# AP Calculus Review 2023

For several years now, I’ve been posting a series of notes on reviewing for the AP Calculus Exams. The questions on the AP Calculus exams, both multiple-choice and free response, fall into ten types. I’ve published posts on each. The ten types have not changed over the years, so there is not much to add. They are updated from time to time. The posts may be found under the “Blog Guide” tab above: click on AP Exam Review. The same links are below with a brief explanation of each.

I hope these will help as you review for this year’s exam.

## General information and suggestions

• AP Exam Review – Suggestions, hints, information, and other resources for reviewing. How to get started. What to tell your students. Simulated (mock) exams.
• To dx or not dx – Yes, use past exams and the scoring guideline to review, but don’t worry about the fine points of scoring; be more stringent than the readers.
• Practice Exams – A Modest Proposal Like it or not (and the AP folks certainly do not) the answers are all online. What to do about that. Don’t overlook the replies at the end of this post.

The Ten Type Questions.

Other than simply finding a limit, a derivative, an antiderivative, or evaluating a definite integral, the AP Calculus exam questions fall into these ten types. These are different from the ten units in the CED. Students are often expected to use knowledge from more than one unit in a single question.

These posts outline what each type of question covers and what students should be able to do. They include references to good questions, free-response and multiple-choice, and links to other posts on the topic.

• Type 3 questions – Graph analysis. Given the derivative often as a graph, students must answer questions about the function – extreme values, increasing, decreasing, concavity, etc.
• Type 6 questions – Differential equations. Students are asked to solve a first-order separable differential equation, work with a slope field, or other related ideas. BC students may be asked to use Euler’s Method to approximate a value and discuss the logistic equation.
• Type 7 questions – Miscellaneous. These include finding the first and second derivative of implicitly defined relation, solving a related rate problem or other topics not included in the other types.
• Type 10 questions – Sequences and Series (BC topic) Questions ask student to determine the convergence of series using various convergence tests and to write and work with a Taylor and Maclaurin series, find its radius and interval of convergence.

Also, Calc-Medic has posted a searchable database of all the AP Calculus Free-response questions from 1998 on. The link is here. While you’re there take a look at their website which has lots of resources and free lesson plans. For mor on Calc-medic see this post.

This year’s exam will be given on Monday May 8, 2023, at 8:00 am local time.

Update March 9, 2023 – Calc-medic

# AP Exam Review – General Suggestions

It will soon be time to start reviewing for the AP Calculus Exams. So, it’s time to start planning your review. For the next weeks through the beginning of April I will be posting notes for reviewing. These are not new; versions have been posted for the last few years and these are only slightly revised and updated. The post will appear on Tuesdays and Fridays for the next few weeks. Posts are intentionally scheduled before you need them, so you can plan ahead. Most people start reviewing around the beginning or middle of April.

Student Goals

During the exam review period the students’ goal is to MAKE MISTAKES!  This is how you and they can know what they don’t know and learn or relearn it. Encourage mistakes!

Ideas for reviewing for the AP Exam

Part of the purpose of reviewing for the AP calculus exams is to refresh your students’ memory of all the great things you’ve taught them during the rear. The other purpose is to inform them about the format of the exam, the style of the questions, the way they should present their answer, and how the exam is graded and scored.

Using AP questions all year is an effective way to accomplish this. Look through the released multiple-choice exams and pick questions related to whatever you are doing at the moment. Free-response questions are a little trickier since the parts of the questions come from different units. These may be adapted or used in part.

At the end of the year, I suggest you review the free-response questions by type – table questions, differential equations, area/volume, rate/accumulation, graph, etc. More detailed notes on what students needed to know about each of the ten types will be the topic of future posts on Tuesdays and Fridays over the next few weeks. Plan to spend a few days doing a selection of questions of one type so that student can see how that type of question is asked, the format of the question (i.e. does it start with an equation, a table, or a graph), and the various topics that are tested. Then go onto the next type. Many teachers keep a collection of past free-response questions filed by type rather than year. This makes it easy to study them by type. The “types” do not align exactly with the units of the Course and Exam Description (CED) since parts of each question often come from different units.

