- Course type: Self-paced
- Available Lessons: 82
- Average Lesson Length: 8 min
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Watch a preview:chapter 1 / lesson 1Functions: Identification, Notation & Practice Problems
Course SummaryThis College Precalculus Syllabus Resource & Lesson Plans course is a fully developed resource to help you organize and teach precalculus. You can easily adapt the video lessons, transcripts, and quizzes to take full advantage of the comprehensive and engaging material we offer. Make planning your course easier by using our syllabus as a guide.
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Course Practice TestCheck your knowledge of this course with a 50-question practice test.
- Comprehensive test covering all topics
- Detailed video explanations for wrong answers
How It Works
You can use this precalculus course as a template for designing and implementing your course. Here are the key components of the course and how you can use them:
- Chapters - Each chapter covers a unit of precalculus, from function notation to how to use scientific calculators. Use these chapters as mile markers as you map out your course. We recommend planning to spend a week on each chapter, but you can always allocate the chapters according to the length of your specific precalculus course.
- Lessons - Within each chapter are video lessons that further break down topics into bite-sized chunks. These lessons cover single topics like graphing sine and cosine or solving exponential equations. Each one is often appropriate for a single class.
- Key Terms - Within each lesson are key terms. These are emphasized on screen and in the transcript. As you develop your syllabus, these key terms help you focus on the most important learning objectives. For example, the lesson on set notation and inequalities includes key terms like 1-variable inequality, 2-variable inequality, set notation, compound inequality and system of inequalities.
As you work on your precalculus lesson plans, save time by incorporating video lessons from this resource. Here's how:
- Introduce Topics - Your students will be in the right mindset for understanding topics like the three forms of parabolas if you begin class with a short video. It can be a jumping-off point for a lecture, group activity or class discussion.
- Break Up Lectures - The video format, which often includes animation, helps students visualize topics like graphing reflections across axes and defining a zero and negative exponent.
- Assign For Homework - Each lesson in the course, from exponential functions to practice problems in completing the square, can be assigned to your students as homework.
Each video lesson includes a complete transcript. You can utilize these transcripts in several ways:
- Lecture Notes - Do you need a guide as you plan a lecture, such as one on inverse functions or parts of a graph? The transcripts cover each topic in depth, with key terms highlighted for quick reference.
- Student Reading - Perhaps you'd like your students to learn about basic trig identities, but you don't have class time available. Assign the transcript as extra reading.
- Study Tools - When it's time for a unit exam on factoring and graphing quadratic equations, you can point your students to the transcripts on multiplying binomials, factoring quadratic equations, solving quadratics that are not in the standard form, graphing circles and related topics to help them study.
Each video lesson has a corresponding quiz. Here's how to use the quizzes:
- Homework - Assign a quiz to your students as homework. You'll receive an email with the results, which enables you to verify they've completed the assignment and that they've understood the material. Questions cover everything from systems of equations to key facts, like the Pythagorean theorem.
- Tests - You can meld the material in the quizzes into your own student assessments, saving you valuable time. Need a few questions on piecewise functions? There are plenty!
- Discussions - Jump-start a discussion with questions like: What makes logarithms useful?
Below is a sketch of the precalculus syllabus modeled on an 11-week course. This sample can be adapted based on your course schedule. Navigate the chapters and lessons for more detail.
|Week||Unit||Sample of Topics Covered|
|Week 1||Functions||Function notation, how to shift graphs, inverse functions, function operations|
|Week 2||Exponential and Logarithmic Functions||Definition of exponential functions, uses for logarithms, logarithmic properties|
|Week 3||Inequalities||Definition of inequalities, how to graph 1- and 2-variable inequalities|
|Week 4||Foundations and Linear Equations||Types of numbers, fundamentals of graphing, how to write linear equations|
|Week 5||Graphing and Rational Equations||How to graph reflections, rational equations, how to determine the lowest common denominator|
|Week 6||Quadratic Equations||Definition of parabola, definition of function, quadratic equations, the quadratic formula,|
|Week 7||Exponents and Polynomials||Exponent properties, how to graph cubics, quartics, quintics and more, how to add, subtract, multiply and divide polynomials|
|Week 8||Piecewise and Composite Functions||Definition of a piecewise function, how to graph piecewise functions, how to solve equations for different variables|
|Week 9||Geometry and Trigonometry||Approaches to visualizing geometry problems, how to use the Pythagorean theorem to determine distance, sine and cosine|
|Week 10||Using Scientific Calculators||Methods of using scientific calculators with radians, degrees, trigonometry functions and exponentials, how to solve equations with scientific calculators|
|Week 11||Trigonometry||Law of sines, law of cosines, ways to graph sine and cosine, the double angle formula, how to solve trigonometric equations for X|
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