Pre-Calculus Academic Library

First Semester

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Pre-calculus Academic Library (1st Semester)

Pre-calculus Online

Pre-calculus is a full-year, high school honors credit course that is intended for the student who has successfully mastered the core algebraic and conceptual geometric concepts covered in the prerequisite courses: Algebra I, Geometry, and Algebra II.

The course primarily focuses on the skills and methods of analytic geometry and trigonometry while investigating further relationships in functions, probability, number theory, limits, and the introduction of derivatives.

The Math Academic Libraries are not considered as a replacement for the online curriculum, the media presentations, and instruction with daily lessons which must be completed including daily quizzes and unit tests or help from your teacher, but a supplement to the curriculum for additional practice and instruction available 24/7.

Pre-Calculus 2nd Semester

Pre-Calculus Online First Semester

UNIT 1 – RELATIONS AND FUNCTIONS

Course Overview
Ordered-Pair Numbers: Relations
Ordered-Pair Numbers: Functions
- Relations and Functions
- Testing If a Relationship Is a Function
Ordered-Pair Numbers: Rules of Correspondence
Quiz 1: Relations and Functions
Algebra of Functions: Notation
- Evaluating With Function Notation
Algebra of Functions: Arithmetic
Algebra of Functions: Composition
- Function from Composition
- Evaluating Composite Functions Example 1
Algebra of Functions: Inverse
- Introduction to Function Inverses
- Function Inverses Example 2
Quiz 2: Relations and Functions
Test
Alternate Test
Glossary and Credits

UNIT 2 – FUNCTIONS

Linear Functions: Graphs
- X and Y Intercepts
- X and Y Intercepts 2
Linear Functions: Equations
- Linear Equations in Slope Intercept Form
- Equation of a Line 2
- Equations of a Line 3
- Worked example: slope from graph
- Point slope form of a line
Quiz 1: Linear Functions
2nd-Degree Functions: Solutions
- Solving Quadratic Equations by Factoring
- How to Use the Quadratic Formula
Relationships Between Zeros and Coefficients
- Discriminant of Quadratic Equations
- Discriminant for Types of Solutions for a Quadratic
- Parabola Vertex and Axis of Symmetry
- Shifting and Scaling Parabolas
Quadratic Inequalities
- Algebra 2 – Graphing a Quadratic Inequality
- Graphing Quadratic Inequalities in Two Variables
Quiz 2: Second-Degree Functions
Polynomial Functions
- Synthetic Division
- Remainder Theorem and Synthetic Division
- The Factor Theorem
- The Factor Theorem and The Remainder Theorem
Nth-Degree Equations
- Finding all the Zeros of a Polynomial – Example 1
- Finding all the Zeros of a Polynomial – Example 2
- Upper and Lower bound test for polynomials
Solving Polynomial Equations
- Example 4: Applying the Quadratic formula – Quadratic Equations
- Example 5: Using the Quadratic formula – Quadratic equations
Quiz 3: Polynomial Functions
Complex Numbers
- Intro to complex numbers
- Introduction to Complex Numbers
- Rectangular to polar form of complex number | Precalculus|
- Complex Numbers in Polar Form
Operations with Complex Numbers
- Adding Complex Numbers
- Subtracting Complex Numbers
- Multiply Complex Numbers
Conjugates and Polynomial Identities
- Intro to Complex Number Conjugates
- Complex number conjugates
- Dividing Complex Numbers
- Complex Numbers: Graphing and Finding the Modulus
Distant and Midpoint
- Distance & Midpoint of Complex Numbers
Quiz 4: Complex Numbers
Rational Inequalities
- Rational Inequalities: one side is zero
- Rational Inequalities: both sides are not zero
Greatest Integer Function
- Precalculus – The Greatest Integer Function
- Graphing the Greatest Integer or Floor Function
Exponential Function
- Graphing Exponential Functions
Logarithmic Function
- Comparing Exponential and Logarithmic Functions
- Graphing Logarithmic Functions
Function Combinations
- Function Arithmetic – Determine Function Values from a Graph
Quiz 5: Special Functions
Test
Alternate Test
Glossary and Credits

