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Study type: Online

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Overview

Become a Master of Pre Calculus & Trigonometry and Ace your next Exam! In this course, you will master the concepts of PreCalculus from beginner to advanced, with our step-by-step video tutorials and test your knowledge with over 1100 Practice Test Questions. The concepts you will learn are fundamental to success in higher math classes such as Calculus and Linear Algebra. The topics of the course include:

  • Functions and Their Graphs

  • The Rectangular Coordinate Plane

  • Midpoint of a Line Segment

  • The Pythagorean Formula

  • Complex Plane – Distance and Midpoint Formulas

  • Absolute Value of a Complex Number

  • Vertices of a Right Triangle Formula

  • Collinear Points Formula

  • Equations of Circles

  • Function Definition

  • Domain and Range of Relations and Functions

  • Vertical Line Test

  • Function Notation

  • Graphing Linear Functions

  • Finding the Slope of a Line

  • Finding the Equation of a Line

  • Parallel and Perpendicular Lines

  • Graphs of Basic Functions

  • Piecewise-Defined Functions

  • Increasing, Decreasing, and Constant Intervals

  • Graphing Transformations – stretching, shrinking, reflecting

  • Graphing Transformations – horizontal and vertical shifts

  • Even and Odd Functions

  • Finding the Difference Quotient

  • Function Composition

  • Polynomial and Rational Functions

  • Finding the Vertex Form of a Parabola

  • Graphing Parabolas

  • The Remainder Theorem

  • The Factor Theorem

  • The Rational Zeros Theorem

  • The Fundamental Theorem of Algebra

  • Conjugate Zeros Theorem

  • Descartes’ Rule of Signs

  • Intermediate Value and Boundedness Theorems

  • Finding the Zeros of a Polynomial Function

  • Exponential and Logarithmic Functions

  • The Horizontal Line Test

  • Finding One-to-One Functions Algebraically

  • Finding the Inverse of a Function

  • Proving that two functions are inverses

  • Domain Restrictions, Finding the Inverse

  • Exponential Functions and Their Graphs

  • Solving Exponential Equations without Logs

  • Solving Compound Interest Formula Word Problems

  • Solving Continuous Compound Interest Formula Word Problems

  • Logarithmic Functions

  • Properties of Logarithms

  • Inverse of an Exponential / Logarithmic Function

  • Evaluating Logarithms Using the Change of Base Formula

  • Solving Exponential Equations with Logarithms

  • Solving Logarithmic Equations

  • Systems of Equations and Inequalities

  • Solving Linear Systems in Two Variables

  • Solving Linear Systems in Three Variables

  • FInding the Equation of a Parabola Given Three Points

  • Linear Systems Word Problems

  • Partial Fraction Decomposition

  • Solving Nonlinear Systems of Equations

  • Solving Nonlinear Systems of Inequalities

  • Matrices and Determinants

  • Gauss-Jordan Elimination

  • Matrix Addition and Subtraction

  • Scalar Multiplication

  • Matrix Multiplication

  • Inverse of a Matrix

  • Matrix Equations

  • Determinants Using Laplace Expansion

  • Determinants Using Triangular Form

  • Transpose of a Matrix

  • Adjugate of a Matrix

  • Inverse Using the Adjugate and Determinant

  • Cramer’s Rule

  • Area of a Triangle – Determinants

  • Collinear Points – Determinants

  • Writing the Equation of a Line – Determinants

  • Analytic Geometry

  • Conic Sections

  • The Parabola

  • The Ellipse

  • The Hyperbola

  • Sequences

  • Series and Summation Notation

  • Finding the nth term for an arithmetic sequence

  • Finding the nth term for a geometric sequence

  • Evaluating arithmetic series

  • Evaluating infinite and finite geometric series

  • Counting Theory

  • Combinations

  • Permutations

  • Angles in Trigonometry

  • Measuring angles using degrees

  • Complementary angles

  • Supplementary angles

  • Degrees, Minutes, and Seconds

  • Converting Between Decimal Degrees and Degrees, Minutes, and Seconds

  • Determine if two Angles are Coterminal Angles

  • Relationships between Angles: Vertical Angles, Angles formed by a Transversal and Parallel Lines

  • Solving for the Missing Angle Measurements with Similar Triangles

  • Solving for the Missing Lengths with Similar Triangles

  • Finding the Trigonometric Function Values of an Angle

  • Finding Trigonometric Function Values Given One Value and the Quadrant

  • Finding Trigonometric Function Values Based on Reciprocal Identities

  • Finding Trigonometric Function Values Based on Pythagorean Identities

  • Finding Trigonometric Function Values Based on Quotient Identities

  • Finding Trigonometric Function Values of an Acute Angle

  • Writing a Function in Terms of its Cofunction

  • Solving Equations Using Cofunction Identities

  • Finding Reference Angles

  • Special Angles as Reference Angles

  • Finding Angle Measures with Special Angles

  • Finding Trigonometric Function Values of Non-Acute Angles

  • Finding Trigonometric Function Values Using a Calculator

  • Finding Unknown Angle Measures Using Inverse Trigonometric Functions: arcsin, arccos, arctan

