How to Study for AP® Calculus

GENIUS METHOD for Studying (Remember EVERYTHING!)
GENIUS METHOD for Studying (Remember EVERYTHING!)

Introduction

Congratulations on signing up for the AP® Calculus AB or AP® Calculus BC exams! Both AP® Calculus exams cover a fair amount of material, and you may not be sure where to begin studying, or what you should be studying in the first place. Don’t worry! You’ve come to the right place. Here at Albert.io, we’ve written up several articles specifically designed to help you ace the AP® Calculus exams.

In this article, we’re going to go over how exactly you should be studying for the AP® Calculus exams, and what topics you need to know to ace the exam. This article will not be going over any practice problems (those can be found in the Albert.io AP® Calculus AB-BC section), and instead will focus mostly on creating an AP® Calculus study plan and tips for acing the AP® Calculus exams. If you’re looking for practice problems or review articles on topics that will be on the AP® Calculus exams, feel free to check out the links scattered throughout the rest of this article, or surf around Albert.io’s AP® Calculus blog articles.

An Overview of the AP® Calculus Exams

To start, let’s talk about the format of the AP® Calculus exams. The AP® Calculus AB and BC exams are formatted in the same way but cover different material. AP® Calculus AB covers a subset of the information covered on the AP® Calculus BC exam. Both exams are divided into a multiple choice section and a free response section, and you will be given three hours and fifteen minutes in total to complete each exam. There are two multiple-choice sections and two free response sections. You will be given 60 minutes to complete the first multiple choice section, which contains 30 questions, and you will not be allowed to use a calculator. You will then be given 45 minutes to complete the second multiple choice section, which contains 15 questions, and you will be allowed to use a calculator. From there, you will move on to the first free response section, which you will be given 30 minutes to complete and which contains two questions.

Finally, you will complete the second free response section, which you will be given 60 minutes to complete and which contains four questions. Unlike the multiple choice section, you can use a calculator on the first free response section, but cannot on the second.

Feeling a bit exhausted already? Don’t worry! The exam format is nice to know so that you know what to expect when you take the exam, but you will become very familiar with it as you study for the AP® Calculus exams through practice tests and problems.

Big Ideas

So, knowing the format of the exam should be helpful for you, but that still doesn’t tell you what exactly is going to be on the exam. The Collegeboard AP® Calculus AB/BC Course and Exam Description breaks down the material that is covered in both AP® Calculus exams into four Big Ideas. We will go through each Big Idea individually to highlight what they encompass.

1. Limits (AB/BC)

The first Big Idea – Limits – can be considered the foundation that all of the other Big Ideas are based on. This section requires you to be able to compute several different types of limits and know how to apply limits at specific points of a function.

2. Derivatives (AB/BC)

The second Big Idea – Derivatives – applies the properties of limits to looking at the rate of change of a function or variable over time. This section covers several different definitions of the derivative, analysis of graphs of functions, and properties of derivatives.

3. Integrals and the Fundamental Theorem of Calculus (AB/BC)

The third Big Idea – Integrals – builds upon the first two. This section covers the topics of the Fundamental Theorem of Calculus, indefinite and definite integrals, Riemann sums, and applications of integrals (largely based in physics).

4. Series (BC only)

The fourth Big Idea – Series – is only addressed on the AP® Calculus BC exam, and can, therefore, be disregarded if you plan to take the AP® Calculus AB exam. This section covers the topics of series of numbers, power series, and the convergence or divergence of a series. Problems from this section may involve writing a power series based on a given function, using Taylor series, or estimating the sum of a series.

Learning Objectives

If the format of the AP® Calculus exams is thought of as a birds-eye view of the exam, then the Learning Objectives can be thought of as the problems on the exams themselves. The Learning Objectives of the AP® Calculus exams are the skills that Collegeboard expects students to have gained over the course of the year and are the skills that you will be tested on during the exam. The Learning Objectives can be rather specific, and there can be up to fifteen Learning Objectives for each Big Idea, so we won’t be going into detail on the specifics of each learning objective. If you are interested in learning more about what the specific Learning Objectives are, you can find them in the Collegeboard AP® Calculus AB/BC Course and Exam Description.

