MATH 180 – Honors Pre-Calculus

Syllabus

Course Title: Honors Precalculus

Course Description: Honors Precalculus is an advanced mathematics course designed to prepare students for the study of calculus. This course covers a wide range of topics, including advanced functions, trigonometry, and mathematical concepts needed for calculus. It is intended for highly motivated students who have a strong foundation in algebra and geometry.

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

  1. Understand and work with advanced functions, including polynomial, rational, exponential, and logarithmic functions.
  2. Master trigonometric functions, identities, and their applications.
  3. Solve complex equations and inequalities.
  4. Analyze and graph functions and their transformations.
  5. Develop proficiency in problem-solving and critical thinking.
  6. Apply mathematical concepts to real-world situations.

Textbook:

  • [Insert Honors Precalculus 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.
  • Access to online resources (if applicable).

Grading:

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

Course Outline:

Unit 1: Advanced Functions

  • Polynomial and rational functions.
  • Exponential and logarithmic functions.
  • Analyzing and graphing functions.

Unit 2: Trigonometry

  • Trigonometric functions and their properties.
  • Trigonometric identities.
  • Solving trigonometric equations and applications.

Unit 3: Complex Numbers

  • Introduction to complex numbers.
  • Operations with complex numbers.
  • Complex numbers in trigonometry.

Unit 4: Systems of Equations and Inequalities

  • Solving systems of equations and inequalities.
  • Matrices and determinants.

Unit 5: Conic Sections

  • Introduction to conic sections (circles, ellipses, hyperbolas, parabolas).
  • Graphing and analyzing conic sections.

Unit 6: Review and Final Exam Preparation

Note: This is a general example of a high school Honors Precalculus 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 Textbooks

Finding free textbooks for Honors Precalculus can be challenging because Honors-level courses often have specific requirements and standards. However, you can explore Open Educational Resources (OER) and online resources that may offer relevant content for your Honors Precalculus studies. While these resources may not be comprehensive textbooks, they can supplement your learning. Here are some places to look for free Honors Precalculus materials:

  1. OpenStax Precalculus:
  2. Khan Academy:
    • Khan Academy offers a comprehensive set of free math courses, including Precalculus. While it may not be a traditional textbook, the video lessons, practice exercises, and explanations can serve as valuable resources.
    • Website: https://www.khanacademy.org/math/precalculus
  3. Paul’s Online Math Notes – Precalculus:
  4. Purplemath:
  5. MIT OpenCourseWare (OCW):
    • MIT OCW provides free access to course materials from Massachusetts Institute of Technology (MIT) courses, including Precalculus and related topics.
    • Website: https://ocw.mit.edu/index.htm
  6. Textbook Revolution:
    • Textbook Revolution is a resource dedicated to the free distribution of textbooks and educational materials. While it may not have a specific Honors Precalculus textbook, it’s worth searching for relevant resources.
    • Website: http://textbookrevolution.org/

While these resources may not be labeled as “Honors Precalculus,” they often cover the same content that you would encounter in an Honors-level Precalculus course. Additionally, consider consulting your teacher or school for any recommended online resources or supplementary materials that align with your specific Honors Precalculus curriculum.

MOOCs


As of my last knowledge update in January 2022, several Massive Open Online Course (MOOC) platforms offer free courses that cover Precalculus topics. These courses can help you build a strong foundation in mathematics before moving on to more advanced courses like calculus. Please note that course availability and offerings may change over time, so it’s a good idea to check the current course listings on these platforms. Here are some MOOC platforms where you can often find free Precalculus courses:

  1. Khan Academy:
  2. Coursera:
    • Coursera offers free courses in precalculus and related math topics, provided by universities and institutions. Some courses offer free access to course materials, with an option to pay for a certificate.
    • Website: https://www.coursera.org/
  3. edX:
    • edX provides free precalculus 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/
  4. MIT OpenCourseWare (OCW):
    • MIT OCW provides free access to course materials from Massachusetts Institute of Technology (MIT) courses, including Precalculus.
    • Website: https://ocw.mit.edu/index.htm
  5. Harvard Online Courses (HarvardX):
  6. FutureLearn:

These platforms offer a variety of Precalculus courses that cover topics like functions, trigonometry, algebra, and more. 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.

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