AP

AP Calculus (known as Advanced Placement Calculus) is the course that comes after successful completion of your pre-calculus class. It covers a range of topics, like derivatives, integrals, calculus theorems and limits of functions. The topics you learn in your AP Calculus course will, like other AP classes, help to prepare you for future AP courses and your college career. The final AP Calculus exam you’ll take can also count toward your college credit completion amount, which helps you to reach your next step quickly.

Read on to learn everything you need to know about AP Calculus and the AP Calculus exam.

You’ve likely heard calculus as a topic referred to in different ways: Calculus I and Calculus II, or Calculus AB and BC. Each covers their own set of topics, including differential equations, functions, definite integrals and more — but there are more differences that separate the two from each other. These include:

**Differences in course material.**Calculus BC covers the fundamentals of Calculus AB, but at a faster pace. Additionally, it will delve deeper into parametric functions, polar functions, vector functions, and analysis of theories.

**Duration of each course.**Generally speaking, Calculus AB is just a single semester’s worth of learning, covering Calculus I concepts. Calculus BC is two semesters’ worth of topics, all of which can be found in both Calculus I and Calculus II.

If you’re here, you’re likely looking to wow the College Board with a high AP Calculus AB exam score. If so, you’re in good company. Below, we dig into some insight to help you master your high school AP Calculus AB exam — helping you to keep your sanity all the way through finals week.

High school students generally do best pursuing their own personalized studying strategies pre-exam. If you’re in the middle of preparations, you can take the opportunity to inquire about AP Calculus pre-test options to determine how effective your current study regimen is.

If you’re not sure where to start, we recommend speaking with your teachers. They can give you support as you find your specific studying style. For example, do you prefer flash card learning (maybe to learn the properties of definite integrals?), or do you prefer pen-to-paper or pen-to-calculator “hands-on” learning — such as you might encounter as you work out the derivatives of a function? Only you can answer those questions!

You can also start by printing out or listing out all of your current course materials and notes, creating a strategic review schedule that focuses on each core concept.

Here’s our list of resources to reference as you hit the critical points of your review period(s) for your upcoming AP test:

**Your College Board.**The College Board has resources and modules to help you master certain different concepts. You can also try to access past AP Calculus “free response” questions that they have on file to give you an idea of what will be asked.

**Your Textbook.**Reviewing questions and answers throughout your textbook can help you to apply your “book knowledge” to the problems that you’ll face.

**Your Course Materials.**If you’ve been given a course study guide or outline, be sure to look over that. You can determine which areas you’ll need to focus on as you prep for AP tests.

Wondering if you’ll encounter the mean value theorem or the squeeze theorem in your AP Calculus AB course? While we can’t tell you exactly what you’ll find, we can provide a pretty helpful overview covering what to expect on your test day.

Your AP Calculus exam will have two parts: A multiple choice section and a free response section. The order in which you’ll take these parts depends on your proctor and any instructions given by your school. There are Part A and Part B components to each section.

Course content in the multiple choice section may vary, spanning cross sections of content covered in class (ranging from accumulation of change, to tangent line operations and other key concepts). If you’re looking for other possible topics, we strongly recommend picking up a reputable review book as you prepare.

Free response sections contain written questions and answers; giving you the opportunity to show your work and knowledge as you solve the answer. You may be required to create your own graph as well — so be sure to brush up on your graph skills.

Like other AP scores, you will be graded using values 1 through 5. Students are generally looking to get a “high score” for college credit, which is generally regarded to be a 4 or a 5. The test may be curved, which can affect the given score.

Times might feel tough — but your time management regimen doesn’t have to be. Stay connected with your schedule to keep yourself mentally healthy, strong, and in the “flow” for learning. If you need help, reach out to a trusted counselor, parent, or friend. You can also use calendars or planners to help you keep everything straight.

While your exam is important, the grade you get on it doesn’t determine how strong you are as a student or as a person. Be sure to assign the exam the stress that it warrants — but not more than that. Remembering your value and taking ownership of your perception and learning journey is key to acing this exam season and the ones to come.

