# Online Class: Precalculus 101

no certificate

with CEU Certificate*

## Course Description

Calculus is a mathematical tool that is required in a variety of scientific, technical, and other professional fields. Because it is a higher-level area of math, many people think it is a subject that they can never understand. Unfortunately, such an attitude limits an individual's career choices, particularly in a technology-focused society.

This course, therefore, provides a bridge between algebra and calculus, guiding students through the underlying mathematical concepts needed to understand and appreciate calculus. The course reviews real and complex numbers, functions, and equations and inequalities. It then goes into some detail on specific types of functions, such as polynomials, exponentials, and logarithms. It also provides a derivation of the principles of trigonometry on the basis of simple right-triangle and circle geometry. After reviewing vectors, polar coordinates, and conic sections, the material sets up calculus proper by examining limits as well as sequences and series.

The final lessons of the course use the basic principles of algebra to derive the two key tools of calculus: differentiation (the derivative) and integration (the integral). At the end of this course, students will be prepared to study calculus in greater depth, further investigating and applying derivatives and integrals to solve a variety of math, physics, and other problems.

## Course Requirements

Anyone over the age of 13 is welcome to join this course. However, to understand these concepts and successfully complete this course, it is strongly recommended that individuals have obtained a ninth grade education and already have a solid understanding of Algebra.

## Course Topics

Real and complex numbers

Functions I

Functions II

Equations and Inequalities

Polynomials and rational functions I

Polynomials and rational functions II

Exponential/logarithmic functions

Trigonometric functions I

Trigonometric functions II

Trigonometric functions III

Vectors I

Vectors II

Polar coordinates

Conic sections I

Conic sections II

Limits

Sequences and series

Introduction to derivatives

Introduction to integrals

## Course Materials

## Grading Policy

A brief 10 pt. quiz will follow each lesson. Students will successfully complete this course by mastering all learning outcomes with 70% or higher overall grade.

## Learning Outcomes

- Define, identify and demonstrate use of real and complex numbers.
- Define, identify and demonstrate use of functions.
- Define, identify and demonstrate use of equations and inequalities.
- Define, identify and demonstrate use of polynomials and rational functions.
- Define, identify and demonstrate use of exponential and logarithmic functions.
- Define, identify and demonstrate use of trigonometric functions.
- Define, identify and demonstrate use of vectors.
- Define, identify and demonstrate use of polar coordinates.
- Define, identify and demonstrate use of conic sections.
- Define, identify and demonstrate use of limits, sequences, and series.
- Define, identify and demonstrate use of derivatives and integrals, and
- Demonstrate mastery of lesson content at levels of 70% or higher.

## Assessment Guide

Assessment | Points |
---|---|

Introduction | 1 |

Lesson 1 Exam | 20 |

Lesson 2 Exam | 20 |

Lesson 3 Exam | 20 |

Lesson 4 Exam | 20 |

Lesson 5 Exam | 20 |

Lesson 6 Exam | 20 |

Lesson 7 Exam | 20 |

Lesson 8 Exam | 20 |

Lesson 9 Exam | 20 |

Lesson 10 Exam | 20 |

Lesson 11 Exam | 20 |

Lesson 12 Exam | 20 |

Lesson 13 Exam | 20 |

Lesson 14 Exam | 20 |

Lesson 15 Exam | 20 |

Lesson 16 Exam | 20 |

Lesson 17 Exam | 20 |

Lesson 18 Exam | 20 |

Lesson 19 Exam | 20 |

The Final Exam | 80 |

Total Points: | 461 |

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