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Calculus 1 – Homeschool

Course Description

The Cool Math Guy Calculus 1 course is a comprehensive, full-year homeschool program that guides students through the foundational concepts of Calculus using clear, concept-driven video instruction. The course begins with a review of precalculus functions and graphs before moving into:

  • Limits and continuity

  • Differentiation techniques, including implicit differentiation and related rates

  • Applications of derivatives (graph analysis, first and second derivative tests, optimization)

  • Introduction to integration, including substitution and numerical methods

  • Differential equations (growth and decay)

This course is ideal for students preparing for AP Calculus AB, though it is not branded as an AP course. Students regularly report strong AP scores after using this program alongside additional AP-specific prep resources.

AP Exam Preparation Note

While this course is not marketed as an official AP program, it is designed to cover all standard Calculus 1 topics taught in AP Calculus AB, and even includes a few advanced topics from Calculus 2.

Cool Math Guy videos are concept-driven, making them highly effective for students aiming to succeed on the AP Calculus exam. Many homeschoolers and AP teachers use this course successfully for AP preparation — we simply recommend supplementing with sample free-response questions and test-taking strategies closer to exam time.

How the Course Works

  1. Students begin each section by watching a video lesson (typically 30–50 minutes).

  2. They then start the textbook assignment and work until the end of their scheduled math time.

  3. On the following day(s), they continue the assignment until it’s complete.

  4. After a few sections or at the end of a chapter, the student completes a practice test, followed the next day by the chapter test.

  5. The cycle repeats until the course is completed.

When Help Is Needed

If students or parents encounter difficulties, support is available through multiple methods:

  1. Re-watch the video lesson.
  2. Review similar examples in the textbook.
  3. Consult the solutions manual for step-by-step guidance.
  4. Submit a question through the Cool Math Guy website. Replies typically arrive within 24 hours.

 

Sample Videos from this Course

Section 2.4 The Chain Rule
Section 3.3 Increasing and Decreasing Functions and the First Derivative Test
Section 4.2 Area
Section 6.2 Differential Equations: Growth and Decay

Table of Contents

  • P.1  Graphs and Models
  • P.2  Linear Models and Rates of Change
  • P.3  Functions and Their Graphs
  • P.4  Fitting Models to Data
  • 1.1  A Preview of Calculus
  • 1.2  Finding Limits Graphically and Numerically
  • 1.3  Evaluating Limits Analytically
  • 1.4  Continuity and One-Sided Limits
  • 1.5  Infinite Limits
  • 2.1  The Derivative and the Tangent Line Problem
  • 2.2  Basic Differentiation Rules and Rates of Change
  • 2.3  The Product and Quotient Rules and Higher-Order Derivatives
  • 2.4  The Chain Rule
  • 2.5  Implicit Differentiation
  • 2.6  Related Rates
  • 3.1  Extrema on an Interval
  • 3.2  Rolle’s Theorem and the Mean Value Theorem
  • 3.3  Increasing and Decreasing Functions and the First Derivative Test
  • 3.4  Concavity and the Second Derivative Test
  • 3.5  Limits at Infinity
  • 3.6  A Summary of Curve Sketching
  • 3.7  Optimization Problems
  • 3.8  Newton’s Method
  • 3.9  Differentials
  • 4.1  Antiderivatives and Indefinite Integration
  • 4.2  Area
  • 4.3  Riemann Sums and Definite Integrals
  • 4.4  The Fundamental Theorem of Calculus
  • 4.5  Integration by Substitution
  • 4.6  Numerical Integration
  • 5.1  The Natural Logarithmic Function: Differentiation
  • 5.2  The Natural Logarithmic Function: Integration
  • 5.3  Inverse Functions
  • 5.4  Exponential Functions: Differentiation and Integration
  • 5.5  Bases Other than e and Applications
  • 5.6  Inverse Trigonometric Functions: Differentiation
  • 5.7  Inverse Trigonometric Functions: Integration
  • 5.8  Hyperbolic Functions
  • 6.1  Slope Fields and Euler’s Method
  • 6.2  Differential Equations: Growth and Decay
  • 6.3  Separation of Variables and the Logistic Equation
  • 6.4  First-Order Linear Differential Equations
  • 7.1  Area of a Region Between Two Curves
      • Area of a Region Between Two Curves
      • Area of a Region Between Intersecting Curves
      • Integration as an Accumulation Process
  • 7.2  Volume: The Disk Method
      • The Disk Method
      • The Washer Method
      • Solids with Known Cross Sections
  • 7.3  Volume: The Shell Method
      • The Shell Method
      • Comparison of Disk and Shell Methods
  • 8.7  Indeterminate Forms and L’Hopital’s Rule
      • Indeterminate Forms
      • L’Hopital’s Rule

Supporting Parents

We understand that questions can come up, especially in the beginning. Personal support is available via text, email, or phone. We’re here to help both parents and students every step of the way.

Course Materials

Textbook Recommendations

Below are the recommended textbook and companion solutions guide for this course. The textbook includes answers to selected problems, while the solutions manual provides detailed, step-by-step explanations—which are especially helpful at this level.

Calculus of a Single Variable, 9th Edition by Larson

Solutions Guide (Recommended):

The textbook includes answers to homework problems in the back. The solutions manual is especially helpful for working through complex problems step-by-step.

 

Practice Tests, Tests, and Answer Keys

All assignments and testing materials are available to subscribers through a password-protected link.

Subscribe and Get Started

Annual Flat Rate: $150 for One Year of Access

Start your Calculus 1 journey today with easy-to-follow instruction, responsive support, and a proven method trusted by homeschool families and educators nationwide.

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