Preface 

xiii  
AIM for Success 

xxv  


1  (52) 


2  (1) 

Introduction to Real Numbers 


2  (12) 

Inequality and absolute value 


2  (4) 

Set operations and interval notation 


6  (8) 

Operations on Rational Numbers 


14  (14) 


14  (3) 

Operations on rational numbers 


17  (3) 


20  (1) 

The Order of Operations Agreement 


21  (7) 


28  (8) 

The Properties of the Real Numbers 


28  (1) 

Evaluate variable expressions 


29  (2) 

Simplify variable expressions 


31  (5) 

Verbal Expressions and Variable Expressions 


36  (17) 

Translate a verbal expression into a variable expression 


36  (2) 


38  (4) 

Focus on Problem Solving: Polya's FourStep Process 


42  (2) 

Projects & Group Activities: Water Displacement 


44  (1) 


45  (3) 


48  (1) 


49  (4) 

FirstDegree Equations and Inequalities 


53  (70) 


54  (1) 

Equations in One Variable 


54  (10) 

Solve equations using the Addition and Multiplication Properties of Equations 


54  (4) 

Solve equations using the Distributive Property 


58  (1) 


59  (5) 

Coin, Stamp, and Integer Problems 


64  (7) 


64  (2) 


66  (5) 

Value Mixture and Motion Problems 


71  (10) 


71  (2) 


73  (8) 

Applications: Problems Involving Percent 


81  (9) 


81  (2) 


83  (7) 

Inequalities in One Variable 


90  (11) 

Solve inequalities in one variable 


90  (3) 

Solve compound inequalities 


93  (2) 


95  (6) 

Absolute Value Equations and Inequalities 


101  (22) 


101  (1) 

Absolute value inequalities 


102  (2) 


104  (4) 

Focus on Problem Solving: Understand the Problem 


108  (2) 

Projects & Group Activities: Venn Diagrams 


110  (1) 


111  (3) 


114  (2) 


116  (2) 


118  (1) 

Cumulative Review Exercises 


119  (4) 

Linear Functions and Inequalities in Two Variables 


123  (82) 


124  (1) 

The Rectangular Coordinate System 


124  (15) 

Points on a rectangular coordinate system 


124  (3) 

Find the length and midpoint of a line segment 


127  (2) 


129  (2) 


131  (8) 

Introduction to Functions 


139  (12) 


139  (12) 


151  (12) 


151  (2) 

Graph an equation of the form Ax + By = C 


153  (5) 


158  (5) 


163  (10) 

Find the slope of a line given two points 


163  (4) 

Graph a line given a point and the slope 


167  (6) 

Finding Equations of Lines 


173  (7) 

Find the equation of a line given a point and the slope 


173  (2) 

Find the equation of a line given two points 


175  (1) 


175  (5) 

Parallel and Perpendicular Lines 


180  (6) 

Find equations of parallel and perpendicular lines 


180  (6) 

Inequalities in Two Variables 


186  (19) 

Graph the solution set of an inequality in two variables 


186  (5) 

Focus on Problem Solving: Find a Pattern 


191  (1) 

Projects & Group Activities: Evaluating a Function with a Graphing Calculator 


192  (1) 

Introduction to Graphing Calculators 


192  (1) 


193  (2) 


195  (2) 


197  (3) 


200  (2) 

Cumulative Review Exercises 


202  (3) 

Systems of Equations and Inequalities 


205  (64) 


206  (1) 

Solving Systems of Linear Equations by Graphing and by the Substitution Method 


206  (8) 

Solve a system of linear equations by graphing 


206  (3) 

Solve a system of linear equations by the substitution method 


209  (5) 

Solving Systems of Linear Equations by the Addition Method 


214  (10) 

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


214  (3) 

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


217  (7) 

Solving Systems of Equations by Using Determinants and by Using Matrices 


224  (16) 


224  (3) 

Solve systems of linear equations by using Cramer's Rule 


227  (2) 

Solve systems of linear equations by using matrices 


229  (11) 


240  (11) 

Rateofwind and watercurrent problems 


240  (2) 


242  (9) 

Solving Systems of Linear Inequalities 


251  (18) 

Graph the solution set of a system of linear inequalities 


251  (3) 

Focus on Problem Solving: Solve an Easier Problem 


254  (1) 

Projects & Group Activities: Using a Graphing Calculator to Solve a System of Equations 


255  (2) 

Solving a FirstDegree Equation with a Graphing Calculator 


257  (2) 


259  (3) 


262  (1) 


263  (2) 

Cumulative Review Exercises 


265  (4) 

