1. THE REAL NUMBERS College Algebra

2. Sets Set notation Union of sets Intersection of sets Subsets Combinations of three or more sets Applications

3. Real Numbers Rational numbers Graphing on the number line Irrational numbers Real numbers Intervals of real numbers

4. Computations Absolute value Addition Subtraction Multiplication Division Division by zero

5. Evaluating Expressions Arithmetic expressions Exponential expressions Square roots Order of operations Algebraic expressions Reading graphs

6. Properties of Real Numbers Commutative properties Associative properties Distributive property Identity properties Inverse properties Multiplication property of zero

7. Computations Using the properties in computation Combining like terms Multiplying and dividing terms Removing parentheses

8. LINEAR EQUATIONS AND INEQUALITIES College Algebra

9. Linear Equations in One Variable Equations Solving equations Types of equations Strategy for solving linear equations Techniques Applications

10. Formulas and Functions Solving for a variable The language of functions Finding the value of a variable Geometric formulas

11. Algebraic Expressions Writing algebraic expressions Solving problems Geometric problems Investment problems Mixture problems Uniform motion problems Commission problems

12. Inequalities Inequality symbols Interval notation and graphs Solving linear inequalities Applications

13. Compound Inequalities Compound inequalities Graphing the solution set Applications

14. Absolute Value Absolute value equations Absolute value inequalities All or nothing Applications

15. Graphing Solutions Graphing ordered pairs Graphing a linear equation in two variables Using intercepts for graphing Applications

16. Finding the Slope of a Line Slope The coordinate formula for slope Parallel lines Perpendicular lines Applications of slope

17. Equations of a Line Slope-intercept form Using slope-intercept form for graphing Standard form Point-slope form Applications

18. Linear Inequalities Graphing linear inequalities The test point method Graphing compound inequalities Absolute value inequalities Inequalities with no solution Applications

19. Functions and Relations Concept of a function Functions expressed by formulas Functions expressed by tables Functions expressed by ordered pairs The vertical-line test Domain and range Function notation

20. SYSTEMS OF LINEAR EQUATIONS College Algebra

21. Graphing and Substitution Solving a system by graphing Types of systems Solving by substitution Applications

22. The Addition Method The addition method Equations involving fractions or decimals Applications

23. Systems in Three Variables Definition Solving a system by elimination Dependent and inconsistent systems Applications

24. Matrices The augmented matrix The Gauss-Jordon elimination method Dependent and inconsistent systems

25. Determinants and Cramer’s Rule Determinants Cramer’s rule (2 x 2) Minors Evaluating a 3 x 3 determinant Cramer’s rule (3 x 3)

26. Linear Programming Graphing the constraints Maximizing or minimizing

27. EXPONENTS AND POLYNOMIALS College Algebra

28. Integral Exponents and Scientific Notation Positive and negative exponents Product rule for exponents Zero exponent Changing the sign of an exponent Quotient rule for exponents Scientific notation

29. Power Rules Raising an exponential expression to a power Raising a product to a power Raising a quotient to a power Variable exponents Summary of the rules Applications

30. Polynomials and Polynomial Functions Polynomials Evaluating polynomials and polynomial functions Addition and subtraction of polynomials Multiplication of polynomials

31. Multiplication of Binomials The FOIL method The square of a binomial Product of a sum and a difference Higher powers of binomials Polynomial functions

32. Factoring Polynomials Factoring out the greatest common factor (GCF) Factoring by grouping Factoring the difference of two squares Factoring perfect square trinomials Factoring a difference or sum of two cubes Factoring a polynomial completely

33. Factoring ax 2 + bx + c Factoring trinomials with leading coefficient 1 Factoring trinomials with leading coefficient not 1 Trial and error Factoring by substitution

34. Factoring Strategy Prime polynomials Factoring polynomials completely Strategy for factoring polynomials

35. Solving Equations The zero factor property Applications

36. RATIONAL EXPRESSIONS AND FUNCTIONS, RADICALS, AND RATIONAL EXPONENTS College Algebra

37. Rational Expressions and Functions Rational expressions Reducing to lowest terms Building up the denominator Rational functions Applications

38. Multiplication and Division Multiplying rational expressions Dividing rational expressions

39. Addition and Subtraction Adding and subtracting with identical denominators Least common denominator (LCD) Adding and subtracting with different denominators Shortcuts Applications

40. Simplifying Complex Fractions Simplifying complex fractions Simplifying expressions with negative exponents Applications

41. Dividing Polynomials Dividing a polynomial by a monomial Dividing a polynomial by a binomial Synthetic division Division and factoring The remainder theorem

