Calculus: Limits and Analysis
Advanced Math Preparation for College Success
Grade 12 · 1.0 Credit · English Instruction
Calculus: Limits and Analysis is an upper-level mathematics course crafted for students entering college-level STEM studies. It explores limits, derivatives, and key function behaviors in real and theoretical settings.
Throughout the course, students participate in hands-on activities, explore modeling, and analyze graphical behaviors. In particular, they study formal definitions of limits, rates of change, and the foundations of calculus. The course emphasizes conceptual understanding while building real-world skills.
By using graphs, tables, and equations, students deepen their ability to explain change and variation. In the process, they gain the tools needed for success in fields like engineering, economics, and physics.
Grade Level: 12
Credits: 1
Delivery Format: Live Online (1:1 or Small Group)
Duration: Full Academic Year (194 instructional days)
Instructional Language: English
This course introduces key calculus ideas using both visual and symbolic tools. Students work through structured problems and learn to reason about change clearly. For example, they apply limits to real-world questions and develop the logic behind derivatives and integrals.
Along the way, students build strong communication skills in mathematics. They describe how functions behave and why those behaviors matter in real situations. Ultimately, the course equips them for college-level coursework with confidence.
Core Academic Content
Functions and Graphical Behavior
Limits and Continuity
Derivatives and Rules of Differentiation
Applications of Derivatives in Context
Definite and Indefinite Integrals
Fundamental Theorem of Calculus
Curve Sketching and Motion Problems
Instructional Framework
Problem solving guided by inquiry
Focus on key concepts with step-by-step methods
Live sessions include examples and feedback
Aligned with U.S. and international expectations
Designed for advanced and multilingual learners
Required Texts and Resources
Calculus: Early Transcendentals – James Stewart (or equivalent)
Online simulations and guided problem sets
Graphing calculator or graphing software access
Assessment Structure
Step-by-step solution writing
Explaining key ideas with clear logic
Short quizzes and major unit tests
Projects using graphs and modeling
Final portfolio showing all core skills