AP® Calculus AB Course And Exam Description
At first glance, the AP® Calculus AB course might seem vast and challenging, but this overview will help you build a strong foundation in Calculus AB and set you up for success at the college level. We’ve broken down the AP Calculus AB course curriculum into simple chunks for an easy read. This page provides a well-rounded AP Calculus AB course outline, from prerequisites to content, including key concepts and topics.
AP Calculus AB Units, Topics, and Key Concepts
The AP Calc AB course comprises two primary components — Course Content and Mathematical Practices. As you progress through the course, you will learn the essential mathematical practices through the course content. Combined, both of these components prepare you to build a solid foundation in Calculus AB and help you succeed in the exam. The course content is further divided into units. Each unit is based on the three big ideas that provide the foundation upon which the course is structured.
Before you embark on your journey through the AP Calculus AB course, it is essential to understand the prerequisites needed to help you grasp the course successfully. Having these requirements met beforehand eases your way through the course. It also lets you decide if you are ready to take a math-heavy course like AP Calculus AB.
As far as prerequisites are concerned, your high school classes should provide you with courses that include Algebra, Geometry, Trigonometry, and Precalculus. These courses will help you build a strong foundation in reasoning with algebraic symbols and working with algebraic structures that are essential to learning Calculus.
AP Calculus AB’s Three Big Ideas
The curriculum for this course revolves around three key AP Calculus AB concepts or big ideas that provide the foundation upon which the course is structured. As you journey through the Cal AB course, you’ll find that each of these key concepts is interwoven into the course units. Let’s take a look at what these big ideas include:
- BIG IDEA 1: Change (CHA)
Using derivatives to describe rates of change of one variable with respect to another or using definite integrals to describe the net change in one variable over an interval of another allows students to understand the concept of ‘change’ in a variety of contexts. The first big idea of Change (CHA) allows you to understand the relationship between integration and differentiation as expressed in the Fundamental Theorem of Calculus.
- BIG IDEA 2: Limits (LIM)
The second idea of Limits (LIM) teaches you to understand essential ideas, definitions, formulae, and theorems in calculus: for example, continuity, differentiation, and integration.
- Differentiation: Defining the derivative of a function, estimating derivatives at a point, connecting differentiability and continuity, determining derivatives of constants, sums, differences, and constant multiples and trigonometric functions. You’ll also need to learn about composite, Implicit, and inverse Functions.
- Integration: Finding the average value of a function, applying accumulation functions, finding the area between curves of functions, and finding volumes from cross-sections and revolutions. You’ll also need to study the Fundamental Theorem of Calculus, finding anti-derivatives and indefinite integrals, and integrating using substitutions.
- BIG IDEA 3: Analysis Of Functions (FUN)
Understanding and analyzing the behaviors of functions by relating limits to differentiation, integration, and infinite series and relating each of these concepts to the others.
As we’ll soon discuss, these three big ideas are distributed across eight units to help students understand each concept efficiently. In doing so, both the big ideas and the course units create a template of the Calculus course, which is similar to many college courses and textbooks. Now let’s walk through each of the eight course units to develop a clearer understanding of how these big ideas and the units intertwine to build a solid foundation in Calculus.
The Eight Units of AP Calculus AB and Their Topics
The units contain the course material you’ll learn throughout your AP classes. Based on what you’ve studied in these units, the AP Calculus AB exam will test you with 45 multiple-choice questions (MCQs) and six free-response questions (FRQs).
Remember the big ideas that we talked about earlier on this page? As we outline each AP Calculus AB unit, we will also see which of those big ideas spiral across the course units. Each of the eight units comes with specific topics you’ll learn during your course.
Understanding how these topics are categorized will help you focus on individual topics in detail. It will also help you assess your target areas and weaknesses to know precisely which unit and topic to work on during your revision period. We’ve also included the relative exam weightage for every unit so that you get all the info in one place. If you’re curious to find detailed information about any particular AP Calculus AB unit, click on the unit widgets below to take you there!
