College Algebra

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Barron's Educational Series, 1995 - Mathematics - 218 pages
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Books in the " EZ-101 Study Keys " series are intended as brush-up reviews for a variety of college-101 courses. They are designed as a set of classroom "notes" that reflect typical lecture material presented in a classroom over the course of a semester. As such, they make handy supplements to college textbooks and serve as valuable pre-exam reviews. Covered in this updated edition are polynomials, radicals, equations and inequalities, polynomial equations, exponential and logarithmic functions, conics, sequences and series, induction, permutations and combinations, determinants and matrices, and more.
 

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Contents

Basic laws and operations of algebra
1
Sets numbers and variables
2
Equality and inequality relations
4
Field properties of real numbers
5
Interval notation
7
Integer exponents
8
Polynomials
11
Factoring polynomials
15
Synthetic division
113
The remainder and factor theorems
116
Zeros of polynomial functions
117
Reducing the degree of a polynomial equation
119
The rational root theorem
121
Descartes rule of signs
123
Locating and approximating irrational roots
125
Exponential and logarithmic functions
127

Radicals and rational exponents
18
Operations with radicals
20
Equations and inequalities
23
Linear equations
24
Linear inequalities
28
Absolute value equations and inequalities
30
Quadratic equations
33
Quadratic inequalities
37
Radical equations
39
Rational expressions
42
Simplifying rational expressions
43
Operations with rational expressions
45
Simplifying complex fractions
49
Fractional equations and inequalities
50
Linear equations and inequalities in twovariables
53
Midpoint and distance formulas
54
Slope formula
58
Equations of lines
61
Graphing linear equations in two variables
64
Graphing linear inequalities in two variables
66
Complex numbers and quadratic equations
68
Complex numbers
69
Solving quadratic equations by completing the square
72
Solving quadratic equations by formula
73
Sum and product of the roots
75
Graphing quadratic equations in two variables
77
Functions and their graphs
82
Functions
83
Vertical and horizontal line tests
86
Symmetry and functions
88
Graphs of special functions
91
Shifts of graphs of functions
96
The composition of two functions
100
Inverse functions
102
Polynomial and rational functions
104
Graphing rational functions
106
Equations that describe variation
109
Polynomial equations
112
Exponential functions
128
Logarithmic functions
131
Logarithm laws
134
Exponential and logarithmic equations
136
Exponential growth and decay
139
Conic sections and their equations
142
The circle
144
The ellipse
145
The hyperbola
149
The parabola
155
The general equation for conic sections
159
Counting methods
161
The basic principles of counting
162
Permutations
163
Combinations
165
The binomial theorem
167
Sequences series and induction
169
Arithmetic sequences and series
170
Geometric sequences and series
172
Generalized sequences
174
Summation notation
176
Mathematical induction part I
179
Mathematical induction part II
182
Linear and nonlinear systems
184
Solving systems of two linear equations
185
Matrices
187
Determinants
190
Cramers rule
193
Triangularizing linear systems
195
Recognizing linear systems that have many or no solutions
198
Finding the inverse of a matrix
199
Solving linear systems by matrix inversion
201
Partial fractions
203
Solving nonlinear systems
206
Glossary
209
Index
216
Copyright

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Popular passages

Page 212 - ... is less than is less than or equal to is greater than is greater than or equal to...
Page 210 - A complex number is any number that can be written in the form a + hi, where a and b are real numbers and / = V— T.
Page 213 - It is also clear that if A is an mxn matrix and B is an nxp matrix, then C is an mxp matrix.

About the author (1995)

Lawrence S. Leff has helped make mathematics and tests more accessible to students through his work and his writing. Leff is assistant principal and math supervisor at Franklin D. Roosevelt High School in Brooklyn, New York. His writing is centered primarily on examination preparation guides. His books, which target high school students, have included, Let's Review: Sequential Mathematics, a teacher planning and student review and math test preparation guide, and Preparation for the CLEP--College-Level Examination Program. Some of Leff's math review guides originally were intended for New York area high school students participating in the three-year mathematics curriculum there. Lawrence Leff has also published mathematics materials not strictly for test-taking, including Geometry the Easy Way.

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