Enrolling Now for 2026-27 School Year.
Enrolling Now for 2026-27 School Year.
AP® Calculus BC Learning Coach Guide Contents Part C Unit Information10 Limits and Continuity Unit11 Definition and Fundamental Properties of Differentiation Unit12 Composite, Implicit and Inverse Differentiation Unit13 Contextual Applications of Differentiation Unit14 Analytical Applications of Differentiation Unit15 Integration and Accumulation of Change Unit16 Differential Equations Unit17 Applications of Integration Unit18 Parametric, Polar and Vector-Valued Equations Unit19 Infinite Sequences and Series Unit20 Part AWelcome to AP® Calculus BC Welcome Letter Dear Learning Coach, Thank you for partnering with CCA and investing in your learner’s education. This Learning Coach Guide is intended to help you support your learner in their AP® Calculus BC course. Within this guide, you will find the goals, components, and features of the online course. Please take time to read and review this information so you understand how to help your learner interact with all the course’s elements. The Learning Coach Guide also includes information about each of the units in this course. On each page of unit information, you will discover the following. The Unit Overview will tell you what the focus, content, and skills of the unit will be. The Unit Assessment section is a place for you and your learner to preview the graded work in the course. At the start of each unit, work with your learner to look at the unit in edio and find out which types of graded work are in this unit. Write them in the box and use it as a checklist. You can check off each one as your learner completes it. The Unit Materials section tells you the materials your learner will need to complete the activities in this unit. You will also find the materials list repeated within each lesson so that your learner has exactly what they need at the right time. The Unit Discussion Questions are optional questions that you may want to ask your learner during the unit to increase home and school connections about what your learner is studying. In the Unit Notables section, you may find optional activities, career connections, technology tips, or ideas to help your learner if they get stuck. CCA wishes you and your learner a terrific school year! Supporting Your Learner Your role as a Learning Coach is very important. Here are a few ways you can help your learner do their very best in the course. Help your learner know what time guided or live class instruction is scheduled for, and prompt them to attend sessions or watch recordings. Remember, it is okay for your learner to get stuck. Learning new material takes time. Encourage them to take breaks, keep trying, and even ask the teacher for help. Help your learner navigate technology. That may mean helping them type information or upload work into edio. Always encourage your learner to do their very best. Review the course syllabus for your learner’s course. Advanced Placement® (AP) courses require more from the learners than other courses. You may find that your learner needs more practice, more review, and more support to be successful when compared to non-AP® courses. Excellent AP® learners should strive for mastery. Think of athletes and musicians. They practice until they are excellent. AP® learners should follow that kind of work ethic. Maintain communication with your learner’s teacher. Part BCourse Information Course Goals In AP® Calculus BC, your learner will: have an understanding of calculus concepts and experience with its methods and application; demonstrate accurate use of definitions and theorems to build arguments and justify conclusions; apply concepts, results, and problems expressed graphically, numerically, analytically, and verbally; explore connections among representations and build an understanding of how calculus applies limits to develop essential ideas, definitions, formulas, and theorems; and communicate their methods, reasoning, justifications, and conclusions mathematically. Course Format Lesson Components: Each day, your learner will spend approximately 50–60 minutes completing an AP® Calculus GC lesson. Some days may take less time, while other days may take a little more time. It is common for learners taking AP® courses to spend time outside of the scheduled class time completing course reading or studying. This section will help you to understand how your learner’s course is structured in edio. Lesson Bundling: Within the lesson bundles, there are different components your learner will interact with. These components will not be used every day. 1. Getting Started Lesson: There is one Getting Started lesson in this course. It can be found on Day 1 of Unit 1. This lesson includes important information about the course and contact information for your teacher. 2. Unit Overview: Each unit will include a unit overview. This describes what your learner will learn in the unit and how many assessments the unit will have. 3. Prep for Success: At the beginning of each unit, your learner will find a Prep for Success. This component offers learners tips to be successful in the course, such as study tips, important software information, safety reminders, and more. 4. Knowledge Check: There will be one Knowledge Check in each unit. The Knowledge Check is designed to check prior learning and understanding about key skills and concepts that will be taught in the unit. The Knowledge Check is not a graded assessment. Each lesson has its own components to help guide your learner through the lesson. 1. Lesson Overview: At the beginning of every lesson, your learner will see the lesson overview. This section contains lesson objectives, lesson vocabulary, materials your learner will need for the lesson, and the suggested lesson length. 2. Engage: The first section of the lesson is Engage. In this section, learners will be introduced to the lesson by making a connection to past and present knowledge and will get ready for the lesson’s instruction. 