Ultimate Guide to AP Calculus AB and BC 

Ultimate Guide to AP Calculus AB and BC
The Advanced Placement examination period is getting closer, and students have another semester to finish preparing for the examination. AP Calculus, amongst other AP exams, attracts a large number of students, with almost 400,000 students worldwide taking either the digital or paper AP exam before June of 2021. As students prepare for the exam, what should they keep in mind, and how should they put their best foot forward? Let’s read the article to learn more.

What will be covered in the article?

1. What is AP Calculus?

AP (Advanced Placement) Calculus is a set of two distinct courses and exams the College Board offers.  AP Calculus AB covers basic introductions to limits, derivatives, and integrals. AP Calculus BC covers all AP Calculus AB topics plus additional topics (including more advanced integration techniques such as integration by parts, Taylor series, parametric equations, vector calculus, polar coordinate functions, and curve interpolations).

ap exams calculus and statistics
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2. What is covered in the AP Calculus courses?

AP Cal AB and BC cover similar topics, with BC going deeper into specific topics. Both courses cover 3 big ideas: Change, Limits, and Analysis of functions. 

  • Changes: Using derivatives to describe rates of change of one variable concerning another or using definite integrals to describe the net change in one variable throughout another allows students to understand the difference in various contexts. It is critical that students grasp the relationship between integration and differentiation as expressed in the Fundamental Theorem of Calculus—a central idea in AP Calculus.
  • Limits: Beginning with a discrete model and then considering the consequences of a limiting case allows us to model real-world behavior and to discover and understand significant ideas, definitions, formulas, and theorems in calculus: for example, continuity, differentiation, integration, and series (BC only).
  • Analysis of Functions:  Calculus allows us to analyze the behaviors of functions by relating limits to differentiation, integration, and infinite series and relating each of these concepts to the others.

Both AP Cal AB and BC share 8 units: Limits and Continuity, Differentiation: Definition

and Fundamental Properties, Differentiation: Composite, Implicit, and Inverse Functions, Contextual Applications of Differentiation, Analytical Applications of Differentiation, Integration, and Accumulation of Change, Differential Equations, Applications of Integration. The other two units that AP Cal BC covers are: Parametric Equations, Polar Coordinates, and Vector-Valued Functions, Infinite Sequences, and Series. 

Due to the difficulty level, Calculus AB and BC are college-level calculus courses; therefore, students are required to take pre-calculus. Depending on your interest and goals, you may take AB or BC, or both. 

3. What is covered in the AP Calculus exams?

Both exams are long – 3 hours and 15 minutes across 2 sections. The first section has 45 multiple-choice questions, makes up 50% of the score, and includes 2 parts: with and without using a graphing calculator. The second section has 6 free-response questions. In part A, you can use a graphing calculator to solve 2 problems in 30 minutes. In part B, you cannot use a graphing calculator to solve 4 problems in 60 minutes. 

Despite AP Calculus BC covering more topics and having more in-depth content – seemingly harder, 38.3% of students score 5 on the AP Calculus BC, compared to the 17.6% of students scoring 5 on the AP Calculus AB. But overall, half of the students who took the same received a passing grade (3 and above). 

Exam

5

4

3

2

1

AP Calculus AB

17.6%

14.1%

19.3%

25.3%

23.7%

AP Calculus BC

38.3%

16.5%

20.4%

18.2%

6.6%

Learn about the difference between AP Calculus AB and BC here

4. How to prepare for the exams

Take practice tests to evaluate your skills. 

Before starting to study and learn / reinforce topics for the exam, we always suggest students take a practice test to gauge their skills and identify areas of knowledge deficit. In addition to learning all the materials, focus your studying effort on the areas that need improvement. After reviewing the AP course content, you should compare it with the syllabus for your class in school to make sure all topics on the exam are covered in class and make sure the exam formats are also discussed in class.  

Practice tests can also be taken throughout the review process to ensure that you’re on track with the learning objectives and that you are all caught up with the knowledge required for the exams. Students have access to AP past tests from 1998 to 2020 on the College Board site and AP Classroom. 

Taking classes and learning the materials

When preparing for the exam, students can have the option to take classes outside of the regular classroom hours. Taking online courses from Aralia Education will provide you with a guide on the course content and structure as well as review sheets and study guides for each unit. The AP Calculus AB and AP Calculus BC classes are taught by experienced AP Calculus teachers.

For students who are taking the AP Calculus BC class, here are 4 tips to get a 5 in the exam!

Make a study plan

Referring to our 4 Steps to Study For The 2022 AP Exams, we have provided a checklist by Trevor Packer, Senior VP of Advanced Placement at the College Board, to make sure students stay on top of their schedules. The schedule is generic to preparing for the AP exams, but overall, students can use this as a guide for preparing for AP Calculus and other AP exams. 

2022 AP Calculus Score Calculator

This is a projected calculation of your AP Calculus for 2022 . Please keep in mind that this score will not accurately reflect your score, but this is our projection based on the scoring guidelines given by College Board.

There are 45 questions for the multiple-choice section, which is worth 50% of your score, and 6 Free Response Questions, which are worth 50% of your score.

You can calculate your point by this formula: 

(Multiple Choice Score / 45 x  2) + 2 x (Free Response Score / 54 x 2) = Total Score

scoring worksheet

FREE 2022 AP Scoring Worksheet

With the scoring worksheet, you will be able to calculate your target score in preparation for the upcoming exam in May. We also have a full scoring worksheet available  below if you want to print it out and keep it in your folder. 

AP CALCULUS

Description:  Improve your AP score with this AP Calculus AB course. Taught by an experienced AP Calculus teacher from Hotchkiss School, the course will review the important knowledge in the exam. In addition, the teacher will cover multiple-choice questions and free-response questions. We will not cover Parametric Equations, Polarm Coordinates, Vector-Valued Functions, and Infinite Sequences and Series in this course. 

Project time: Rolling enrollment throughout the year, one class every weekend, 1.5 hours per class 

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