UNIT 3 – TRIGONOMETRIC FUNCTIONS

Definition of the Trigonometric Functions
- Introduction to Trigonometric Functions Using Triangles
- Determining the Sign of Trigonometric Functions. sin, cos,tan, sec, csc, cot
Quiz 1: Trigonometric Functions
Evaluation of Functions
- Trigonometric Functions of Any Angle
Quiz 2: Evaluation of Functions
Angle Location
- Standard Position Angles & Radians Part 1
Quiz 3: Angle Location
Reduction Formulas
- Reference Angle for an Angle, Ex 1 (Using Degrees)
Quiz 4: Reduction Formulas
Quadrantal Angles
- Quadrantal Angles
- Examples with Trigonometric Functions: Even, Odd or Neither, Example 1
Quiz 5: Quadrantal Angles
Special Angles
- Trigonometric Ratios and Special Angles.avi
Quiz 6: Special Angles
Radian Measure
- Radian and Degree Conversion Practice
Quiz 7: Radian Measure
Test
Alternate Test
Glossary and Credits

UNIT 4 – CIRCULAR FUNCTIONS AND THEIR GRAPHS

Circular Functions
- Introduction to the Unit Circle
Quiz 1: Circular Functions
Circular Functions of Special Angles
- Evaluating Trig Functions w/ Unit Circle Degrees & Radians
Quiz 2: Circular Functions of Special Angles
Graphs of Sin and Cos
Quiz 3: Graphs of Sin and Cos
Other Graphs
Quiz 4: Other Graphs
Applications
- Finding Arc Length and Randian Angle Measure
- Relationship Between Angular Velocity and Speed
Parametric Equations
- Parametric Equations
Quiz 5: Applications
Amplitude of Circular Functions
- Graphing Sine and Cosine With Different Coefficients (Amplitude and Period), Ex1
- Example: Amplitude and Period
Quiz 6: Amplitude of Circular Functions
Period of Circular Functions
- Graphing Sine and Cosine With Different Coefficients (Amplitude and Period), Ex 1
- Example: Amplitude and Period
Quiz 7: Period of Circular Functions
Phase Shift of Circular Functions
- Graphing Sine and Cosine with Phase (Horizontal) Shifts, Example 2
Quiz 8: Phase Shift of Circular Functions
Test
Alternate Test

Glossary and Credits

UNIT 5 – IDENTITIES AND FUNCTIONS OF MULTIPLE ANGLES

Reciprocal Relations
- Finding Reciprocal Trig Relations
Quiz 1: Reciprocal Relations
Pythagorean Relations
- Intro to the Pythagorean Trig Identity
- Using the Pythagorean Trig Identity
Quiz 2: Pythagorean Relations
Quotient Relations
- Verifying Trigonometric Identities
Quiz 3: Quotient Relations
Trigonometric Identities
- Verifying Trigonometric Identities: The Fundamental Identities
Quiz 4: Trigonometric Identities
Cosine of the Sum of Two Angles
- Sum and Difference Identities for Sine and Cosine, More Examples #2
Quiz 5: Cosine of the Sum of Two Angles
Additional Sum and Difference Formulas
- Sum and Difference Identities for Sine and Cosine, More Examples #1
- Sum and Difference Trigonometric Identities
Quiz 6: Additional Sum and Difference Formulas
Double- and Half-Angle Formulas
- Double Angle Formula For Cosine Example
- Trig: Double-Angle Formulas
- Pre-calculus – The Half-Angle Identities
- Trig: Half-Angle Formulas
Quiz 7: Double- and Half-Angle Formulas
Identities
- Multiple Angle Identities
Quiz 8: Identities
Trigonometric Equations
- Trigonometry – Solving Trigonometric Equations
- Pre-calculus – Trigonometric Equations that Require Factoring
Quiz 9: Trigonometric Equations
Test
Alternate Test
Glossary and Credits

UNIT 6 – SEMESTER REVIEW AND EXAM

Review
Exam
Alternate Exam—Form A
Alternate Exam—Form B

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Pre-Calculus Academic Library

First Semester

Pre-calculus Online

Pre-Calculus Online First Semester

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