Unit 1 – Limits and Continuity
Exam Weightage: 10-12 % ｜ Class periods ~ 22-23
This unit introduces you to the idea of change, which is why we study calculus. Calculus allows us to generalize knowledge about motion to diverse problems involving change. Using the concept of limits, you’ll learn the subtle distinction between evaluating a function at a point and considering what value the function is approaching after a point in time. As you progress through this unit, you’ll learn how to determine change by justifying claims about limits and continuity through definitions, theorems, and properties.
The big ideas explored in this unit:
- Big Idea 1: Change – Can change occur in an instant?
- Big Idea 2: Limits – How does knowing the value of a limit, or that a limit does not exist, help you to make sense of interesting features of functions and their graphs?
- Big Idea 3: Analysis Of Functions – How do we close loopholes so that a conclusion about a function is always true?
In this unit, you will learn:
- How the average rate of change of a function can closely approximate the rate of change at an instant: Topic 1.1.
- What a limit is, how to express it, and how to calculate or approximate it from a table, graph, or function: Topics 1.2 – 1.4.
- Properties of limits and how to simplify them with algebra and trigonometry: Topics 1.5 – 1.7, 1.9.
- How limits of known functions can provide information about an unknown function using the squeeze theorem: Topic 1.8.
- What continuity is and how to identify when a function or graph is discontinuous at a point or over an interval: Topics 1.10 – 1.13.
- How to find infinite limits and limits at infinity, and what information these limits can provide about a function’s asymptotes: Topics 1.14 – 1.15.
- How continuity can prove the existence of a function value using the intermediate value theorem: Topic 1.16.
Mathematical Practices for AP Calculus AB
The AP Calculus AB Mathematical Practices describe the skills you should acquire while exploring the Cal AB course units. There are four Mathematical Practices, and they form the core skills that you need to develop for succeeding in the exam. The AP Calculus AB course should enable you to integrate content with the practices mentioned below. With sufficient repetition and revision, you’ll be able to transfer these skills to the AP exam. Now, let’s look at how the College Board® categorizes these core Mathematical Practices:
- Implementing Mathematical Processes
This is the first practice you will learn during the AP Calculus AB course. As the name suggests, this Mathematical Practice will help you determine expressions and values using mathematical procedures and rules and teach you how to implement those rules to solve problems.
- Connecting Representations
This Mathematical Practice will teach you to translate mathematical information from a single representation or across multiple representations.
Justifying how you deduce the solution to a mathematical problem is crucial for the Free-Response Section of the AP Calculus AB exam. This Mathematical practice will equip you with reasoning skills to logically establish the steps required to solve problems.
- Communication and Notation
Understanding and solving a problem are not enough. You also need to know the correct way of communicating it. With the help of this Mathematical Practice, you’ll learn to use correct notation, language, and mathematical conventions to communicate results or solutions.
“Remember to apply the core skills and Mathematical Practices you learned during your course content. Developing a clear understanding of the concepts and theorems and mastering the skill to apply those concepts effortlessly is the key to unlocking that 5 on your AP Calculus AB exam!”
As you journey through each AP Calculus AB concept and topic, remember to go back and review the big ideas that each of these units encompasses. Knowing the fundamentals of a subject is the core of a solid learning process.
If you are preparing for your AP Calculus AB exam, we can help! Challenging practice questions, detailed explanations for correct and incorrect answers, and digital performance tracking are just a part of what makes our online courses for AP second to none. You’ll love your increased understanding in the classroom and the higher test scores you’ll achieve with UWorld. Take our free AP Calculus AB practice exam today and feel the difference!
A Few FAQs to help you prepare for the AP Calculus AB Exam
- (17-20%) Unit 6: Integration and Accumulation of Change
- (15-18%) Unit 5: Analytical Applications of Differentiation
- (10-15%) Unit 4: Contextual Applications of Differentiation
- (10-15%) Unit 8: Applications of Integration
- (10-12%) Unit 1: Limits and Continuity
- (10-12%) Unit 2: Differentiation: Definition and Fundamental Properties
According to the 2021 AP exam results, the most challenging topic in AP Calculus AB is Unit 10: Infinite Sequences and Series.
The College Board®
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