Simulated Exam

Plan to give a simulated (mock) exam. Full exams from past years are available. The free-response questions through 2021 are available here for AB and here for BC. The secure 2014 – 2019 exams are available through your audit website. If possible, find a time when your students can take an entire exam in one sitting (3.25 hours). Teachers often do this on a weekend day or in the evening. This will give your students a feel for what it is like to work calculus problems under test conditions. If you cannot get 3.25 hours to do this, give the sections in class using the prescribed time. Some teachers schedule several simulated exams. Of course, you need to correct them and go over the most common mistakes.

Be aware that all the exams (yes, including the secure exams unfortunately) are available online. Students can find them easily. Here is a modest proposal for how to deal with this:

Don’t grade the practice exam or count it as part of the students’ averages.

Athletes are not graded on their practices, only the game counts. Athletes practice to maintain their skills and improve on their weakness. Make it that way with your practice tests.

Calculus students are intelligent. Explain to them why you are asking them to take a practice exam. Explain how making mistakes is a good thing because it helps them find their weaknesses so they can eliminate them. Use the simulated exam to maintain their skills and find their weakness. This will help them do better on the real exam.  By taking the pressure of a grade away, students can focus on improvement.

Directions

Print a copy of the directions for both parts of the exam and go over them with your students. For the free-response questions emphasize the need to show their work, explain that they do not have to simplify arithmetic or algebraic expressions, and explain the three-decimal place consideration. Be sure they know what is expected of them. The directions are here can be found on any free response released exams. Yes, this is boiler plate stuff, but take a few minutes to go over it with your students. They should not have to see the directions for the first time on the day of the exam. This and other information is explained in detail in this article: How, not only to survive, but to prevail. Copy this article for your students!

Explain the scoring

There are 108 points available on the exam; each half (free-response and multiple-choice) is worth the same – 54 points. The number of points required for each score is set after the exams are graded and changes slightly every year.

For the AB exam, the minimum points required for each score out of 108 points are, very approximately:

• for a 5 – 69 points,
• for a 4 – 52 points,
• for a 3 – 40 points,
• for a 2 – 28 points.

The numbers are similar for the BC exams are again very approximately:

• for a 5 – 68 points,
• for a 4 – 58 points,
• for a 3 – 42 points,
• for a 2 – 34 points.

The actual numbers vary from year to year, but that is not important. What is important for students to know is that they may omit or get a number of questions wrong and still earn a good score. Students may not be used to this (since they skip or get so few questions wrong on your tests!). They should not panic or feel they are doing poorly if they miss a few questions. If they understand and accept this in advance they will calm down and do better on the exams. Help them understand they should gather as many points as they can, and not be too concerned if they cannot get them all. Doing only the first 2 parts of a free-response question will probably put them at the mean for that question. Remind them not to spend time on something that’s not working out, or that they don’t feel they know how to do.

Resources for reviewing

How, Not Only to Survive, but to Prevail… – Notes and advice for your students. You may copy and duplicate this for your class.

Calculator Use on the AP Exams – hints and instruction.

Ted Gott’s Multiple-choice Index – an excel spreadsheet searchable by topic, and referenced to the CED by Learning Objectives (LO) and Essential Knowledge (EK)

Type Analysis 2018 a listing of the questions on both free-response and multiple-choice questions by type, so you can find them easily.

NEW: Searchable index to all FR questions since 1998 is here https://www.calc-medic.com/ap-calc-free-response-questions

Revised March 8,2022, March 12, 2023

# 2021 Review Notes

About this time of year, I have been posting notes on reviewing and on the ten types of problems that usually appear on the AP Calculus Exams AB and BC. Since the types do not change, I am posting all the links below. They are only slightly revised from last year. You can also find them under “AP Exam Review” on the black navigation bar above.

Each link provides a list of “What students should know” and links to other post and questions from past exams related to the type under consideration.

Note that the 10 Types are not the same as the 10 Units in the Fall 2020 Course and Exam Description. This is because many of the exam questions have parts from different units.

Here are the links to the various review posts:

When assigning past exams questions for review (and you should assign past exam question), keep in mind that students can find the scoring standards online. Even though the AP program forbids this and makes every effort to prevent them from being posted, they are there. Students can “research” the solution. Keep this in mind when assigning questions from past exams. Here is a suggestion Practice Exams – A Modest Proposal

# Reviewing Resources 2022

This is a list of links to some resources for reviewing.