3. Discover: New content and instruction is presented in the Discover section. Your learner will interact with the lesson content through defined vocabulary terms, videos, audio, and Pause and Think activities. Your learner will be able to practice and answer questions as they work through the lesson. 4. Show: Learners will demonstrate what they have learned in the lesson through a series of practice questions. 5. Summary: This section recaps the day’s objectives and prepares learners for a future lesson or assessment. This course also includes quizzes, tests, and exams. Quiz: A quiz may be given at the end of a topic or the end of a unit. Test Review: Before a test, learners will have the opportunity to review the content they will be assessed on in the test. Test: A test will assess learning across topics or at the end of a unit. Exam Review: Before an exam, learners will have the opportunity to review the content they will be assessed on in the exam. Exam: An exam assesses learning over multiple units. Exams are usually seen as midterm and final exams in Advanced Placement courses. Course Features This course includes and uses unique features such as: Free-Response Question (FRQ): An FRQ is a free-response question: an open-ended question found on the AP exam that typically includes a real-world context or scenario. Part CUnit Information Limits and Continuity Unit Unit Overview In this unit, your learner will explore how limits will allow them to solve problems involving change, and your learner will better understand math models and how they are used in the real world. Unit Assessments Quiz _________________________ Test _________________________ Assignment ________________ Project _____________________ Exam _______________________ Have your learner identify which assessment type they see in their unit. Check all that apply. Unit Discussion Questions What did you find most challenging about approximate values? Can you identify the exact point where change occurs? If so, how? Unit Notables Limits can help your learner approximate values based on models or equations. Sometimes, the equation is not defined at a point. Some learners struggle with this. However, remind your learners that limits are only interested in where the value is approaching. Kit Materials graph paper, highlighter, notebook, TI-84+ calculator Household Materials none Definition and Fundamental Properties of Differentiation Unit Unit Overview Your learners will determine rates of change through a variety of calculus techniques. Your learner will find derivatives using the power rule, product rule, and quotient rule. Unit Assessments Quiz _________________________ Test _________________________ Assignment ________________ Project _____________________ Exam _______________________ Have your learner identify which assessment type they see in their unit. Check all that apply. Unit Discussion Questions What did you find the most interesting or challenging about making predictions about behaviors? What are some real-world examples of making predictions based on rates of change? Unit Notables In the real world, your learner can make predictions about behavior based on the rates of change. For example, determining when an object is slowing down or speeding up when given the object’s position over a period of time. Kit Materials graph paper, highlighter, notebook, TI-84+ calculator Household Materials none Composite, Implicit and Inverse Differentiation Unit Unit Overview Your learner will apply the chain rule to find derivatives (rates of change) to continue to make predictions. Unit Assessments Quiz _________________________ Test _________________________ Assignment ________________ Project _____________________ Exam _______________________ Have your learner identify which assessment type they see in their unit. Check all that apply. Unit Discussion Questions What did you find easy or challenging about using the chain rule? What did you find the most surprising about this unit? How can divers apply what you learned in this unit? (Hint: If pressure experienced by a diver is a function of depth and depth is a function of time, how can you find the rate of change in pressure with respect to time?) Unit Notables Your learner is learning several ways to find the rates of change, or derivatives, of a function. Remind them that finding the derivative is similar to solving a puzzle and to have fun with it. Kit Materials graph paper, highlighter, notebook, TI-84+ calculator Household Materials none Contextual Applications of Differentiation Unit Unit Overview Your learner will apply L’Hospital’s Rule to find limits in difficult cases. Unit Assessments Quiz _________________________ Test _________________________ Assignment ________________ Project _____________________ Exam _______________________ Have your learner identify which assessment type they see in their unit. Check all that apply. Unit Discussion Questions Unit Notables If your learner struggles with remembering rules, remind them that L’Hospital’s Rule says that the limit when dividing one function by another is the same after taking the derivative of each function. Encourage your learner to create or post images of the rule to help reinforce the concept. Kit Materials graph paper, highlighter, notebook, TI-84+ calculator Household Materials none From the units so far, which concept has been the most challenging? What did you find the most surprising or interesting about this unit? Analytical Applications of Differentiation Unit Unit Overview Your learner will apply the Mean Value Theorem and the Extreme Value Theorem to find the hills and valleys of a graph. These “hills and valleys” are used to determine maximum or minimum values. First and Second Derivatives help us to find these points of interest. Unit Assessments Quiz _________________________ Test _________________________ Assignment ________________ Project _____________________ Exam _______________________ Have your learner identify which assessment type they see in their unit. Check all that apply. Unit Discussion Questions What are some