  • Solving Right Triangles

  • Solving Word Problems that involve angles of elevation

  • Solving Word Problems that involve angles of depression

  • Radian Measure

  • Converting between Radians and Degrees

  • Finding the Arc Length on a Circle

  • Finding the Area of a Sector of a Circle

  • The Unit Circle and Circular Functions

  • Solving Word Problems with Linear & Angular Speed

Expected Outcomes

  1. Functions and Their Graphs
  2. The Rectangular Coordinate Plane
  3. Midpoint of a Line Segment
  4. The Pythagorean Formula
  5. Complex Plane – Distance and Midpoint Formulas
  6. Absolute Value of a Complex Number
  7. Vertices of a Right Triangle Formula
  8. Collinear Points Formula
  9. Equations of Circles
  10. Function Definition
  11. Domain and Range of Relations and Functions
  12. Vertical Line Test
  13. Function Notation
  14. Graphing Linear Functions
  15. Finding the Slope of a Line
  16. Finding the Equation of a Line
  17. Parallel and Perpendicular Lines
  18. Graphs of Basic Functions
  19. Piecewise-Defined Functions
  20. Increasing, Decreasing, and Constant Intervals
  21. Graphing Transformations – stretching, shrinking, reflecting
  22. Graphing Transformations – horizontal and vertical shifts
  23. Even and Odd Functions
  24. Finding the Difference Quotient
  25. Function Composition
  26. Polynomial and Rational Functions
  27. Finding the Vertex Form of a Parabola
  28. Graphing Parabolas
  29. The Remainder Theorem
  30. The Factor Theorem
  31. The Rational Zeros Theorem
  32. The Fundamental Theorem of Algebra
  33. Conjugate Zeros Theorem
  34. Descartes’ Rule of Signs
  35. Intermediate Value and Boundedness Theorems
  36. Finding the Zeros of a Polynomial Function
  37. Exponential and Logarithmic Functions
  38. The Horizontal Line Test
  39. Finding One-to-One Functions Algebraically
  40. Finding the Inverse of a Function
  41. Proving that two functions are inverses
  42. Domain Restrictions, Finding the Inverse
  43. Exponential Functions and Their Graphs
  44. Solving Exponential Equations without Logs
  45. Solving Compound Interest Formula Word Problems
  46. Solving Continuous Compound Interest Formula Word Problems
  47. Logarithmic Functions
  48. Properties of Logarithms
  49. Inverse of an Exponential / Logarithmic Function
  50. Evaluating Logarithms Using the Change of Base Formula
  51. Solving Exponential Equations with Logarithms
  52. Solving Logarithmic Equations
  53. Systems of Equations and Inequalities
  54. Solving Linear Systems in Two Variables
  55. Solving Linear Systems in Three Variables
  56. FInding the Equation of a Parabola Given Three Points
  57. Linear Systems Word Problems
  58. Partial Fraction Decomposition
  59. Solving Nonlinear Systems of Equations
  60. Solving Nonlinear Systems of Inequalities
  61. Matrices and Determinants
  62. Gauss-Jordan Elimination
  63. Matrix Addition and Subtraction
  64. Scalar Multiplication
  65. Matrix Multiplication
  66. Inverse of a Matrix
  67. Matrix Equations
  68. Determinants Using Laplace Expansion
  69. Determinants Using Triangular Form
  70. Transpose of a Matrix
  71. Adjugate of a Matrix
  72. Inverse Using the Adjugate and Determinant
  73. Cramer’s Rule
  74. Area of a Triangle – Determinants
  75. Collinear Points – Determinants
  76. Writing the Equation of a Line – Determinants
  77. Analytic Geometry
  78. Conic Sections
  79. The Parabola
  80. The Ellipse
  81. The Hyperbola
  82. Sequences
  83. Series
  84. Summation Notation
  85. Arithmetic Sequence
  86. Arithmetic Series
  87. Geometric Sequence
  88. Geometric Series
  89. Combinations
  90. Permutations
  91. Counting Theory
  92. Angles
  93. Acute Angles, Obtuse Angles, Right Angles, Straight Angles
  94. Finding the Complement of an angle
  95. Finding the Supplement of an angle
  96. Degrees, Minutes, and Seconds
  97. Converting Between Decimal Degrees and Degrees, Minutes, and Seconds
  98. Determine if two Angles are Coterminal Angles
  99. Solving for Missing Angles in Similar Triangles
  100. Solving for Missing Sides in Similar Triangles
  101. Solving for Missing Angles with a Transversal Crossing Two Parallel Lines
  102. Finding the Trigonometric Function Values of an Angle
  103. Finding Trigonometric Function Values Given One Value and the Quadrant
  104. Finding Trigonometric Function Values Based on Reciprocal Identities
  105. Finding Trigonometric Function Values Based on Pythagorean Identities
  106. Finding Trigonometric Function Values Based on Quotient Identities
  107. Finding the Six Trigonometric Function Values of an Acute Angle
  108. Writing a Trigonometric Function in Terms of its Cofunction
  109. Solving Trigonometric Equations using Cofunction Identities
  110. Finding Reference Angles
  111. Special Angles as Reference Angles
  112. Finding Angle Measures with Special Angles
  113. Finding Trigonometric Function Values of Non-Acute Angles
  114. Finding Trigonometric Function Values Using a Calculator
  115. Finding Unknown Angle Measures Using Inverse Trigonometric Functions
  116. arcsin, arccos, arctan, arcsec, arccsc, arccot
  117. How to Solve Right Triangles When Two Sides are Known
  118. How to Solve Right Triangles Given an Angle and a Side
  119. How to Solve Word Problems that Involve Angles of Elevation
  120. How to Solve Word Problems that Involve Angles of Depression
  121. Radians
  122. Converting Between Radians and Degrees
  123. Finding Arc Length on a Circle
  124. Finding the Area of a Sector of a Circle
  125. Understanding Trigonometry Using the Unit Circle
  126. Circular Functions
  127. Solving Trigonometry word problems with Linear and Angular Speed