Course Syllabus

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Syllabus AP Calculus AB Semester 1

Welcome

Welcome to AP Calculus AB Semester 1! We’re so glad you’re here!

Every lesson is designed to help you grow as a thinker, problem solver, and global learner.  As a Mizzou Academy Global Classroom student, you’ll learn through both online coursework and in-person teacher support at your local school—interacting with course content and group discussions, participating in interactives classroom activities, and completing practice activities and collaborative exercises, as well as drafting and revising assignments, preparing for quizzes and assessments, and taking exams. This blend of online and classroom learning means you’ll have the flexibility of an asynchronous course along with guidance and community in your classroom.

As you begin, remember that success in Global Classroom courses depends on both independence and collaboration. Be curious, stay organized, participate actively, and reach out to your teachers whenever you need support.

We’re excited to learn with you, and we’re happy you’re part of our Mizzou Academy community!

Course Description

This is a 19 week online course composed of an orientation week and 18 weekly sessions. Expect to invest about 5 hours a week on course activities and assignments.

The purpose of the course is to give students a great calculus foundation. The course is designed to emphasize the relationships between the various forms of a function: graphs, equations, tables, and verbal expressions. Successful completion of a pre-calculus course is important for success in AP Calculus.

Calculus is the study of change. It is a place in mathematics where we begin examining the changing situations that surround us. Calculus has two main topics: rate of change and area under a curve. In this half unit we will concentrate on finding rates of change; in other words, differentiation. We will be reviewing familiar functions, exploring the concept of limits, and learning differentiation. Activities and assignments with released AP items are incorporated into each unit. AP Calculus is designed to have you look at functions algebraically, graphically, numerically, and verbally. The quizzes and exams will reflect this by allowing you to take parts with the use of a graphing calculator, and parts without. The difference between a calculus course and an AP Calculus course may seem subtle. After all, good calculus is good calculus. The AP requirements expect students to make connections between algebraic, graphic, and numerical pieces of information.

 

This course provides students with a college-level foundation in calculus. Coursework emphasizes the relationship between the various forms of a function: graphs, equations, tables, and verbal expressions. Calculus has two main topics: rate of change and area under a curve. The fall semester focuses on finding rates of change, i.e. differentiation. Students will review familiar functions and explore the concept of limits and differentiation.

Most AP courses consist of 2 semesters and you should complete semester 1 before starting semester 2. AP exams are offered early in May.

NOTE: If you enroll after the start date in an AP course, it is important that you adjust the pacing chart accordingly so you can complete your course before the scheduled  AP exam dates or use this link to find more information about  Advanced Placement and to see the AP Exam Calendar.

Prerequisites:

Minimum: Successful completion of Algebra 2 or equivalent.

Suggested: Successful completion of Precalculus.

Course Essential Questions

 Essential Question

How can we use limits to define and calculate the instantaneous rate of change for any given function?

Course Overview

Lesson

Objectives

Quiz

Assignment

1: Prerequisites for Calculus
  1. Sketch the graph of an equation using intercepts, slope, and symmetry.
  2. Find the points of intersection of two graphs.
  3. Graph and find formulas for piece-wise defined functions.
  4. Write the equations of lines including regression lines.
  5. Interpret slope as a ratio or rate.
  6. Use function notation to represent and evaluate a function.
  7. Find the domain, range, and graph of a function.
  8. Identify transformations of functions including exponential, logarithmic, and trigonometric functions.
  9. Classify functions and recognize combinations of functions.

20 multiple-choice questions 

Lesson 1 Chat

Lesson 1 Homework Questions

2: Limits and Continuity
  1. Distinguish between average speed and instantaneous speed.
  2. Estimate a limit using a numerical or graphical approach.
  3. Determine if a limit exists and use the formal definition of a limit.
  4. Evaluate a limit using the properties of limits, and understand the use of the Sandwich Theorem, which is also known as the Squeeze Theorem.
  5. Determine infinite limits.
  6. Determine continuity at a point, on an open interval, and on a closed interval.
  7. Use properties of continuity.
  8. Use the Intermediate Value Theorem.
  9. Determine the slope of a curve at a given point, and write the equation for a tangent.

20 multiple-choice questions 

Lesson 2 Chat

Lesson 2 Homework Questions

3: Derivatives
  1. Use the limit definition to find the derivative of a function.
  2. Find the derivative at a point.
  3. Use the various notations for derivative.
  4. Understand the relationship between the graphs of a function and its derivative.
  5. Understand the situations in which a derivative does not exist, and summarize the relationship between differentiability and continuity.
  6. Understand the concept of local linearity.
  7. Evaluate derivatives using a graphing calculator.

