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Algebra and Trigonometry

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Algebra and Trigonometry

Algebra is the study of mathematical symbols and the rules for manipulating these symbols. It is a unifying thread of almost all of mathematics. Elementary algebra is generally considered to be essential for any study of mathematics, science, or engineering, as well as such applications as medicine and economics. Elementary algebra differs from arithmetic in the use of abstractions, such as using letters to stand for numbers that are either unknown or allowed to take on many values.

Mathematics
Author
Jay Abramson
Publisher
Arizona State University
Source
LibreTexts
License
CC BY
Language
EN
Category
Basic Sciences
Read online Download PDF (open licence)
Contents· 151 sections
  1. 01: Prerequisites
  2. 1.01: Prelude to Prerequisites
  3. 1.02: Real Numbers - Algebra Essentials
  4. 1.2E: Real Numbers - Algebra Essentials (Exercises)
  5. 1.03: Exponents and Scientific Notation
  6. 1.3E: Exponents and Scientific Notation (Exercises)
  7. 1.04: Radicals and Rational Expressions
  8. 1.4E: Radicals and Rational Expressions (Exercise)
  9. 1.05: Polynomials
  10. 1.5E: Polynomials (Exercises)
  11. 1.06: Factoring Polynomials
  12. 1.6E: Factoring Polynomials (Exercises)
  13. 1.07: Rational Expressions
  14. 1.7E: Rational Expressions (Exercises)
  15. 02: Equations and Inequalities
  16. 2.01: Prelude to Equations and Inequalities
  17. 2.02: The Rectangular Coordinate Systems and Graphs
  18. 2.2E: The Rectangular Coordinate Systems and Graphs (Exercises)
  19. 2.03: Linear Equations in One Variable
  20. 2.3E: Linear Equations in One Variable (Exercises)
  21. 2.04: Complex Numbers
  22. 2.4E: Complex Numbers (Exercises)
  23. 2.05: Quadratic Equations
  24. 2.5E: Quadratic Equations (Exercises)
  25. 2.06: Other Types of Equations
  26. 2.6E: Other Types of Equations (Exercises)
  27. 2.07: Modeling with Equations
  28. 2.7.01: Models and Applications
  29. 2.7.1E: Models and Applications (Exercises)
  30. 2.7.02: Solve Mixture and Uniform Motion Applications
  31. 2.7.2E: Exercises
  32. 2.7.03: Solve Applications with Rational Equations
  33. 2.7.3E: Exercises
  34. 2.08: Linear and Absolute Value Inequalities
  35. 2.8.01: Linear Inequalities
  36. 2.8.1E: Exercises
  37. 2.8.02: Solve Absolute Value Inequalities
  38. 2.8.2E: Exercises
  39. 2.8E: Linear Inequalities and Absolute Value Inequalities (Exercises)
  40. 03: Functions
  41. 3.01: Prelude to Functions
  42. 3.02: Functions and Function Notation
  43. 3.2E: Functions and Function Notation (Exercises)
  44. 3.03: Domain and Range
  45. 3.3E: Domain and Range (Exercises)
  46. 3.04: Rates of Change and Behavior of Graphs
  47. 3.4E: Rates of Change and Behavior of Graphs (Exercises)
  48. 3.05: Linear Functions
  49. 3.5.01: Prelude to Linear Functions
  50. 3.5.02: Linear Functions
  51. 3.5.03: Graphs of Linear Functions
  52. 3.5.04: Modeling with Linear Functions
  53. 3.5.05: Fitting Linear Models to Data
  54. 3.5.E: Linear Functions(Exercises)
  55. 3.5.R: Linear Functions(Review)
  56. 3.06: Composition of Functions
  57. 3.6E: Composition of Functions (Exercises)
  58. 3.07: Transformation of Functions
  59. 3.7E: Transformation of Functions (Exercises)
  60. 3.08: Absolute Value Functions
  61. 3.8E: Absolute Value Functions (Exercises)
  62. 3.09: Inverse Functions
  63. 3.9E: Inverse Functions (Exercises)
  64. 04: Polynomial and Rational Functions
  65. 4.01: Prelude to Polynomial and Rational Functions
  66. 4.02: Quadratic Functions
  67. 4.2E: Quadratic Functions (Exercises)
  68. 4.03: Power Functions and Polynomial Functions
  69. 4.3E: Power Functions and Polynomial Functions (Exercises)