Resources to Gather Before Studying

AP® Calculus Collegeboard Materials

• AP® Calculus Exam and Course Description

‣ contains the Learning Objectives and Big Ideas of AP® Calculus in more detail and sample problems.

• AP® Calculus Sample Questions

‣ contains more sample questions for the AP® Calculus AB and BC exams.

‣ contains an overview of the topics covered on the AP® Calculus AB exam and in the course.

‣ contains the released free response questions from AP® exams administered in recent years.

‣ contains an overview of the topics covered on the AP® Calculus BC exam and in the course.

‣ contains the released free response questions from AP® exams administered in recent years.

AP® Calculus Videos

‣ contains a compilation of AP® Calculus videos from a range of different YouTube channels.

‣ contains instructional videos that cover topics on the AP® Calculus AB and AP® Calculus BC exams.

AP® Calculus Albert.io Posts

In addition to this article, Albert.io has tens of other articles to help you prepare for the AP® Calculus exams. These include our review articles, which can help you study for the overall exam, our Crash Course articles, which break down smaller topics on the exam into understandable pieces, and our tips articles, which give advice on how best to approach certain problems on the exams. Below are some examples of what Albert.io has to offer!

• The Ultimate List of AP® Calculus Tips

‣ contains a list of 104 (!!!) tips for acing the AP® Calculus exams.

Setting A Baseline: The Pre-Studying Practice Test

This may not be the first thing you think of as you plan out your study schedule, but the best way to begin preparing for the AP® Calculus exams is to take a practice exam! Taking a practice exam before you begin studying helps you to understand what topics you understand fairly well, and therefore do not need to spend a ton of time studying, and what topics you do not understand, and therefore need to spend more of your time studying. You should take your practice exam under the same conditions as you would take the actual AP® Calculus exam. Now, we’ll talk about specific ways to take an AP® Calculus practice exam, to best simulate taking the actual exam in May.

Conditions

In general, you should try to match the conditions that you will be taking the AP® Calculus exam in May as much as possible when taking your practice exam. Do not try to take different sections on different days, or with long breaks between the sections, as that allows you more time to recover mentally from the exam than you will be given on the exam day. Take your practice exam alone, during a time when you will not be expected to interact with other people. If possible, ask a parent or friend to proctor the exam for you, to create the most accurate testing environment. Make sure you use a calculator that is allowed on the AP® Calculus exams, as well as the appropriate writing utensils.

However, in the case of your first practice exam, you do not need to take the exam under the exact testing conditions. Be sure to record how long it takes you to finish each section, but don’t worry if you don’t finish the section in the time allotted. You will have plenty of time to become a faster and more accurate test taker as you continue to study for the exam.

Accuracy

Once you finish taking the practice exam, you should first look to see what problems you got wrong. See whether these problems fit into a certain type, such as problems that focus on Riemann Sums, or problems that use tables of values instead of formulas. This approach will give you a better idea of what types of problems you excel at, and what types of problems you need to focus on in your studies. Also, take note of which problems you answered correctly because you knew the answer, and which problems you answered correctly because you guessed. If you don’t know the answer to a question on the actual AP® Calculus exam, guessing is recommended (as you will not be penalized for incorrect answers), but knowing how to solve the problem is always a better option than guessing.

Timing

The next aspect of your practice exam results that you should look at is the amount of time it takes you to finish each section of the exam. If you’re doing the first multiple-choice section of the exam, and it takes you 75 minutes to complete, that translates to you taking two and a half minutes to finish each question. On the actual exam, you will be given 60 minutes to complete the first section, which translates to two minutes to finish each question. This gives you a goal to work towards – shaving thirty seconds off of the speed at which you finish each multiple-choice section.

If, during the exam, you notice that you’re stalling on one particular question or set of questions, take note of that! It may not be that you’re taking two and a half minutes to complete each question, but that you’re taking one and a half minutes to finish 28 of the questions and eighteen minutes to finish the last two. This is important, as it shows you that this is an area of AP® Calculus that you need to focus on when you create your study plan.