No Quiz

Lesson 3 Chat

Work a Posted Problem #1

Lesson 3 Homework Questions

Lesson 3 Assignment

4: Rules of Differentiation
  1. Find the derivative of a function using the Constant Rule, the Power Rule, the Constant Multiple Rule, and Sum/Difference Rule.
  2. Find the derivative of a function using the Product and Quotient Rules.
  3. Find the higher-order derivative of a function.
  4. Find the connection between the derivative and velocity and acceleration.
  5. Find the derivative of a trigonometric function.

20 multiple-choice questions 

Lesson 4 Chat

Lesson 4 Homework Questions

5: The Chain Rule
  1. Find the derivative of a composite function.
  2. Use the "Outside-Inside" Rule to differentiate.
  3. Differentiate by repeated use of the Chain Rule.
  4. Use the Power Chain Rule.

20 multiple-choice questions 

Lesson 5 Chat

Lesson 5 Homework Questions

Midterm Exam

6: Implicit Differentiation
  1. Distinguish between functions written in implicit form and explicit form.
  2. Use implicit differentiation to find the derivative of a function.
  3. Find derivatives of a higher order using implicit differentiation.
  4. Find tangents and normal lines for implicit functions.

No Quiz

Lesson 6 Chat

Lesson 6 Homework Questions

Lesson 6 Assignment: The lesson 6 assignment is composed of 10 multiple-choice questions and 1 free-response problem worth a total of 20 points.

7: Derivatives of Other Functions
  1. Differentiate inverse trigonometric functions.
  2. Differentiate exponential functions.
  3. Differentiate logarithmic functions.

20 multiple-choice questions 

Lesson 7 Homework Questions

Work a Posted Problem #2

8: Applications of Derivatives
  1. Find extrema on a closed interval.
  2. Use the Extreme Value Theorem.
  3. Find the critical points of a graph of a function.
  4. Use the Mean Value Theorem.
  5. Find an antiderivative.
  6. Determine intervals on which a function is increasing or decreasing.
  7. Apply the first derivative test to find relative extrema of a function.
  8. Determine intervals on which a function is concave upward or concave downward.
  9. Find the points of inflection of the graph of a function.
  10. Apply the second derivative test to find relative extrema of a function.
  11. Analyze and sketch the graph of a function.

20 multiple-choice questions 

Lesson 8 and Final Review Chat

Lesson 8 Homework Questions

Work a Posted Problem #3

Final Exam

Quizzes and Assignments

You should submit all assigned work in sequence (Lesson 1, then Lesson 2, etc.) Assignments for the course are listed at the bottom of this syllabus.

 

Quizzes

All quizzes for Mizzou Academy / MU High School courses are taken online. After you submit them, you’ll quickly receive a report on how you did.

 

Assignments

Assignments may consist of written work (essays, compositions, etc.), collaborative wiki projects, journal entries, audio or video recordings, multimedia presentations, graphics, etc. Each assignment will list the instructions for completing that assignment. Assignments may require you to submit your completed work in the form of a file (such as a text document, image, audio or video recording, or multimedia presentation) or a hyperlink for grading. See your Helpful Resources section of your course for tutorials.

 

Work a Posted Problem

This is a specific problem that I set forth for you to solve. There are 3 opportunities available this semester.

 

Reading and Using Feedback

After your work has been graded, you will receive a report that provides individualized feedback and comments on your work. Look carefully at what you missed and read any corresponding feedback. Then study the lesson materials to make certain that you can accomplish the associated learning objectives.

 

Each lesson provides step-by-step instructions on how to submit your work. Be sure to check submitted work carefully for errors (e.g. spelling, grammar, and punctuation) as they may result in points being deducted.

Exams

You are required to take two proctored exams for this course.

To pass the course, you must earn a minimum of 60 percent on your exams group (see grades section below for details.) See the "About Exams" in the policies section for additional information on exams at Mizzou Academy.

AP Exam

When you register for the AP exam, please use the Mizzou Academy/University of MO High School provider code: 041. If you have any questions, please let your AP instructor or our AP Coordinator, Amelia Howser, know. Ms. Howser’s email is howsera@missouri.edu.

AP - Discussions and Chats

The chat room is intended to create a more interactive classroom atmosphere. These are usually student-driven. I will take questions over the lesson, examples, or suggested problems from the textbook. Together we will work through these questions and clarify lesson topics. To earn chat points, you must ask or answer at least 2 questions during the course of the chat. You should attend each chat as you would a regular classroom, having read the material and prepared to participate in a discussion of the ideas covered in the lesson.

There will also be an introductory chat offered during the first week of the course. Attendance does not count toward your required chat attendance. However, you are strongly encouraged to attend as this provides you with an opportunity to meet your instructor and classmates and to become familiar with the chat format.