Polynomials and Exponents 


269  (78) 


270  (1) 


270  (12) 


270  (2) 

Divide monomials and simplify expressions with negative exponents 


272  (3) 


275  (2) 


277  (5) 

Introduction to Polynomials 


282  (11) 

Evaluate polynomial functions 


282  (5) 

Add or subtract polynomials 


287  (6) 

Multiplication of Polynomials 


293  (7) 

Multiply a polynomial by a monomial 


293  (1) 


294  (1) 

Multiply polynomials that have special products 


295  (1) 


296  (4) 


300  (8) 


300  (2) 


302  (1) 

Evaluate a polynomial using synthetic division 


303  (5) 


308  (11) 

Factor a monomial from a polynomial 


308  (1) 


308  (2) 

Factor trinomials of the form x2 + bx + c 


310  (2) 

Factor trinomials of the form ax2 + bx + c 


312  (7) 


319  (8) 

Factor the difference of two perfect squares and factor perfectsquare trinomials 


319  (2) 

Factor the sum or the difference of two cubes 


321  (1) 

Factor trinomials that are quadratic in form 


322  (1) 


323  (4) 

Solving Equations by Factoring 


327  (20) 

Solve equations by factoring 


327  (3) 


330  (4) 

Focus on Problem Solving: Find a Counterexample 


334  (1) 

Projects & Group Activities: Reverse Polish Notation 


335  (1) 


336  (1) 

Astronomical Distances and Scientific Notation 


336  (2) 


338  (2) 


340  (2) 


342  (1) 

Cumulative Review Exercises 


343  (4) 


347  (62) 


348  (1) 

Introduction to Rational Functions 


348  (8) 

Find the domain of a rational function 


348  (2) 

Simplify rational expressions 


350  (6) 

Operations on Rational Expressions 


356  (10) 

Multiply and divide rational expressions 


356  (2) 

Add and subtract rational expressions 


358  (8) 


366  (5) 

Simplify complex fractions 


366  (5) 


371  (11) 

Solve fractional equations 


371  (2) 


373  (2) 


375  (7) 

Proportions and Variation 


382  (10) 


382  (2) 


384  (8) 


392  (17) 


392  (3) 

Focus on Problem Solving: Implication 


395  (1) 

Projects & Group Activities: Continued Fractions 


396  (1) 

Graphing Rational Functions 


397  (1) 


398  (1) 


399  (3) 


402  (2) 


404  (1) 

Cumulative Review Exercises 


405  (4) 

Rational Exponents and Radicals 


409  (54) 


410  (1) 

Rational Exponents and Radical Expressions 


410  (9) 

Simplify expressions with rational exponents 


410  (2) 

Write exponential expressions as radical expressions and radical expressions as exponential expressions 


412  (2) 

Simplify radical expressions that are roots of perfect powers 


414  (5) 

Operations on Radical Expressions 


419  (9) 

Simplify radical expressions 


419  (1) 

Add and subtract radical expressions 


420  (1) 

Multiply radical expressions 


421  (1) 

Divide radical expressions 


422  (6) 


428  (5) 

Find the domain of a radical function 


428  (1) 


429  (4) 

Solving Equations Containing Radical Expressions 


433  (8) 

Solve equations containing one or more radical expressions 


433  (3) 


436  (5) 


441  (22) 


441  (1) 

Add and subtract complex numbers 


442  (1) 


443  (2) 


445  (4) 

Focus on Problem Solving: Another Look at Polya's FourStep Process 


449  (1) 

Projects & Group Activities: Graphing Complex Numbers 


450  (2) 

Solving Radical Equations with a Graphing Calculator 


452  (1) 


452  (2) 


454  (1) 


455  (2) 


457  (1) 

Cumulative Review Exercises 


458  (5) 

Quadratic Equations and Inequalities 


463  (72) 


464  (1) 

Solving Quadratic Equations by Factoring or by Taking Square Roots 


464  (7) 

Solve quadratic equations by factoring 


464  (1) 

Write a quadratic equation given its solutions 


465  (1) 

Solve quadratic equations by taking square roots 


466  (5) 

Solving Quadratic Equations by Completing the Square and by Using the Quadratic Formula 


471  (13) 

Solve quadratic equations by completing the square 


471  (4) 

Solve quadratic equations by using the quadratic formula 


475  (9) 

Equations that are Reducible to Quadratic Equations 


484  (6) 

Equations that are quadratic in form 


484  (1) 


485  (2) 


487  (3) 

Applications of Quadratic Equations 


490  (6) 


490  (6) 


496  (5) 

