Grade 12 Calculus Online High School Course
Grade 12 Calculus
Grade 12 Calculus Course Outline (1.0 Credit)
This Grade 12 Calculus course provides a thorough study of differentiation and integration, with a strong focus on real-world applications. Key concepts such as limits and continuity are explored in depth to prepare students for advanced mathematical thinking.
The course emphasizes the importance of mathematics studied to date and builds a solid foundation for future academic success. Upon completion, students may choose to pursue the Advanced Placement (AP) Calculus examination.
Course Overview
This online Grade 12 Calculus course is designed for high school students seeking to strengthen their understanding of advanced mathematical concepts. The course supports independent learning while preparing students for college-level mathematics and standardized assessments.
Course Outline
Introduction & Review
- Welcome to Calculus
- Course Outline
- Course Syllabus
- Completing Math Assessments
- Calculus On The Web
- Review — Stuff You Should Already Know
- Pretest
- Assignment: Calculus Pretest
Limits & Continuity
- An Introduction to Limits & Continuity
- Quiz: Introduction to Limits & Continuity
- Tangent Lines & Rates of Change
- Handout: Tangent Lines & Rates of Change Worksheet
- Assignment: Tangent Lines & Rates of Change
- The Limit
- Handout: The Limit Worksheet
- Assignment: The Limit
- One-Sided Limits
- Handout: One-Sided Limits Worksheet
- Assignment: One-Sided Limits
- Computing Limits
- Handout: Computing Limits Worksheet
- Assignment: Computing Limits
- Infinite Limits
- Handout: Infinite Limits Worksheet
- Assignment: Infinite Limits
- Limits at Infinity
- Handout: Limits at Infinity Worksheet
- Assignment: Limits at Infinity
- Continuity
- Handout: Continuity Worksheet
- Assignment: Continuity
- Additional Resources
- Handout: Limits & Continuity Exam
- Assignment: Limits & Continuity Exam
Derivatives
- Introduction to Derivatives
- Definition & Interpretation of the Derivative
- Handout: Definition & Interpretation of the Derivative Worksheet
- Assignment: Definition & Interpretation of the Derivative
- Differentiation Formulas
- Handout: Differentiation Formulas Worksheet
- Assignment: Differentiation Formulas
- Product & Quotient Rule
- Handout: Product & Quotient Rule Worksheet
- Assignment: Product & Quotient Rule
- Derivatives of Trig Functions
- Handout: Derivatives of Trig Functions Worksheet
- Assignment: Derivatives of Trig Functions
- Derivatives of Exponential & Logarithm Functions
- Handout: Derivatives of Exponential & Logarithm Functions Worksheet
- Assignment: Derivatives of Exponential & Logarithm Functions
- The Chain Rule
- Handout: The Chain Rule Worksheet
- Assignment: The Chain Rule
- Implicit Differentiation
- Handout: Implicit Differentiation Worksheet
- Assignment: Implicit Differentiation
- Related Rates
- Handout: Related Rates Worksheet
- Assignment: Related Rates
- Higher Order Derivatives
- Handout: Higher Order Derivatives Worksheet
- Assignment: Higher Order Derivatives
- Additional Resources
- Handout: Derivatives Exam
- Assignment: Derivatives Exam
Applications of Derivatives
- What’s the Big Deal About Derivatives, Anyway?
- Rates of Change
- Critical Points & Extrema
- Handout: Critical Points & Extrema Worksheet
- Assignment: Critical Points & Extrema
- The Shape of a Graph
- Handout: The Shape of a Graph Worksheet
- Assignment: The Shape of a Graph
- The Mean Value Theorem
- Handout: The Mean Value Theorem Worksheet
- Assignment: The Mean Value Theorem
- Optimization
- Handout: Optimization Worksheet
- Assignment: Optimization
- Linear Approximations
- Handout: Linear Approximations Worksheet
- Assignment: Linear Approximations
- Midtest
- Assignment: Calculus Midtest
- Handout: Applications of Derivatives
- Assignment: Applications of Derivatives
Integrals
- Working Backwards
- Indefinite Integrals
- Handout: Indefinite Integrals Worksheet
- Assignment: Indefinite Integrals
- Computing Indefinite Integrals
- Handout: Computing Indefinite Integrals Worksheet
- Assignment: Computing Indefinite Integrals
- Substitution Rule for Indefinite Integrals
- Handout: Substitution Rule Worksheet
- Assignment: Substitution Rule
- Area Problem
- Handout: Area Problem Worksheet
- Assignment: Area Problem
- Definite Integrals
- Handout: Definite Integrals Worksheetv
- Assignment: Definite Integrals
- Computing Definite Integrals
- Handout: Computing Definite Integrals Worksheet
- Assignment: Computing Definite Integrals
- Substitution Rule for Definite Integrals
- Handout: Substitution Rule for Definite Integrals Worksheet
- Assignment: Substitution Rule for Definite Integrals
- Integration by Parts
- Handout: Integration by Parts Worksheet
- Assignment: Integration by Parts
- Partial Fractions
- Handout: Partial Fractions Worksheet
- Assignment: Partial Fractions
- Improper Integrals
- Handout: Improper Integrals Worksheet
- Assignment: Improper Integrals
- Additional Resources
- Handout: Integrals Exam
- Assignment: Integrals
Applications of Integrals
- What’s the Big Deal About Integrals, Anyway?
- Area Between Curves
- Handout: Area Between Curves Worksheet
- Assignment: Area Between Curves
- Volumes of Solids of Revolution (Part 1)
- Handout: Method of Rings Worksheet
- Assignment: Method of Rings
- Volumes of Solids of Revolution (Part 2)
- Handout: Method of Cylinders Worksheet
- Assignment: Method of Cylinders
- Volume
- Work
- Handout: Work Worksheet
- Assignment: Work
- Assignment: Applications of Integrals
Sequences & Series
- Sequences & Series
- Sequences
- Series: The Basics
- Series: Convergence & Divergence
- Special Series
- Integral Test
- Comparison Test
- Alternating Series Test
- Absolute Convergence
- Ratio & Root Tests
- Strategy for Series
- Estimating the Value of a Series
- Power Series
- Taylor Series
- Additional Resources
- Post-Test
- Assignment: Sequences & Series
Course Survey
- Handout: Course Survey
- Assignment: Course Survey