In order to keep the chats manageable and effective for everyone, I ask that you sign up for the chat by the Friday before each chat. Space in the sessions is limited, so contact your instructor to sign up as soon as possible. The introductory chat is the only one for which you are not required to register before attending. If the chat is full, the instructor will contact you via e-mail.

 

Homework Discussion Forum

The homework forum is designed for you to ask your classmates and instructor questions in a timely manner. This gives everyone the opportunity to not only ask their own questions, but also to share their understanding with those in need. Each lesson has a homework forum, and you can receive 5 points per lesson (not per post) for posting. To receive participation points, your posts (minimum of two) must be made within 1 week of the due date for that lesson’s progress evaluation. This is designed to be more of an ongoing conversation and a way to connect to others between chats. Space on these is unlimited, making it a great way to earn online participation points. I will monitor the forum and step in when necessary, but my goal is you to take control of these conversations and make it fit your needs.

AP Late Work and Absences

Work must be turned in on time for full credit. If you are unable to complete an assignment on time, contact your instructor immediately. Prior permission from the online course instructor must be obained for special circumstances to receive credit for late work. These decisions will be made on an individual basis.

You must notify your instructor if you expect to be offline for more than 1 week.

AP - Exam Prep Through LearningExpress Library

In the next section, you will find "Getting Started Resources." Within the Library Material is LearningExpress Library, which contains AP practice exams and study material, in addition to what is on the AP website. 

Below we are providing you with a direct link to the College Prep Center of the LearningExpress Library. You can only launch it through this link. When you arrive, you should see "Mizzou K-12" on the left-hand side, showing that you are with our institution. You will want to create an account in order to save any work or test prep you do.  

Once you click the link below, select "Prepare for your AP Exam". Please create a help ticket (Help -> Report a problem) if you cannot find what you are looking for.

EBSCOhost

 

Grades

Your final grade will be based on the number of points you earn on submitted work and exams. The available points are distributed as follows:

Source Available Points
Lesson Assignments 40
Lesson Quizzes 120
Midterm Exam 200
Final Exam 200
Participation 100
Total 660

 

Textbook & Technology Requirements

To fully participate, make sure you have:

  • A computer that meets our Mizzou Academy technology requirements
  • A microphone and webcam for recording audio and video assignments
  • Any other required textbooks or materials for the course

Textbook

Demana, Franklin D., Waits, Bert K., Kennedy, Daniel, Bressoud, David M., Boardman, Michael. Calculus: Graphical, Numerical, Algebraic, AP Edition. (6th Edition). Boston: Pearson, 2020. [ISBN: 978-1418300203]

There are two ways to purchase the textbook: a print book with an etext or just the etext. Please click HERE to purchase your options, then follow these steps.

  1. Enter "65211" when asked for a zip code.
  2. Select "Mizzou Academy" as the school.
  3. Enter the ISBN for your choice of textbook.
    1. Physical book with etext - 9781418300227
    2. Etext only - 9780132962377
  4. Click on the book that appears in the Search Results.
  5. Follow the directions to the add book to your cart and purchase.

Materials

You will need a graphing calculator that can find roots and intersections of functions, calculate derivatives and integrals. I would suggest either a TI-83 Plus or TI-84 Plus graphing calculator (~$110).

These advanced calculators are useful or required for other high school and college courses. Some schools let students check these out. The Silver Edition's added memory is not needed for textbook exercises. The TI-85, 86, and 89 calculators can also be used for this course. However, their keypads operate very differently from the TI-83 Plus and TI-84 Plus calculators. Since the lesson notes and instructions are based on the 83 and 84 configuration, you will need to be proficient in the operation of your calculator if you use one of the other models.

Note: On portions of quizzes and exams, you will be instructed to not use your calculator. You are on your honor to follow these instructions, even when the assessment is not proctored and there are no penalties for using your calculator. You will be required to complete sections of the AP Calculus AB exam without your calculator, and it is to your advantage to get used to working without one now when instructed to do so.

Students will be required to upload documents in Word format (.doc, .docx,) or Rich Text (.rtf) format. These documents can be created in Microsoft Word or another office suite that saves in the .doc, .docx, or .rtf format

Technology

The most up-to-date requirements can be found here: 

Additional requirements for the course are below: 

  • audio and video recording capabilities (e.g., smartphone, camera)

If you ever have trouble accessing course materials or recording tools, reach out to your teacher for support. We are here to help!

Accessibility

If you anticipate barriers related to the format or requirements of this course, please let Mizzou Academy know as soon as possible. If disability-related accommodations are necessary (for example, a scribe, reader, extended time on exams, captioning), please contact Mizzou Academy.

Canvas Technical Support

Canvas will be used as the primary platform for accessing course materials and assignments for this class.

Course Summary:

Course Summary
Date Details Due