
Basic Concepts of Algebra 





Real Numbers and Their Graphs 


1  (5) 


6  (8) 

Operating with Real Numbers 



Basic Properties of Real Numbers 


14  (7) 


21  (6) 


27  (6) 


33  (4) 

Solving Equations and Solving Problems 



Solving Equations in One Variable 


37  (6) 


43  (6) 

Problem Solving with Equations 


49  (10) 



Working with Inequalities 



Solving Inequalities in One Variable 


59  (6) 

Solving Combined Inequalities 


65  (4) 

Problem Solving Using Inequalities 


69  (4) 

Working with Absolute Value 



Absolute Value in Open Sentences 


73  (3) 

Solving Absolute Value Sentences Graphically 


76  (5) 




81  (7) 

Theorems about Order and Absolute Value 


88  (13) 

Linear Equations and Functions 



Linear Equations and Their Graphs 



Open Sentences in Two Variables 


101  (6) 

Graphs of Linear Equations in Two Variables 


107  (5) 


112  (6) 

Finding an Equation of a Line 


118  (6) 



Systems of Linear Equations in Two Variables 


124  (7) 

Problem Solving: Using Systems 


131  (4) 

Linear Inequalities in Two Variables 


135  (6) 




141  (5) 


146  (7) 


153  (14) 

Products and Factors of Polynomials 






167  (4) 


171  (3) 


174  (5) 



Using Prime Factorization 


179  (4) 


183  (5) 

Factoring Quadratic Polynomials 


188  (6) 

Applications of Factoring 



Solving Polynomial Equations 


194  (4) 

Problem Solving Using Polynomial Equations 


198  (4) 

Solving Polynomial Inequalities 


202  (9) 



Using the Laws of Exponents 




211  (5) 

Zero and Negative Exponents 


216  (5) 

Scientific Notation and Significant Digits 


221  (6) 



Rational Algebraic Expressions 


227  (5) 

Products and Quotients of Rational Expressions 


232  (3) 

Sums and Differences of Rational Expressions 


235  (3) 


238  (4) 

Problem Solving Using Fractional Equations 




242  (5) 


247  (12) 

Irrational and Complex Numbers 






259  (5) 


264  (6) 


270  (4) 

Binomials Containing Radicals 


274  (3) 

Equations Containing Radicals 


277  (6) 

Real Numbers and Complex Numbers 



Rational and Irrational Numbers 


283  (5) 


288  (4) 


292  (15) 

Quadratic Equations and Functions 



Solving Quadratic Equations 




307  (4) 


311  (6) 

Roots of Quadratic Equations 




317  (5) 

Equations in Quadratic Form 


322  (4) 

Quadratic Functions and Their Graphs 



Graphing y  k = a(x  h)2 


326  (7) 


333  (5) 

Writing Quadratic Equations and Functions 


338  (13) 

Variation and Polynomial Equations 





Direct Variation and Proportion 


351  (7) 

Inverse and Joint Variation 


358  (6) 




364  (4) 


368  (4) 

The Remainder and Factor Theorems 


372  (5) 


377  (24) 

Solving Polynomial Equations 




382  (4) 

Approximating Irrational Roots 


386  (5) 


391  (10) 



Conic Sections: Circles and Parabolas 



Distance and Midpoint Formulas 


401  (6) 


407  (5) 


412  (6) 

Conic Sections: Ellipses and Hyperbolas 




418  (8) 


426  (6) 


432  (4) 



The Geometry of Quadratic Systems 


436  (3) 

Solving Quadratic Systems 


439  (5) 

Systems of Linear Equations in Three Variables 


444  (11) 

Exponential and Logarithmic Functions 






455  (4) 


459  (4) 

Composition and Inverses of Functions 


463  (5) 




468  (5) 


473  (5) 



Applications of Logarithms 


478  (5) 

Problem Solving: Exponential Growth and Decay 


483  (6) 

The Natural Logarithm Function 


489  (12) 






501  (6) 


507  (3) 


510  (8) 



Series and Sigma Notation 


518  (7) 

Sums of Arithmetic and Geometric Series 


525  (6) 

Infinite Geometric Series 


531  (6) 




537  (3) 

The General Binomial Expansion 


540  (9) 





Angles and Degree Measure 


549  (6) 

Trigonometric Functions of Acute Angles 


555  (6) 

Trigonometric Functions of General Angles 


561  (7) 

Values of Trigonometric Functions 


568  (6) 




574  (6) 


580  (6) 


586  (5) 

Solving General Triangles 


591  (6) 


597  (10) 

Trigonometric Graphs; Identities 



Circular Functions and Their Graphs 




607  (6) 


613  (6) 


619  (5) 

Graphs of the Sine and Cosine 


624  (6) 

Graphs of the Other Functions 


630  (6) 



The Fundamental Identities 


636  (5) 

Trigonometric Addition Formulas 


641  (5) 

DoubleAngle and HalfAngle Formulas 


646  (4) 


650  (9) 

Trigonometric Applications 








659  (7) 


666  (9) 

Polar Coordinates and Complex Numbers 




675  (5) 

The Geometry of Complex Numbers 


680  (5) 


685  (4) 



The Inverse Cosine and Inverse Sine 


689  (4) 


693  (4) 


697  (12) 

Statistics and Probability 





Presenting Statistical Data 


709  (4) 

Analyzing Statistical Data 


713  (6) 


719  (5) 


724  (6) 



Fundamental Counting Principles 


730  (4) 


734  (4) 


738  (5) 




743  (2) 


745  (9) 

Mutually Exclusive and Independent Events 


754  (13) 

Matrices and Determinants 






767  (3) 

Addition and Scalar Multiplication 


770  (4) 


774  (5) 


779  (8) 




787  (3) 


790  (4) 

Working with Determinants 



Expansion of Determinants by Minors 


794  (4) 

Properties of Determinants 


798  (3) 


801  (9) 
Tables 

810  (22) 
Explorations 

832  (16) 
Portfolio Projects 

848  (21) 
Appendix 


A1 Common Logrithms: Notation and Interpolation 


856  (2) 

A2 Common Logrithms: Computation 


858  (4) 


862  (2) 

A4 Preparing for College Entrance Exams 


864  (5) 
Glossary 

869  (10) 
Index 

879  