42. Equations Involving Rational Expressions Multiplying by the LCD Proportions Applications

43. Applications of Rational Expressions Formulas Uniform motion problems Work problems Miscellaneous problems

44. Radicals Roots Roots and variables Product rule for radicals Quotient rule for radicals Domain of a radical function

45. Rational Exponents Rational exponents Using the rules of exponents Simplifying expressions involving variables

46. Arithmetic Operations Adding and subtracting radicals Multiplying radicals Conjugates Multiplying radicals with different indices

47. Additional Operations Rationalizing the denominator Simplifying radicals Dividing radicals Rationalizing denominators using conjugates Powers of radical expressions

48. Equations with Radicals and Exponents The odd-root property The even-root property Equations involving radicals Equations involving rational exponents Applications

49. Complex Numbers Definition Addition, subtraction, and multiplication of complex numbers Division of complex numbers Square roots of negative numbers Imaginary solutions to equations

50. QUADRATIC EQUATIONS, INEQUALITIES, AND FUNCTIONS College Algebra

51. Factoring and Completing the Square Review of factoring Review of the even-root property Completing the square Radicals and rational expressions Imaginary solutions

52. The Q uadratic Formula Developing the formula Using the formula Number of solutions Applications

53. Additional Topics Writing a quadratic equation with given solutions Using the discriminant in factoring Equations quadratic in form Applications

54. Quadratic Functions and Their Graphs Quadratic functions Graphing quadratic functions The vertex and intercepts Applications

55. Quadratic and Rational Inequalities Solving quadratic inequalities with a sign graph Perfect square inequalities Solving rational inequalities with a sign graph Quadratic inequalities that cannot be factored Applications

56. Graphs and Functions of Relations Linear and constant functions Absolute value functions Quadratic functions Square-root functions Piecewise functions Graphing relations

57. Transformations of Graphs Reflecting Translating Stretching and shrinking Multiple transformations

58. Combining Functions Basic operations with functions Composition

59. Inverse Functions Inverse of a function Identifying inverse functions Switch-and-solve strategy Even roots or even powers Graphs of f and f -1

60. Variation in Functions Direct, inverse, and joint variation Finding the variation constant Finding a new value for the dependent variable Applications

61. POLYNOMIAL, RATIONAL, EXPONENTIAL, AND LOGARITHMIC FUNCTIONS College Algebra

62. The Factor Theorem The factor theorem Solving polynomial equations

63. The Zeros of a Polynomial Function The remainder theorem The fundamental theorem of algebra The rational root theorem

64. The Theory of Equations The number of roots to a polynomial equation The conjugate pairs theorem Descartes’ rule of signs Bounds on the roots

65. Graphing Polynomial Functions Symmetry Behavior at the x-intercepts Sketching graphs of polynomial functions

66. Graphing Rational Functions Rational functions Asymptotes Sketching graphs of rational functions

67. Exponential Functions Exponential functions Domain Graphing exponential functions Transformations of exponential functions Exponential equations Applications

68. Logarithmic Functions Logarithmic functions Domain and range Graphing logarithmic functions Logarithmic equations Applications

69. Properties of Logarithms Inverse properties Product rule for logarithms Quotient rule for logarithms Power rule for logarithms Using the properties

70. Solving Equations Logarithmic equations Exponential equations Changing the base Strategy for solving equations Applications

71. NONLINEAR SYSTEMS, CONIC SECTIONS, SEQUENCES, AND SERIES College Algebra

72. Nonlinear Systems of Equations Solving by elimination Applications

73. Parabolas Distance and midpoint formulas Geometric definition of parabola Developing the equation Parabolas in the form y = a(x - h) 2 + K Finding the vertex, focus, and directrix Axis of symmetry Changing forms Parabolas opening to the right or left

74. Circles The equation of a circle Equations not in standard form Systems of equations

75. Ellipses and Hyperbolas The ellipse The hyperbola

76. Second-Degree Inequalities Graphing a second-degree inequality Systems of inequalities

77. Sequences Finding a formula for the nth term

78. Series Summation notation Series Changing the index

79. Arithmetic Sequences and Series Arithmetic sequences Arithmetic series

80. Geometric Sequences and Series Geometric sequences Finite geometric series Infinite geometric series Applications

81. Binomial Expansions Some examples Obtaining the coefficients The binomial theorem

82. COUNTING AND PROBABILITY College Algebra

83. Counting and Permutations The fundamental counting principle Permutations

84. Combinations Permutations, combinations, or neither Labeling

85. Basic Probability The probability of an event The addition rule Complementary events Odds