## Syllabus

Certainly, here’s a sample high school Calculus 1 syllabus. Please note that this is a general example, and you may need to adapt it to meet the specific requirements and standards of your school or district:

**Course Title: Calculus 1 (High School Level)**

**Course Description:** Calculus 1 is an introductory calculus course designed to provide students with a foundational understanding of differential calculus. This course covers topics such as limits, derivatives, and their applications in real-world scenarios.

**Course Objectives:** By the end of this course, students should be able to:

- Understand the concept of limits and apply them to functions.
- Calculate derivatives and determine their geometric interpretations.
- Solve problems involving rates of change and optimization.
- Analyze and graph functions and their derivatives.
- Apply calculus concepts to real-world situations.

**Textbook:**

- [Insert Calculus 1 Textbook Title and Author(s)]

**Materials:**

- Notebook or binder for class notes and assignments.
- Graphing calculator (if required by the school or teacher).
- Pencils, erasers, and a ruler.

**Grading:**

- Homework/Classwork: XX%
- Quizzes: XX%
- Tests: XX%
- Projects: XX%
- Final Exam: XX%

**Course Outline:**

**Unit 1: Introduction to Calculus**

- Historical background of calculus.
- Understanding the concept of a limit.
- Evaluating limits analytically and graphically.

**Unit 2: Derivatives and Their Properties**

- Definition of a derivative.
- Calculation of derivatives using various techniques.
- Derivative rules (power rule, product rule, quotient rule).

**Unit 3: Applications of Derivatives**

- Rates of change and related rates.
- Local and global extrema.
- Optimization problems.

**Unit 4: Graphs and Analysis of Functions**

- Understanding the behavior of functions using derivatives.
- Concavity and inflection points.
- Curve sketching and applications.

**Unit 5: The Fundamental Theorem of Calculus**

- Introduction to the definite integral.
- Fundamental Theorem of Calculus Part I and Part II.
- Area under curves and interpretation of the integral.

**Unit 6: Review and Final Exam Preparation**

**Note:** This is a general example of a high school Calculus 1 syllabus. It’s important to adapt it to meet the specific needs and standards of your school or district. The percentages for grading, the textbook, and materials may vary. Additionally, consult with your school’s curriculum guidelines and any state or district standards that may apply.

## Free Textbook

Finding completely free high school-level Calculus 1 textbooks can be challenging, as calculus is often taught at the college level. However, there are open educational resources (OER) and free online resources that can help you study high school-level calculus. Here are some options:

**OpenStax Calculus Volume 1**:- OpenStax offers a free calculus textbook designed for college students, but it covers topics that are typically taught in high school Calculus 1 as well.
- Website: https://openstax.org/details/books/calculus-volume-1

**Paul’s Online Math Notes – Calculus I**:- Paul’s Online Math Notes provides free notes and tutorials on Calculus I topics. While it’s not a traditional textbook, it’s a valuable resource for learning and understanding calculus concepts.
- Website: http://tutorial.math.lamar.edu/Classes/CalcI/CalcI.aspx

**MIT OpenCourseWare (OCW)**:- MIT OCW offers free access to course materials from Massachusetts Institute of Technology (MIT) courses, including calculus. You can find lecture notes, assignments, and exams that cover high school-level calculus topics.
- Website: https://ocw.mit.edu/index.htm

**Khan Academy**:- Khan Academy provides a comprehensive set of free math courses, including calculus. While it’s not a traditional textbook, it offers video lessons, practice exercises, and assessments that cover high school-level calculus.
- Website: https://www.khanacademy.org/math/calculus-1

**Textbook Revolution**:- Textbook Revolution is a resource dedicated to the free distribution of textbooks and educational materials. You can search for free calculus textbooks and related resources.
- Website: http://textbookrevolution.org/

While these resources may not be labeled specifically as “high school Calculus 1,” they cover the relevant topics and can be used for high school-level calculus studies. Additionally, please be aware that high school calculus courses may vary in depth and content from one school or district to another, so it’s essential to align your studies with your specific curriculum.

## MOOCs

As of my last knowledge update in January 2022, several Massive Open Online Course (MOOC) platforms offer free Calculus 1 courses. These courses are typically designed for college-level calculus, but they cover the topics that are often taught in high school Calculus 1 as well. Please keep in mind that course offerings on MOOC platforms can change, so it’s a good idea to check the current course listings. Here are some MOOC platforms where you can often find free Calculus 1 courses:

**Coursera**:- Coursera offers free courses in calculus, including Calculus 1. Some courses provide free access to course materials, with the option to pay for a certificate.
- Website: https://www.coursera.org/

**edX**:- edX provides free Calculus 1 courses from universities and institutions. Similar to Coursera, you may have the option to audit courses for free or pay for a verified certificate.
- Website: https://www.edx.org/

**MIT OpenCourseWare (OCW)**:- MIT OCW offers free access to course materials from Massachusetts Institute of Technology (MIT) courses, including calculus courses. You can find lecture notes, assignments, and exams for Calculus 1.
- Website: https://ocw.mit.edu/index.htm

**Khan Academy**:- Khan Academy offers a comprehensive set of free math courses, including calculus. While it may not be a traditional MOOC, it provides video lessons, practice exercises, and assessments covering Calculus 1 topics.
- Website: https://www.khanacademy.org/math/calculus-1

**Harvard Online Courses (HarvardX)**:- Harvard University offers free calculus courses through their HarvardX program on edX, including Calculus 1 content.
- Website: https://online-learning.harvard.edu/catalog?keywords=calculus

**FutureLearn**:- FutureLearn offers free math courses that include calculus topics. Some courses provide free access to content, while certificates may be available for a fee.
- Website: https://www.futurelearn.com/subjects/mathematics-and-stats-courses/calculus

These platforms offer courses that cover calculus concepts, including limits, derivatives, and integrals, which are typically part of Calculus 1. Be sure to explore the course descriptions to find the specific content you’re interested in, and choose the one that aligns best with your learning objectives and needs.