Baseline Analysis

So, you’ve taken your first practice exam, and you’re going through the exam to break down all the considerations that we’ve talked about in the past couple of sections. Here’s a step-by-step method of going through each exam section that encompasses everything we’ve talked about:

1. Determine why you got a question wrong

As you go through each question, mark the questions that you got wrong. Then, go back over the questions that you got wrong, and determine exactly why you got those questions wrong. In some cases, you may not have known how to compute the math necessary to complete the problem. In other cases, you may not have understood the wording of the question. Each of these issues requires different approaches in your study plan. For questions where you understood the question, but could not do the math, reviewing the topics that the questions were based on may prove to be helpful to getting them right the next time. For questions where you did not understand the question, reviewing questions with similar wording and their answers may give you some insight into the true meaning of the question. Include questions that you guessed on, regardless of whether you got them right, in this analysis.

2. Determine your strengths and your weaknesses

After going through your practice exam to dissect the questions you got wrong, go through the questions that you got right (not including the ones that you guessed on). Make a list of the topics that those questions are based on. Those topics are your “Strengths.” This is not to say that you do not have to study these topics, but you do not have to focus on them as much as you might on other topics. Next, take the questions that you got wrong or guessed on, and make a list of the topics that those questions are based on. These topics are your “Weaknesses.” It is totally okay if one of these lists of longer than the other, as well as if there is overlap in topics between the two lists.

3. Make a study plan!

Using the Strengths and Weaknesses lists that you just made, we’re going to create a study plan! The main key to creating a study plan is to focus on the topics listed in the Weaknesses list by practicing them daily while making sure to reinforce the topics on your Strengths list by practicing them every couple of days. Additionally, you should schedule in regular full AP® Calculus practice exams, to evaluate your studying progress. We will talk more in detail about making study plans for different time frames in the next section.

4. Repeat!

Each time you take a new AP® Calculus practice exam, repeat the three steps above to re-evaluate your Strengths and Weaknesses lists. As topics move from your Weaknesses list to your Strengths list, you will be able to focus less on those topics and more on the topics still on your Weaknesses list. The goal is to get to the point where your Weaknesses list is empty!

Study Plans

One of the main things that we’ve talked about in this AP® Calculus review article is creating a study plan! Study plans are incredibly helpful for keeping you on track with your studying as the AP® Calculus exams approach, whether they be three months or three weeks away. We’re going to look at how to create study plans for three different time periods, so that, no matter when you decide to start studying for the AP® Calculus exams, you will be as prepared as possible for the exams come testing day.

Long Term ( more than five months)

If you’re starting to study for the AP® Calculus exams five months or more away from the exam date, congratulations! You are way ahead of the game, and your head start gives you more time to learn any material that you find difficult. It also allows you to have to study fewer days per week, which means less stress about the exam overall!

In preparing your study plan, block out a couple of hours on three or four days of the week that you plan to devote to studying. Take one or two Strengths, and assign it to one of your study days. On this day, you will only review that topic. Assign each of your other study days one or two Weaknesses. Every two weeks, take another practice exam and update your strengths and weaknesses accordingly. You do not have to review every topic on both lists within the two week period, as long as you make sure all of your Weaknesses become Strengths about two weeks before the exam date. During the two weeks before your exam, do daily practice tests (one section per day) to make sure that you are answering questions both accurately and quickly. Pay attention to the questions you get wrong during this period, and briefly review those topics after taking the practice exam.

Medium Term (2-3 months)

Most people begin studying for the AP® Calculus exams two or three months before the exam date, so if you’re starting here, you’re in good company!

This study plan happens to be similar to the Long Term Plan, in that it approaches studying using your Strengths and Weaknesses (as opposed to breaking the material down by topic, which is a method we will use for the short term study plan). Instead of picking three or four days to study, however, you’ll be studying six out of the seven days of the week. You should be studying for about two hours on each of these days. For this example, we’ll say that Sunday is your day off. Two of the six days – Wednesday and Saturday – will focus on one or two topics in your Strengths list. The other four days – Monday, Tuesday, Thursday, and Friday – will each focus on one or two topics from your Weaknesses list. Again, you do not need to review every topic on each list each week, so long as all of your Weaknesses become Strengths by a week before the exam date. You will also be taking weekly practice exams (this is easiest done at the end of the week), and will be re-evaluating your Strengths and Weaknesses according to the steps we went over earlier. A week before the exam, switch to only taking practice exams on each of your six study days. You should still note the questions that you get wrong and why, and try to review those topics after finishing the practice exam.

