Comprehensive Precalculus: From Functions to Calculus Preparation
Master essential precalculus concepts through a structured, collaborative learning experience. This course covers functions, trigonometry, and analytical geometry, preparing you for success in calculus and advanced mathematics.
What You'll Learn
- Master fundamental concepts of functions and their transformations
- Develop strong understanding of polynomial and rational functions
- Learn exponential and logarithmic functions with real-world applications
- Master trigonometric functions and their applications
- Understand conic sections and parametric equations
AI Mentor Inspiration
Isaac Calculate
Inspired by the mathematical genius of Isaac Newton, Calculate is an AI tutor specializing in precalculus and mathematical analysis, making complex concepts accessible through clear, step-by-step explanations.
Detailed Schedule
Week 1
Functions and Graphs: Understanding Transformations and Inverse Functions
Master the fundamentals of functions, their properties, and graphical representations.
- Topics:
- Function properties and transformations
- Domain and range analysis
- Inverse functions
- Live Session Duration: 90 minutes
- Homework Duration: 180 minutes
- Discussion Points:
- How do transformations affect function graphs?
- What makes a function invertible?
- Real-world applications of function transformations
- Reading Assignments:
- Stewart/Redlin/Watson: Chapters 1-2 (Functions and Graphs)
- Practice problems set on function transformations
- Real-world application cases
- Video Assignments:
- Watch: 'Introduction to Function Transformations'
- Tutorial: 'Finding and Graphing Inverse Functions'
Week 2
Polynomial and Rational Functions: Analysis and Applications
Explore polynomial and rational functions, focusing on their behavior and characteristics.
- Topics:
- Polynomial functions and their zeros
- Rational functions and asymptotes
- Synthetic division
- Live Session Duration: 90 minutes
- Homework Duration: 180 minutes
- Discussion Points:
- How do you determine end behavior of polynomials?
- What are the key steps in finding asymptotes?
- Applications of polynomial and rational functions
- Reading Assignments:
- Sullivan: Chapter 3 (Polynomial and Rational Functions)
- Practice worksheet on synthetic division
- Case studies on real-world applications
- Video Assignments:
- Watch: 'Understanding Polynomial Behavior'
- Tutorial: 'Analyzing Rational Functions'
Week 3
Exponential and Logarithmic Functions: Properties and Real-world Applications
Master exponential and logarithmic functions and their applications.
- Topics:
- Exponential functions and growth
- Logarithmic properties
- Applications in science and finance
- Live Session Duration: 90 minutes
- Homework Duration: 180 minutes
- Discussion Points:
- How are exponential functions used in real life?
- Common applications of logarithms
- Solving exponential and logarithmic equations
- Reading Assignments:
- Demana/Waits/Foley/Kennedy: Chapter 3
- Case studies on compound interest
- Scientific applications of logarithms
- Video Assignments:
- Watch: 'Exponential Growth and Decay'
- Tutorial: 'Solving Logarithmic Equations'
Week 4
Trigonometric Functions: From Unit Circle to Graphs
Understand trigonometric functions and their graphical representations.
- Topics:
- Unit circle and basic trigonometry
- Graphing trigonometric functions
- Trigonometric identities
- Live Session Duration: 90 minutes
- Homework Duration: 180 minutes
- Discussion Points:
- Understanding the unit circle
- Relationships between trigonometric functions
- Applications of periodic functions
- Reading Assignments:
- Stewart/Redlin/Watson: Chapter 5
- Practice problems on trigonometric graphs
- Applications in physics and engineering
- Video Assignments:
- Watch: 'Mastering the Unit Circle'
- Tutorial: 'Graphing Trigonometric Functions'
Student Experiences
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Learning with Cohorts and AI
Learn Better with Cohorts
Working with peers helps solidify mathematical concepts through discussion, explanation, and collaborative problem-solving, creating a supportive learning environment.
AI-Powered Learning
Our AI tutor provides step-by-step problem solutions, identifies patterns in your learning, and offers personalized practice problems tailored to your needs.
Frequently Asked Questions
What is the main focus of the course?
The course focuses on building a strong foundation in precalculus concepts, preparing students for success in calculus and higher mathematics.
What are the prerequisites?
Students should have a solid understanding of algebra and basic geometry. Familiarity with graphing functions is recommended.
How is the course structured?
The course includes weekly live sessions, interactive problem-solving, collaborative group work, and personalized AI tutoring support.
What kind of support is provided?
Students receive support through live sessions, AI tutoring, peer study groups, and access to comprehensive practice materials.
Is there a certificate upon completion?
Yes, students receive a certificate after successfully completing all course requirements and assessments.
Course Details
- 6 weeks
- Cohort-based learning
- Start anytime
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