Solve nonlinear inequalities 


496  (5) 

Properties of Quadratic Functions 


501  (13) 

Graph a quadratic function 


501  (4) 

Find the xintercepts of a parabola 


505  (9) 

Applications of Quadratic Functions 


514  (21) 

Minimum and maximum problems 


514  (1) 

Applications of minimum and maximum 


515  (6) 

Focus on Problem Solving: Inductive and Deductive Reasoning 


521  (1) 

Projects & Group Activities: Completing the Square 


522  (1) 

Using a Graphing Calculator to Solve a Quadratic Equation 


523  (1) 

Finding the Maximum or Minimum of a Function Using a Graphing Calculator 


524  (1) 

Business Applications of Maximum and Minimum Values of Quadratic Functions 


525  (1) 


526  (3) 


529  (1) 


530  (1) 

Cumulative Review Exercises 


531  (4) 


535  (46) 


536  (1) 


536  (10) 


536  (10) 


546  (7) 

Graph by using translations 


546  (7) 


553  (6) 

Perform operations on functions 


553  (2) 

Find the composition of two functions 


555  (4) 

OnetoOne and Inverse Functions 


559  (22) 

Determine whether a function is onetoone 


559  (2) 

Find the inverse of a function 


561  (7) 

Focus on Problem Solving: Proof in Mathematics 


568  (1) 

Projects & Group Activities: Applications of the Composition of Functions 


569  (2) 


571  (2) 


573  (2) 


575  (1) 

Cumulative Review Exercises 


576  (5) 

Exponential and Logarithmic Functions 


581  (60) 


582  (1) 


582  (8) 

Evaluate exponential functions 


582  (2) 

Graph exponential functions 


584  (6) 

Introduction to Logarithms 


590  (14) 

Write equivalent exponential and logarithmic equations 


590  (3) 

The Properties of Logarithms 


593  (11) 

Graphs of Logarithmic Functions 


604  (7) 

Graph logarithmic functions 


604  (7) 

Exponential and Logarithmic Equations 


611  (7) 

Solve exponential equations 


611  (2) 

Solve logarithmic equations 


613  (5) 

Applications of Exponential and Logarithmic Functions 


618  (23) 


618  (10) 

Focus on Problem Solving: Proof by Contradiction 


628  (1) 

Projects & Group Activities: Fractals 


629  (1) 

Credit Reports and FICO® Scores 


630  (2) 


632  (1) 


633  (2) 


635  (1) 

Cumulative Review Exercises 


636  (5) 


641  (42) 


642  (1) 

Introduction to Sequences and Series 


642  (6) 

Write the terms of a sequence 


642  (2) 


644  (4) 

Arithmetic Sequences and Series 


648  (7) 

Find the nth term of an arithmetic sequence 


648  (2) 

Evaluate an arithmetic series 


650  (2) 


652  (3) 

Geometric Sequences and Series 


655  (10) 

Find the nth term of a geometric sequence 


655  (2) 


657  (2) 

Infinite geometric series 


659  (2) 


661  (4) 


665  (18) 


665  (6) 

Focus on Problem Solving: Forming Negations 


671  (2) 

Projects & Group Activities: ISBN and UPC Numbers 


673  (1) 


674  (2) 


676  (2) 


678  (1) 

Cumulative Review Exercises 


679  (4) 


683  (40) 


684  (1) 


684  (6) 


684  (6) 


690  (6) 

Find the equation of a circle and then graph the circle 


690  (2) 

Write the equation of a circle in standard form and then graph the circle 


692  (4) 

The Ellipse and the Hyperbola 


696  (7) 

Graph an ellipse with center at the origin 


696  (2) 

Graph a hyperbola with center at the origin 


698  (5) 

Solving Nonlinear Systems of Equations 


703  (5) 

Solve nonlinear systems of equations 


703  (5) 

Quadratic Inequalities and Systems of Inequalities 


708  (15) 

Graph the solution set of a quadratic inequality in two variables 


708  (1) 

Graph the solution set of a nonlinear system of inequalities 


709  (5) 

Focus on Problem Solving: Use a Variety of ProblemSolving Strategies 


714  (1) 

Projects & Group Activities: The Eccentricity and Foci of an Ellipse 


715  (1) 

Graphing Conic Sections Using a Graphing Calculator 


716  (1) 


717  (2) 


719  (2) 


721  (2) 


723  (4) 




727  (2) 

Calculator Guide for the TI83 and TI83 Plus 


729  
Solutions to Student Problems 

1  (1) 
Answers to Selected Exercises 

1  (1) 
Glossary 

1  (1) 
Index 

1  