Making waves in STEM

Precalculus, Semester B

  • Date created

    June 30, 2020

  • Last updated

    June 1, 2021

Enroll in Precalculus with Dolphin STEM Academy

Course Overview

Precalculus encompasses the rudiments of calculus, analytical geometry, and
trigonometry. In Precalculus B, you will explore and build your knowledge of conic
sections, matrices, sequences, induction, and probability and apply this knowledge to
real-world situations. You will also study basic concepts of calculus, such as the limits of
a function and area under the curve.

Course Goals

This course will help you meet these goals:
Understand the conic section while exploring parabolas, ellipses, hyperbolas, and circles and their graphs.
Use Cavalieri’s principle to derive formulas for spheres, cylinders, and other solid figures.
Solve systems of linear equations with two or three variables using Gauss-Jordan elimination.
Identify and perform addition, subtraction, and multiplication on matrices.
Compute the determinant of a matrix.
Solve systems of linear equations using an inverse matrix.
Use matrices to transform vectors in a plane.
Calculate the expected value of a random variable and interpret it as the mean of the probability distribution.
Develop a probability distribution for a random variable defined for a sample space in which
you can calculate probabilities empirically or theoretically and find the expected value.
Weigh the possible outcomes of a decision by assigning probabilities to payoff values and
finding expected values.
Explore limits and techniques used to find the limit of a function.
Explore tangent lines and area under curves.

General Skills

To participate in this course, you should be able to do the following:

Complete basic operations with word-processing software, such as Microsoft Word or
Google Docs.
Perform online research using various search engines and library databases.
Communicate through email and participate in discussion boards.

For a complete list of general skills that are required for participation in online courses,
refer to the Prerequisites section of the Plato Student Orientation document, found at
the beginning of this course.

Credit Value

Precalculus B is a 0.5-credit course.

Course Materials

Notebook
Computer with Internet connection and speakers or headphones
Microsoft Word or equivalent
Microsoft Excel or equivalent

Course Pacing Guide

This course description and pacing guide is intended to help you stay on schedule with
your work. Note that your course instructor may modify the schedule to meet the
specific needs of your class.

Unit 1: Conic Sections

Summary

This unit introduces you to conic sections. You will explore ellipses and parabolas
and their graphs. Using Cavalieri’s principle, you will derive the formulas to find the
volume of a sphere and other solid figures.

Unit 2: Matrices

Summary

In this unit, you will focus on matrices and operations on matrices. You will use
Gauss-Jordan elimination to solve linear equations with two or three variables.
You will add, subtract, and multiply matrices and find the determinant of a matrix.
At the end of the unit, you will use matrices to represent vectors in a plane.

Unit 3: Sequences, Induction, and Probability

Summary

In this unit, you will calculate expected values and make predictions based on
theoretically and empirically calculated probability.

Unit 4: Limits: Introduction to Calculus

Summary

This unit introduces you to calculus. You will define and find the limit of a function.
Additionally, you will explore tangent lines and the areas under curves and solve
problems about them.

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Laurie, mom of Christopher

We are super proud of him and appreciate your support! Christopher has had some great positive things to say. It’s really cool that he is connecting with kids and teachers from all over – a great “virtual” way to open up his world and perspective. 

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Erin, mom of a 5th grader

This is our 1st year homeschooling and we are so glad that we chose Dolphin STEM Academy

Thank you for always being here for me!

Big thanks to Mrs Debbie for all the support and encouragement!

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Mirabel from Malaysia

Thank you for always being here for me! Big thanks to Mrs Debbie for all the support and encouragement! Mirabel from Malaysia Dolphin STEM Academy 5 2021-06-15T15:36:43+00:00 Mirabel from Malaysia Big thanks to Mrs Debbie for all the support and encouragement! https://dolphinstemacademy.com/testimonials/thank-you-for-always-being-here-for-me/

I believe his confidence in himself has grown!

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Keenna H.

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Keenna H.

I believe his confidence in himself has grown! Mrs. Debbie and her team have been awesome through this entire school year and I appreciate your support and patience with me! Keenna H. Dolphin STEM Academy 5 2021-06-18T01:33:46+00:00 Keenna H. Mrs. Debbie and her team have 
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Dolphin STEM

Inspiring passions in STEM.  Educating a new generation.
Dolphin STEM Academy
2017-03-13T11:54:16+00:00
Dolphin STEM Inspiring passions in STEM.  Educating a new generation. Dolphin STEM Academy 2017-03-13T11:54:16+00:00 Inspiring passions in STEM.  Educating a new generation. https://dolphinstemacademy.com/testimonials/testimonials/
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