B Inverse variation 


469  (6) 


475  (1) 



Projects and Group Activities 


476  (2) 






478  (3) 


481  (2) 


483  (2) 

Cumulative Review Exercises 


485  (2) 


487  (42) 


488  (1) 


489  (4) 

Objective A Percents as decimals or fractions 


489  (1) 

Objective B Fractions and decimals as percents 


490  (3) 

Section 8.2 The Basic Percent Equation 


493  (10) 

Objective A The basic percent equation 


493  (2) 

Objective B Percent problems using proportions 


495  (2) 


497  (6) 

Section 8.3 Percent Increase and Percent Decrease 


503  (4) 

Objective A Percent increase 


503  (1) 

Objective B Percent decrease 


504  (3) 

Section 8.4 Markup and Discount 


507  (6) 


507  (2) 


509  (4) 

Section 8.5 Simple Interest 


513  (16) 

Objective A Simple interest 


513  (4) 


517  (1) 

Using a Calculator as a ProblemSolving Tool 



Projects and Group Activities 


518  (3) 








521  (2) 


523  (2) 


525  (2) 

Cumulative Review Exercises 


527  (2) 


529  (78) 


530  (1) 

Section 9.1 Introduction to Geometry 


531  (16) 

Objective A Problems involving lines and angles 


531  (5) 

Objective B Problems involving angles formed by intersecting lines 


536  (3) 

Objective C Problems involving the angles of a triangle 


539  (8) 

Section 9.2 Plane Geometric Figures 


547  (18) 

Objective A Perimeter of a plane geometric figure 


547  (5) 

Objective B Area of a plane geometric figure 


552  (13) 


565  (10) 

Objective A The Pythagorean Theorem 


565  (2) 

Objective B Similar triangles 


567  (2) 

Objective C Congruent triangles 


569  (6) 


575  (10) 

Objective A Volume of a solid 


575  (3) 

Objective B Surface area of a solid 


578  (7) 

Section 9.5 Composite Figures 


585  (22) 

Objective A Perimeter of a composite plane figure 


585  (1) 

Objective B Area of a composite plane figure 


586  (1) 

Objective C Volume of a composite solid 


587  (1) 

Objective D Surface area of a composite solid 


588  (7) 


595  (1) 



Projects and Group Activities 


596  (2) 






598  (3) 


601  (2) 


603  (2) 

Cumulative Review Exercises 


605  (2) 

Statistics and Probability 


607  (42) 


608  (1) 

Section 10.1 Organizing Data 


609  (8) 

Objective A Frequency distributions 


609  (2) 


611  (1) 

Objective C Frequency polygons 


612  (5) 

Section 10.2 Statistical Measures 


617  (10) 

Objective A The mean, median, and mode of a distribution 


617  (3) 

Objective B Boxandwhiskers plots 


620  (1) 

Objective C The standard deviation of a distribution 


621  (6) 

Section 10.3 Introduction to Probability 


627  (22) 

Objective A The probability of simple events 


627  (4) 

Objective B The odds of an event 


631  (6) 


637  (1) 

Applying Solutions to Other Problems 



Projects and Group Activities 


638  (2) 






640  (3) 


643  (2) 


645  (2) 

Cumulative Review Exercises 


647  (2) 


649  




1  (2) 

Answers to OddNumbered Exercises 


1  