We said it before and we’ll say it again, because it’s just that important: Everyone studies differently. Working to test and tune your habits to see which ones help you feel prepared and confident is a great way to support yourself for your upcoming AP exam.

While AP Calculus can be useful for those wanting to pursue engineering or STEM careers, there are other suitable alternatives that can give you equal benefit. If you’re not sure if AP Calculus is right for you, you can reach out to your guidance counselor and ask about alternatives — like statistics, precalculus or advanced trigonometry.

Here’s what you can expect when you sign up for Calculus AB with Apex Learning Virtual School.

It’s always good to brush up on old skills! Calculus AB will open with precalculus review topics, ranging from functions to polar curves. Other areas of learning include trigonometric functions, the product rule, theorems, and applications of skills learned in previous precalculus and trig lessons.

After the precalc refresher is complete, students will explore introductory Calc I skills. These include topics like:

**Intro to Calculus.**Mathematical reasoning for real-world problems, exponential growth, rates of change and more will all be covered in this first part of the Calculus AB curriculum.

**Functions.**Students will enjoy multiple-choice questions and word problems covering inverse functions, the derivative of a function (and how to find it), and more.

**Graphical Symmetry.**Graph topics (like graphical symmetry) will be covered, as well as related applications of each.

**Patterns in Graphs.**Students will brush up on pattern and graphing skills as they relate to calculus and will experiment with applications of each.

**Parameters.**Parametric equations are vital to learn to fully grasp calculus. Teachers and students will be exploring this subject in detail, dissecting solutions and tackling hands-on problems.

**Bridge to Calculus: Wrap-Up.**Cumulative exams and review tasks will be given to ensure students have fully explored these introductory areas of learning.

Limits explore how a function behaves with different input values. Continuity builds on this, verifying that the projected behavior of a function is aligned with the total functional value. Understanding these relationships brings calculus alive in a new way, and lays the groundwork for more advanced theorems. Here’s what students will learn in Unit 3:

**Limits and Continuity.**These two concepts are complimentary, as we see above. They’ll be one of the first topics students cover in Unit 3.

**Asymptotic and Unbounded Behavior.**These topics introduce students to how a function behaves in certain environments or with certain inputs. These areas of learning will build off of limit and continuity-related topics.

**Continuous Functions.**Continuous functions are shown on graphs, and are foundational concepts for both extreme and intermediate value theorems.

**Limits and Continuity Wrap-Up.**Before moving on to Unit 4, students will recap all of the skills related to limits, continuity, and behavior found in Unit 3.

Derivatives are key to breaking down equation formats found in both Calc I and II. Other related topics of coverage include:

**Computing Derivatives.**Learning how to compute rates of change and variables is an essential concept to master as students begin learning derivatives.

**Derivative of Functions.**Learning to graph in the scope of this subtopic will prepare students to tackle more advanced calculus graphing in both Calc I and Calc II.

**Higher-Order Derivatives.**This is defined as a student’s ability to take derivatives of derivatives — further applying them to motion problems and sketch curves (among other problem types).

**Chain Rule and Implicit Differentiation.**Students will explore new applications of these derivative rules, as well as use cases.

**Derivatives Wrap-Up.**Before moving on to Unit 5, learners will recap all of the skills related to derivatives found in Unit 4.

Change and measurement of change are integral topics that students learn in Calculus I; further applying them in Calculus II. Some areas of learning in this domain include:

**Externa and Optimization.**Learning how to manage these topics in the context of calculus-related constraints will be integral to students’ understanding of calculus overall.

**Tangent and Normal Lines.**Understanding the foundational graph notations, such as tangent lines and normal lines, will be helpful to refine and build confidence in future graph-related problems.

**Rates of Change.**This concept will build on earlier lessons from Unit 4.

**Rectilinear Motion.**This type of motion over a line will marry velocity and positioning concepts as they relate to the function of an object.

