## Course Syllabus for "K12MATH013: Calculus AB"

Calculus AB is primarily concerned with developing your understanding of the concepts of calculus and providing you with its methods and applications. The course emphasizes a multi-representational approach to calculus, with concepts, results, and problems being expressed graphically, numerically, analytically, and verbally. Broad concepts and widely applicable methods are also emphasized. The focus of the course is neither manipulation nor memorization of an extensive taxonomy of functions, curves, theorems, or problem types, but rather, the course uses the unifying themes of derivatives, integrals, limits, approximation, and applications and modeling to become a cohesive whole. The course is a yearlong high school mathematics course designed to prepare you to write and pass the AP Calculus AB test in May. Passing the test can result in one semester of college credit in mathematics.

### Learning Outcomes

Upon successful completion of this course, you will be able to:

- Work with and understand the connections among functions represented in four major ways: graphically, numerically, analytically, or verbally.
- Understand the meaning of the derivative in terms of a rate of change and local linear approximation and be able to use derivatives to solve a variety of problems.
- Understand the meaning of the definite integral both as a limit of Riemann sums and as the net accumulation of change and be able to use integrals to solve a variety of problems.
- Understand the relationship between the derivative and the definite integral as expressed in both parts of the Fundamental Theorem of Calculus.
- Communicate mathematics and explain solutions to problems both verbally and in written sentences.
- Model a written description of a physical situation with a function, a differential equation, an integral, or with a graph.
- Use technology to help solve problems, experiment, interpret results, and support conclusions.

### Course Requirements

In order to take this course, you must:

√ Have access to a computer.

√ Have continuous broadband Internet access.

√ Have the ability/permission to install plug-ins or software (e.g., Adobe Reader or Flash).

√ Have the ability to download and save files and documents to a computer.

√ Have the ability to open Microsoft files and documents (.doc, .ppt, .xls, etc.)

√ Have competency in the English language.

√ Have read the Saylor Student Handbook.

√ Have completed a K12 Precalculus course or its equivalent.

√ Have access to a TI-84 graphic calculator or equivalent or use one
of the following downloads:

○ Desmos

○
Microsoft

○
HRW

○
iTunes

○ Quick Graph: Your Scientific Graphing
Calculator (iOS)

○ Algeo Graphing
Calculator (Android)

### Course Information

Welcome to Calculus AB. Below, please find general information on this
course and its requirements.

**Course Designer:** Mr. Eric
Clark

**Primary Resources:** This course is comprised of a range of different
free, online materials. However, the course makes primary use of the
following:

- Khan Academy
- CK-12 Many of the CK-12 resources you will come across in this course can also be accessed on the free iOS app. For those students using mobile devices, this app can be a great supplementary tool.
- North Carolina School of Science and Mathematics
- CK-12: Texas Instruments Calculus—Student Edition. This is a graphing calculator resource that contains directions for various graphing calculator activities related to calculus.

**Requirements for Completion:**

In order to complete this course, you will need to work through each
unit and all of its assigned materials. You will also need to complete
the final exam.

Please note that you will only receive an official grade on your final
exam. However, in order to adequately prepare for this exam, you will
need to work through all of the resources in each unit.

In order to pass this course, you will need to earn a 70% or higher on
the final exam. Your score on the exam will be tabulated as soon as you
complete it. If you do not pass the exam, you may take it again.

**Time Commitment: **This course should take you a total of
approximately **131 hours** to complete. Each unit includes a “time
advisory” that lists the amount of time you are expected to spend on
each subunit. It may be useful to take a look at these time advisories
and determine how much time you have over the next few weeks to complete
each unit and then set goals for yourself. For example, unit 1 should
take approximately 15.5 hours to complete. Perhaps you can sit down with
your calendar and decide to complete subunit 1.1 (a total of 4.5 hours)
on Monday and Tuesday nights; subunit 1.2 (a total of 7.5 hours) on
Wednesday, Thursday, and Friday nights, and so forth.