Homeschool Highschool Math (and Physics)

Algebra 1, Geometry, Algebra 2/Trigonometry, Precalculus, Calculus, Physics

All courses are now available for immediate digital download.

The Math Without Borders, Inc. Home Study Companion series provides a complete high school math experience for homeschoolers by supplementing the best classic high school math textbooks (Foerster for the algebra sequence and Chakerian, Crabill, and Stein, for geometry) with solid teaching by an experienced teacher.


New: Free HSC Sampler Pack download with the complete first chapter of each course.
Now you can judge the quality of instruction for yourself before committing to buy.


Coming in Fall 2020: A completely new high school physics course!
See sample video lessons below.



NewSampleLessons-648x70Home Study Companion: Algebra 1

Companion to Algebra 1: Expressions, Equations, and Applications, by Paul A. Foerster

Whiteboard video lessons covering the “classroom presentation” portion of a full high school Algebra 1 course based on Algebra 1: Expressions, Equations, and Applications by Paul Foerster. Also includes a video solution guide for the recommended assignment for each lesson.

Review by mathmammoth.com

Chapter 3-1: Distributing

Chapter 7-9: Solving Systems by Linear Combinations

Purchase HSC Algebra 1


Home Study Companion: Geometry

Companion to Geometry-A Guided Inquiry, by G. D. Chakerian, Calvin D. Crabill, and Sherman K. Stein

Solution manual, with commentary, extensions, and nearly 300 dynamic demonstrations using GeoGebra software designed to accompany the exceptional text, Geometry: A Guided Inquiry, by G.D. Chakerian, Calvin D. Crabill, and Sherman K. Stein. Includes a complete video introduction and video solution guide to the Review section of each chapter.

Review by mathmammoth.com

Chapter 6 Introduction

Chapter 12 Introduction

Purchase HSC Geometry


Home Study Companion: Algebra 2 with Trigonometry

Companion to Algebra and Trigonometry: Functions and Applications, by Paul A. Foerster

Whiteboard video lessons covering the “classroom presentation” portion of a full high school Algebra 2 course based on Algebra and Trigonometry: Functions and Applications by Paul Foerster. Also includes a video solution guide for the recommended assignment for each lesson.

Chapter 6-8: Exponential Equations Solved by Logarithms

Chapter 9-3: Ellipses

Purchase HSC Algebra 2 / Trigonometry

(Here and here are two more Algebra 2 videos (from chapter 4) demonstrating how to use a spreadsheet to solve systems of 3 (or 5) equations for 3 (or 5) unknowns. The same method can be applied to problems requiring even more variables. Solving large systems of equations is common in circuit analysis in electronics. Educationally, learning how to program the solutions is an excellent way to learn the solution methods while not becoming overwhelmed by busywork. When you’re done, you also have a tool you can save and use later.


Home Study Companion: Precalculus

Companion to Precalculus with Trigonometry: Concepts and Applications, by Paul A. Foerster

Whiteboard video lessons covering the “classroom presentation” portion of a full high school Precalculus course based on Precalculus with Trigonometry: Concepts and Applications by Paul Foerster. Also includes a video solution guide for the recommended assignment for each lesson.

Chapter 13-6: Fractal Dimensions

Chapter 16-1: Introduction to Calculus

Purchase HSC Precalculus


Home Study Companion: Calculus

Companion to Calculus Concepts and Applications, by Paul A. Foerster

Whiteboard video lessons covering the “classroom presentation” portion of a full year Calculus course based on Calculus: Concepts and Applications by Paul Foerster. Also includes a video solution guide for the recommended assignment for each lesson.

Chapter 5-03: Formal Definition of Antiderivative and Indefinite Integral

Purchase HSC Calculus


Home Study Companion: Physics

(Partial download available now / Remaining units can be downloaded as they are released)

Math Without Borders is introducing a complete high school level non-calculus physics course to be released sometime in late spring, or early summer 2020.  The new course will include video lectures, problem solving demonstrations, and physics labs (structured as “projects”). The course will make use of data gathering and analysis tools, such as PocketLab sensors, video analysis using Tracker, data analysis with spreadsheets, graphical analysis with GeoGebra, and the HP scientific calculator simulator (for phones and computer) Free42.

Chap 6: Work and Energy–Conceptual Introduction


(About the Math Without Borders, Inc., “Golden Logo”)


The challenge facing homeschool students and adults studying mathematics at home is that mathematics textbooks are not designed to be used alone. A lot goes on in a good math class besides reading the text and doing problem sets. Textbooks are designed to be taught by an experienced teacher. A good teacher should be able to:

  • give an overview of the subject to “put the text in context.”
  • model the thinking skills and strategies that go into analysis and problem solving.
  • illustrate, demonstrate, and clarify (as well as prove) the underlying concepts.
  • point out links between different parts of the subject and applications beyond what is in the text.

Rather than start from scratch with yet another textbook, I decided to start with the best existing textbooks (selected based on 35 years of teaching experience) and provide the kinds of additional support for home study students that a good teacher would provide in a classroom.


I am frequently asked about testing and assessment issues. Here is an essay I published in Homeschool Magazine on that subject: Assessment and Grading for Homeschoolers.
For an online “crowd-sourced” solution guide to these and many other textbooks, see Slader.com.