Download presentation
Presentation is loading. Please wait.
Published byDrusilla Parsons Modified over 9 years ago
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
Similar presentations
© 2024 SlidePlayer.com Inc.
All rights reserved.