# AP Calculus AB & BC

Age 15-18

## Course Description

AP Calculus is a rigorous high-school level course that is designed to build students’ in-depth understanding of calculus. The course is aligned with College Board standards and is designed to prepare students for the AP Calculus AB or BC exam.

This course is suitable for students who are taking AP Calculus concurrently in school or are studying for the exam independently. We require that students have completed Pre-Calculus / Trigonometry as a prerequisite to this course. Due to the length and rigor of this course, we strongly recommend all students enroll in this course with two classes per week or more.

For students who are taking AP Calculus AB, the course will cover: Limits and Continuity, Differentiation, Applications of Derivatives, Integration and Accumulation of Change, Differential Equations, and Applications of Integrations. For students who are taking AP Calculus BC, this course will also cover Parametric Equations, Polar Coordinates, and Vector-Valued Functions.

Age 15-18

## Prerequisites

Pre-Calculus / Trigonometry A and B

This course typically takes 9 months to complete. This depends on the student's dedication to homework, their previous experience, and the difficulty of course material. Our instructors move at the pace of the student, taking extra time to reinforce concepts as needed. As mentioned above, due to the length and rigor of this course, we strongly recommend all students enroll in this course with two classes per week or more.

• ## Limits and Continuity

APC1 Introduction to Limits

APC2 Calculating Limits

APC3 Continuity

APC4 Limits and Continuity Topic Review

• ## Differentiation

APC5 Introduction to Derivatives

APC6 Derivative Rules

APC7 Derivatives of Trigonometric and Other Functions

APC8 Derivatives of Composite, Implicit, and Inverse Functions

APC9 Differentiation Topic Review

• ## Applications of Derivatives

APC10 Contextual Applications of Differentiation

APC11 Analytical Applications of Differentiation

APC12 A Function and Its Derivatives

APC13 Applications of Derivatives Topic Review

• ## Integration and Accumulation of Change

APC14 Accumulation of Change

APC15 Integrals

APC16 Integration and Accumulation of Change Topic Review

• ## Differential Equations

APC17 Introduction to Differential Equations

APC18 Solutions to Differential Equations

APC19 Differential Equations Topic Review

• ## Applications of Integration

APC20 Interpreting Context for Definite Integrals

APC21 Volumes of Solids Using Integrals

APC22 Applications of Integration Topic Review

• ## Parametric Equations, Polar Coordinates, and Vector-Valued Functions (BC only)

APC23 Parametric Equations, Polar Coordinates, and Vector-Valued Functions (BC only)

APC24 Parametric Equations, Polar Coordinates, and Vector-Valued Functions Topic Review (BC only)

• ## Infinite Sequences and Series (BC only)

APC25 Infinite Series (BC only)

APC26 Infinite Sums and Representing Infinite Series (BC only)

APC27 Infinite Sequences and Series Topic Review (BC only)

My favorite course to teach is AP Calculus. Often with math the problem solving technique shouldn't be the focus but instead the ideas behind the techniques, and that's the beauty of math that I want to share with students. I think this course provides a very fresh look into calculus. While it's built to fit the standards of the AP curriculum and prepare students for the AP test, there are a lot of learning/teaching resources incorporated into the course to make the concepts more intuitive.

#### Joshua R., Juni instructor

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