Course Description : Grade 11-12 ( Calculus )

 

Course Objective: Calculus is designed to give students an overview of Calculus topics such as limits and continuity, derivatives, anti-derivatives, integrals and differential equations. While this course covers many of the same concepts found in Advanced Placement Calculus, it is not bound by the pace and rigor necessary for success on the AP Calculus exam. Therefore, this course best suits the student who is mathematically ready to learn Calculus but does not want the “stress” of AP Calculus. Students have the option of taking the AP Calculus exam after completing this course.

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• College-Level Calculus Without Unnecessary Pressure — Students can learn rigorous Calculus without being forced into the pace and stress of an AP classroom.

• Complete Calculus Curriculum — Limits, derivatives, applications, integrals, differential equations, and advanced integration techniques.

• Small Classes for Difficult Concepts — 3–6 students means more opportunities to ask questions and work through challenging problems with an instructor.

• Prepare for College STEM — Build a foundation for Engineering, Computer Science, Physics, Mathematics, Economics, and other quantitative majors.

• Optional AP Calculus Pathway — Students who are ready can transition into focused AP preparation with exam-style questions, FRQs, timed practice, and mock exams.​

 

Materials:

• Student textbook

• Practice and enrichment worksheets

• Manipulative materials

• Calculators

 

Time Allotment:

• 45 minutes per day, 2 days per week

 

Course Content:

 

1. Functions, Limits, Continuity

2. Derivatives

3. Applications of Derivatives

4. Integration

5. Applications of Definite Integrals

6. Transcendental Functions

7. Integration Techniques

 

The instructor reserves the right to modify this syllabus for the needs of the class.

Course Outline

Chapter 1 — Functions, Graphs, Limits and Continuity

• 1.0 Slopes & Velocities

• 1.1 Limit of a Function

• 1.2 Limit Properties

• 1.3 Continuous Functions

• 1.4 Formal Definition of Limit

 

Chapter 2 — The Derivative

• 2.0 Slope of a Tangent Line

• 2.1 Definition of Derivative

• 2.2 Differentiation Formulas

• 2.3 More Differentiation Patterns

• 2.4 Chain Rule (!!!)

• 2.5 Using the Chain Rule

• 2.6 Related Rates

• 2.7 Newton’s Method

• 2.8 Linear Approximation

• 2.9 Implicit Differentiation

 

Chapter 3 — Derivatives and Graphs

• 3.1 Introduction to Maximums & Minimums

• 3.2 Mean Value Theorem

• 3.3 f’ and the Shape of f

• 3.4 f” and the Shape of f

• 3.5 Applied Maximums & Minimums

• 3.6 Asymptotes

• 3.7 L’Hospital’s Rule

 

Chapter 4 — The Integral

• 4.0 Introduction to Integrals

• 4.1 Sigma Notation & Riemann Sums

• 4.2 The Definite Integral

• 4.3 Properties of the Definite Integral

• 4.4 Areas, Integrals and Antiderivatives

• 4.5 The Fundamental Theorem of Calculus

• 4.6 Finding Antiderivatives

• 4.7 First Applications of Definite Integrals

• 4.8 Using Tables to Find Antiderivatives

• 4.9 Approximating Definite Integrals​