ways this information is used in the real world? What did you find interesting about this unit? What do you need to work on in order to prepare for the midterm exam? Unit Notables In this unit, your learner will explore the ways a graph of real data helps to predict behavior. For example, a graph of stock prices can help determine (when to sell) maximum or (when to buy) minimum values. Your learner will take a midterm exam at the end of this unit. Kit Materials graph paper, highlighter, notebook, TI-84+ calculator Household Materials none Integration and Accumulation of Change Unit Unit Overview Your learner will find the integral or the area under the curve to determine the accumulation of change. This accumulation has practical uses, but it also helps to better stand the behavior of the graph or data. Unit Assessments Quiz _________________________ Test _________________________ Assignment ________________ Project _____________________ Exam _______________________ Have your learner identify which assessment type they see in their unit. Check all that apply. Unit Discussion Questions If you had difficulty understanding derivatives, how did you improve your understanding? What was the most interesting part of this unit? Given information about a rate of population growth over time, how can you determine how much the population changed over a given interval of time? Unit Notables Your learner will investigate how derivatives help to understand the change in behavior of a graph or function. An integral can help use the change in behavior to understand the graph or function. Kit Materials graph paper, highlighter, notebook, TI-84+ calculator Household Materials none Differential Equations Unit Unit Overview In this unit, your learner will learn how to solve certain differential equations and apply that knowledge to deepen the understanding of exponential growth and decay. Unit Assessments Quiz _________________________ Test _________________________ Assignment ________________ Project _____________________ Exam _______________________ Have your learner identify which assessment type they see in their unit. Check all that apply. Unit Discussion Questions What are some ways you might use the knowledge and skills in this unit in your everyday life? Unit Notables In this unit, your learner will explore how slope fields help your learner find specific behaviors of change, and more importantly the specific and unique points of interest. Kit Materials graph paper, highlighter, notebook, TI-84+ calculator Household Materials none Applications of Integration Unit Unit Overview In this unit, your learner will make mathematical connections that will allow you to solve a wide range of problems involving net change over an interval of time and to find areas of regions or volumes of solids defined using functions. Unit Assessments Quiz _________________________ Test _________________________ Assignment ________________ Project _____________________ Exam _______________________ Have your learner identify which assessment type they see in their unit. Check all that apply. Unit Discussion Questions Do you feel that you are better able to solve net change problems? Why or why not? What are some real-life applications of this skill? (Hint: How is finding the number of visitors to a museum over an interval of time based on information about the rate of entry similar to finding the area of a region between a curve and the x-axis?) Unit Notables Remind your learner that the area under the curve is the accumulation of change. Kit Materials graph paper, highlighter, notebook, TI-84+ calculator Household Materials none Parametric, Polar and Vector-Valued Equations Unit Unit Overview In this unit, your learner will build on your understanding of straight-line motion and area between curves to finding how particles move along curves in the plane defined by parametric, vector, and polar equations and area between polar curves. Unit Assessments Quiz _________________________ Test _________________________ Assignment ________________ Project _____________________ Exam _______________________ Have your learner identify which assessment type they see in their unit. Check all that apply. Unit Discussion Questions How can you model motion not constrained to a linear path? How does the chain rule help you to analyze graphs defined using parametric equations or polar functions? Unit Notables Sometimes your learner will need to track the behavior of two variables that depend on a third. In other words, y may not depend on the value of x. In fact, x and y might depend on the variable t (time). Your learner will represent the value of x and y based on their dependence of t. Kit Materials graph paper, highlighter, notebook, TI-84+ calculator Household Materials none Infinite Sequences and Series Unit Unit Overview In this unit, your learner will learn how to test if a series converges or diverges using a variety of scenarios and will learn how a discrete set of values can represent a continuous function. And, how differentiation and integration applies to series. Unit Assessments Quiz _________________________ Test _________________________ Assignment ________________ Project _____________________ Exam _______________________ Have your learner identify which assessment type they see in their unit. Check all that apply. Unit Discussion Questions What concepts or real-life applications did you find interesting or surprising? What do you need to work on in order to prepare for the final exam? What is your plan? Unit Notables This is the final unit of the course. Your learner is preparing for the AP® exam and the final exam. To help your learner understand converging on a value, you could slice a pizza in half. Repeat this process to see how each new slice gets smaller and smaller. The slice size seems to converge on zero, but theoretically you should have some pizza, just a very small slice. Kit Materials graph paper, highlighter, notebook, TI-84+ calculator Household Materials none
Enrolling Now for 2026-27 School Year.