**Semester Wrap-Up.**Before moving on to Unit 6, learners will recap all of the skills related to rates of change found in Unit 5.

These theorems are essential for a full understanding of Calculus II and the Calculus AP exam, and explore antiderivatives, indefinite integrals, and continuous functions. Additional areas of learning include:

**Area Under a Curve.**Students will find the area under a portion of a function using integrals.

**Definite Integrals.**This calculation includes limit(s), summation, and net area between functions and their x-axis.

**Antiderivatives.**These functions reverse previously established derivatives, and are essential to understand for the exam and Calculus II.

**The Fundamental Theorems of Calculus.**Students will explore the application of this fundamental theorem, which explains the link between differentiation and integration.

**The Integral and the Fundamental Theorems of Calculus Wrap-Up.**Before moving on to Unit 7, students will recap all of the skills related to the fundamental theorem of calculus found in Unit 6.

Building on prior knowledge of geometry, trig, and precalculus, this area of study focuses on finding factual dimensions and areas of known shapes and objects.

**Area.**Students will learn how to find both area and volume via integration and with respect to x.

**Other Applications of the Definite Integral.**After learning how to find these variables and values, students will be able to apply them in word problems or across other use cases.

**Applications of the Integral Wrap-Up.**Before moving on to Unit 8, learners will recap all of the skills related to applications of the integral found in Unit 7.

Transcendental functions, in this case, mean anything that’s beyond what traditional algebra teaches. Students will explore trig functions, exponential functions, and other key skills in this unit of study, preparing them for deeper understanding in Calculus II or equivalent courses.

**Inverse Functions.**This area of focus generally focuses on the inverse of exponential and trig-related functions.

**Review of Logarithmic and Exponential Functions.**Students will build on any previously-established understanding of these concepts, and will learn how to apply them in the context of Calculus I or II.

**Computation of Derivatives for Some Transcendental Functions.**This is just one of the many applications of derivatives, which students will master in Calculus I.

**Inverse and Transcendental Functions Wrap-Up.**Before moving on to Unit 9, students will recap all of the skills related to inverse and transcendental functions found in Unit 8.

Students will learn applications of calculus as they apply to differential equations and slope fields in this unit, further cementing their knowledge of advanced math skills.

**Separable Differential Equations.**These types of equations can be separated into functions of x and y,then integration of both sides can be taken to find a solution. .

**Exponential Growth and Decay and Related Applications.**Students will encounter these concepts in word problems and throughout practical mathematical applications as they work with exponential functions.

**Separable Differential Equations and Slope Fields Wrap-Up.**Before moving on to Unit 10, learners will recap all of the skills related to separable differential equations and slope fields found in Unit 9.

Preparation for the AP exam can never start too early.

**Review of Topics.**Students will begin to explore a comprehensive review of topics, dating back to the very start of Calculus AB.

**Practice Final Exams.**Practice exams will be a handy tool to help students overcome exam jitters.

**Final Exam.**Students will take a comprehensive final exam to assess their knowledge of Calculus I concepts.

Taking the AP Calculus exam is worth it if you’re looking to secure college credit. This perk can be especially helpful to people pursuing STEM careers or a career in any sub discipline of engineering.

Integrals, derivatives, inverse functions, transcendental functions, limits, fundamental theorems and more are all commonly covered in Calculus I or Calculus AB.

AP Calculus can help in your college admissions process depending on the type of degree that you wish to pursue. You can reach out to your guidance counselor for more information, or to determine if an alternative would be equally helpful.

As an ALVS student, there are many resources available to help you as you begin the prep process for your upcoming AP Calculus exam. Some of the most common options include College Board test prep materials, test books, and trusted review book and video content provided by your experienced AP instructors who may have served as test readers.

Ready to take the next step and enroll in AP Calc? Our online application process is designed to make enrollment as stress-free as possible. Take the next step toward your academic success today — browse our catalog to learn more about course offerings or contact us at 1.855.550.2547 to speak to an admissions advisor.