Short Term (less than a month)

So, you have four weeks (or less) until the AP® Calculus exam, and you’re trying to figure out where to start with your study plan. The easiest way to break down the material on the AP® Calculus is by the four Big Idea – Limits, Derivatives, Integrals, and Series. Assign each of the four weeks (or divide the number of days you have left by four, if you have less than four weeks) to one of those topics, and focus on mastering each of those Big Ideas by being able to accurate answer practice questions on those topics. Take practice exams every week, and continue to review material from previous Big Ideas at the end of each week.

For a more detailed, day-by-day short term guide to studying for the AP® Calculus exam in a month or less, check out our 30 Day Guide to Studying for AP® Calculus!

Strategies to Ace The AP® Calculus Exams

By taking a practice exam to establish your baseline knowledge, and by applying that baseline knowledge to your study plan, you will be as prepared as possible come exam day. But what about exam day itself? Sometimes, even though you study according to your plan, you get nervous or stressed before the exam and don’t do as well as you could have. With the knowledge that this may happen, we’re going to talk about some strategies to ace the AP® Calculus exams that are specifically aimed at the day of the exam.

1. Don’t study on the day of the exam!

You might think that reviewing some of the material before the start of the exam will help you to remember the material in a few hours on the exam, but this often causes students to become stressed about the material they may not completely understand. If there is a topic that you don’t understand, it is unlikely that you will be able to pick it up in a couple of minutes before the exam starts (Note: the AP® Calculus exams are typically in the morning). Instead, have a relaxed, AP® Calculus-free morning before your exam, and arrive at the test well-rested and ready to take the exam!

2. Eat breakfast (or don’t!)

There are a lot of mixed messages about whether you need to eat breakfast in the first place, let alone whether you need to do so before an exam. If you are someone who can’t get through their first class without having had something to eat that morning, you should make sure to have a delicious, hearty breakfast before you take the AP® Calculus exam. Try to stay away from sugary cereals, as they may make your energy crash during the exam. If you’re comfortable going the morning without eating anything (like me!), you can choose to skip breakfast in favor of some hot coffee or tea in the morning. Again, avoid sugary drinks like hot chocolate, as they may cause your energy to crash midway through the exam.

3. Take breaks between sections!

You will be given breaks between each section on the exam, so make the most of them! Try not to think about questions you may have answered wrong in the previous section, or worry about the questions on the next section. Instead, take a trip to the bathroom, or take a walk down the hallway, and think about anything that isn’t AP® Calculus. This gives your brain a break from the intense focus required during the testing periods of the AP® Calculus exams, and will leave you feeling more refreshed once you start the next section.

4. Skip questions you don’t know, and guess!

If you come across a question that takes you more than a minute or two to answer, or that you don’t know the answer to at all, skip it and come back to it later! For the multiple choice sections, you will likely be able to answer more questions this way, and then can come back to the questions that you skipped near the end of the time allowed for the section and make an educated guess on the answer. For the free response sections, this means skipping a section of a problem to do the next sections, or to set up the math necessary for the next sections if they are dependent on the ones that you are stuck on. Always put an answer down for a question, even if it is a guess! You will not be penalized for guessing.

In this article, we’ve outlined some AP® Calculus study plans, gone over some AP® Calculus tips, talked about the format of the AP® Calculus exams, and reviewed how to interpret the results of a practice exam.With the use of this information, you will have every resource and advantage you can to do well on the AP® Calculus exams! Here at Albert.io, we love to get feedback on our articles from the students who use them. If you have an AP® Calculus review book that you think is fantastic, or you have an article that you think we should write, don’t hesitate to reach out to us! Otherwise, happy studying!

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