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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

• Scalar Multiplication

• Matrix Multiplication

• Inverse of a Matrix

• Matrix Equations

• Determinants Using Laplace Expansion

• Determinants Using Triangular Form

• Transpose 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

• 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
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
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