About This Chapter
Who's it for?
This unit of our High School Precalculus Homeschool course will benefit any student who is trying to learn about the fundamentals of geometry for precalculus. There is no faster or easier way to learn about precalculus. Among those who would benefit are:
- Students who require an efficient, self-paced course of study to learn to complete the square by writing standard-form equations.
- Homeschool parents looking to spend less time preparing lessons and more time teaching.
- Homeschool parents who need a precalculus curriculum that appeals to multiple learning types (visual or auditory).
- Gifted students and students with learning differences.
How it works:
- Students watch a short, fun video lesson that covers a specific unit topic.
- Students and parents can refer to the video transcripts to reinforce learning.
- Short quizzes and a Geometry Basics unit exam confirm understanding or identify any topics that require review.
Geometry Basics Unit Objectives:
- Learn about the area and circumference of circles.
- Discover how to use the distance formula.
- Learn to graph circles and identify the radius, formula and center.
- Calculate the volume of pyramids and spheres.
- Study trigonometry and the Pythagorean Theorem.
1. Circles: Area and Circumference
Understanding how to calculate the area and circumference of circles plays a vital role in some of our everyday functions. They serve as the foundation for operating with three-dimensional figures. Learn more about the area and circumference of circles in this lesson.
2. Graphing Circles: Identifying the Formula, Center and Radius
Discover how to graph circles by finding key information like the center and radius. Identify circles by simply looking at the formula, and vice versa.
3. Write the Standard Form of an Equation by Completing the Square
In math, we have a process called completing the square where you take your quadratic equation and rewrite it to make it easier to solve. Watch this video lesson to learn how you can do this process easily yourself.
4. How to Use The Distance Formula
You can't always rely on your smartphone to tell you how far you need to travel to get from point A to point B. The distance formula will tell you the distance between any two points on a graph. In this lesson, you'll learn where it comes from and how to use it!
5. How to Use The Midpoint Formula
The formula for the midpoint of a line segment will tell you how to find the middle of any line segment on the x, y plane. Learn about this formula and see how it is used to find the midpoint of a line segment.
6. How to Solve Visualizing Geometry Problems
A picture is worth a thousand words, but sometimes drawing that picture can be like doing origami with your eyes closed. Practice translating complex problems into simple, meaningful images in this lesson.
7. How to Calculate the Volumes of Basic Shapes
Squares pegs = square holes. Triangular pegs = triangular holes. But where does a sphere go? In this lesson, review volumes of common shapes while contrasting a sphere and a cylinder - after all, they both go into the circular hole... right?
8. Finding Distance with the Pythagorean Theorem
How much faster is it to cut the corners in a race around the block? In this lesson, review the Pythagorean Theorem, and figure out how to solve without a right triangle.
9. Trigonometry and the Pythagorean Theorem
Explore how the Pythagorean Theorem can be used in conjunction with trigonometric functions. In this lesson, take an inverse trigonometric function, and define all three sides of a right triangle.
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Other chapters within the High School Precalculus: Homeschool Curriculum course
- Graphing Linear Equations: Homeschool Curriculum
- Solving & Graphing Inequalities: Homeschool Curriculum
- Absolute Value Expressions: Homeschool Curriculum
- Graphing Complex Numbers: Homeschool Curriculum
- Solving Linear Systems: Homeschool Curriculum
- Linear Models: Homeschool Curriculum
- Quadratics: Homeschool Curriculum
- Quadratic Functions & Equations: Homeschool Curriculum
- Functions for Precalculus: Homeschool Curriculum
- Using Function Operations: Homeschool Curriculum
- Recognizing Graph Symmetry: Homeschool Curriculum
- How to Graph Functions: Homeschool Curriculum
- Rate of Change: Homeschool Curriculum
- Polynomial Functions: Homeschool Curriculum
- Higher-Degree Polynomials: Homeschool Curriculum
- Difference Quotients in Precalculus: Homeschool Curriculum
- Working with Rational Expressions: Homeschool Curriculum
- Evaluating Logarithmic Functions: Homeschool Curriculum
- Functions in Trigonometry: Homeschool Curriculum
- Using Trigonometric Graphs: Homeschool Curriculum
- Trigonometric Equations: Homeschool Curriculum
- Basic Trigonometric Identities: Homeschool Curriculum
- Laws of Sine & Cosine: Homeschool Curriculum
- Graphing Piecewise Functions: Homeschool Curriculum
- Vectors & Matrices: Homeschool Curriculum
- Mathematical Sequences: Homeschool Curriculum
- Identifying Conic Sections: Homeschool Curriculum
- Parametric Equations: Homeschool Curriculum
- Continuity: Homeschool Curriculum
- Limits in Precalculus: Homeschool Curriculum
- Groups & Sets in Algebra: Homeschool Curriculum