  70. 4.04: Graphs of Polynomial Functions
  71. 4.4E: Graphs of Polynomial Functions (Exercises)
  72. 4.05: Dividing Polynomials
  73. 4.5E: Dividing Polynomials (Exercises)
  74. 4.06: Zeros of Polynomial Functions
  75. 4.6E: Zeros of Polynomial Functions (Exercises)
  76. 4.07: Rational Functions
  77. 4.7E: Rational Functions (Exercises)
  78. 4.08: Non-linear Inequalities
  79. 4.8.01: Solve Quadratic Inequalities
  80. 4.8.1E: Exercises
  81. 4.8.02: Solve Rational Inequalities
  82. 4.8.2E: Exercises
  83. 05: Exponential and Logarithmic Functions
  84. 5.01: Prelude to Exponential and Logarithmic Functions
  85. 5.02: Exponential Functions
  86. 5.2E: Exponential Functions (Exercises)
  87. 5.03: Graphs of Exponential Functions
  88. 5.3E: Graphs of Exponential Functions (Exercises)
  89. 5.04: Logarithmic Functions
  90. 5.4E: Logarithmic Functions (Exercises)
  91. 5.05: Graphs of Logarithmic Functions
  92. 5.5E: Graphs of Logarithmic Functions (Exercises)
  93. 5.06: Logarithmic Properties
  94. 5.6E: Logarithmic Properties (Exercises)
  95. 5.07: Exponential and Logarithmic Equations
  96. 5.7E: Exponential and Logarithmic Equations (Exercises)
  97. 5.08: Exponential and Logarithmic Models
  98. 5.8E: Exponential and Logarithmic Models (Exercises)
  99. 5.09: Fitting Exponential Models to Data
  100. 5.9E: Fitting Exponential Models to Data (Exercises)
  101. 06: Systems of Equations and Inequalities
  102. 6.01: Prelude to Systems of Equations and Inequalities
  103. 6.02: Systems of Linear Equations - Two Variables
  104. 6.2E: Systems of Linear Equations - Two Variables (Exercises)
  105. 6.03: Systems of Linear Equations with Three Variables
  106. 6.3E: Systems of Linear Equations with Three Variables (Exercises)
  107. 6.04: Systems of Nonlinear Equations and Inequalities - Two Variables
  108. 6.4E: Systems of Nonlinear Equations and Inequalities - Two Variables (Exercises)
  109. 6.05: Solving Systems with Gaussian Elimination
  110. 6.5E: Solving Systems with Gaussian Elimination (Exercises)
  111. 07: Analytic Geometry
  112. 7.01: Prelude to Analytic Geometry
  113. 7.02: The Parabola
  114. 7.2E: The Parabola (Exercises)
  115. 7.03: The Ellipse
  116. 7.3E: The Ellipse (Exercises)
  117. 7.04: The Hyperbola
  118. 7.4E: The Hyperbola (Exercises)
  119. 08: Sequences Probability and Counting Theory
  120. 8.01: Prelude to Sequences Probability and Counting Theory
  121. 8.02: Sequences and Their Notations
  122. 8.2E: Sequences and Their Notations (Exercises)
  123. 8.03: Arithmetic Sequences
  124. 8.3E: Arithmetic Sequences (Exercises)
  125. 8.04: Geometric Sequences
  126. 8.4E: Geometric Sequences (Exercises)
  127. 8.05: Series and Their Notations
  128. 8.5E: Series and Their Notations (Exercises)
  129. 09: Additional Topics for Ch 4 6 7 and 8
  130. 9.01: Inverses and Radical Functions
  131. 9.1.01: Inverses and Radical Functions (Exercises)
  132. 9.02: Modeling Using Variation
  133. 9.2E: Modeling Using Variation (Exercises)
  134. 9.03: Partial Fractions
  135. 9.3.01: Partial Fractions (Exercises)
  136. 9.04: Matrices and Matrix Operations
  137. 9.4E: Matrices and Matrix Operations (Exercises)
  138. 9.05: Solving Systems with Inverses
  139. 9.5E: Solving Systems with Inverses (Exercises)
  140. 9.06: Solving Systems with Cramer's Rule
  141. 9.6E: Solving Systems with Cramer's Rule (Exercises)
  142. 9.07: Rotation of Axes
  143. 9.7E: Rotation of Axes (Exercises)
  144. 9.08: Conic Sections in Polar Coordinates
  145. 9.8E: Conic Sections in Polar Coordinates (Exercises)
  146. 9.09: Counting Principles
  147. 9.9E: Counting Principles (Exercises)
  148. 9.10: Binomial Theorem
  149. 9.10E: Binomial Theorem (Exercises)
  150. 9.11: Probability
  151. 9.11E: Probability (Exercises)