The 2020 AP Calculus AB and BC Course and Exam Description (CED) The 10 units in this document list which topics may be tested on the exams. The rule of thumb is that is a topic is not listed, then it will not be tested on the exams.

How, Not Only to Survive, but to Prevail… –  Notes and advice for your students. You may copy and duplicate this for your class.

Calculator Use on the AP Exams – hints and instruction.

Ted Gott’s Free-response Index – an excel spreadsheet searchable by topic, and referenced to the 2016 CED by Learning Objectives (LO) and Essential Knowledge (EK). While this is not the current CED, the EKs and LOs are similar and will help you find past questions on the topics.

Type Analysis 2021 a listing of the questions on both free-response (1998 – 2019) and and multiple-choice questions (2003, 2008, 2012 – 2019)  by type, so you can find them easily. I will update this as soon as the 2019 exams are released.

Next Tuesday I will begin a series of posts on the various “type” questions that appear on the AP Calculus exams. The schedule is below.

# AP Exam Review

It will soon be time to start reviewing for the AP Calculus Exams. So, it’s time to start planning your review. For the next weeks through the beginning of April I will be posting notes for reviewing. There are not new; versions have been posted for the last few years and these are only slightly revised and updated. A schedule for the dates of the posts appears at the end of this post. My posts are intentionally scheduled before you will probably be needing them, so you can plan ahead. Most people start reviewing around the beginning or middle of April.

Ideas for reviewing for the AP Exam

Part of the purpose of reviewing for the AP calculus exams is to refresh your students’ memory on all the great things you’ve taught them during the rear. The other purpose is to inform them about the format of the exam, the style of the questions, the way they should present their answer, and how the exam is graded and scored.

Using AP questions all year is a good way to accomplish some of this. Look through the released multiple-choice exams and pick questions related to whatever you are doing at the moment. Free-response questions are a little trickier since the parts of the questions come from different units. These may be adapted or used in part.

At the end of the year I suggest you review the free-response questions by type – table questions, differential equations, area/volume, rate/accumulation, graph, etc. More detailed notes on what students needed to know about each of the ten types will be the topic of future posts over the next few weeks. Plan to spend a few days doing a selection of questions of one type so that student can see how that type question is asked, the format of the question (i.e. does it start with an equation, a table, or a graph), and the various topics that are tested. Then go onto the next type. Many teachers keep a collection of past free-response questions filed by type rather than year. This makes it easy to study them by type. The “types” do not align exactly with the units of the 2019 Course and Exam Description, since parts of each question often come from different units.

Student Goals

During the exam review period the students’ goal is to MAKE MISTAKES!  This is how you and they can know what they don’t know and learn or relearn it. Encourage mistakes!

Simulated Exam

Plan to give a simulated (mock) exam. Each year the College Board makes a full exam available. The free-response questions through 2019 are available here for AB  and  here for BC and the secure 2014 – 2019 exams are available through your audit website. If possible, find a time when your students can take an entire exam in one sitting (3.25 hours). Teachers often do this on a weekend day or in the evening. This will give your students a feel for what it is like to work calculus problems under test conditions. If you cannot get 3.25 hours to do this give the sections in class using the prescribed time. Some teachers schedule several simulated exams. Of course, you need to correct them and go over the most common mistakes.

Be aware that all the exams (yes, including the secure exams unfortunately) are avail online. Students can find them easily. For suggestions on how to handle this see Practice Exams – A Modest Proposal.

Explain the scoring

There are 108 points available on the exam; each half (free-response and multiple-choice) is worth the same – 54 points. The number of points required for each score is set after the exams are graded.

For the AB exam, the minimum points required for each score out of 108 point are, very approximately:

• for a 5 – 69 points,
• for a 4 – 52 points,
• for a 3 – 40 points,
• for a 2 – 28 points.

The numbers are similar for the BC exams are again very approximately:

• for a 5 – 68 points,
• for a 4 – 58 points,
• for a 3 – 42 points,
• for a 2 – 34 points.

The actual numbers vary from year to year, but that is not important. What is important is that students to know is that they can omit or get wrong many questions and still earn a good score. Students may not be used to this (since they skip or get so few questions wrong on your tests!). They should not panic or feel they are doing poorly if they miss a number of questions. If they understand and accept this in advance they will calm down and do better on the exams. Help them understand they should gather as many points as they can, and not be too concerned if they cannot get them all. Doing only the first 2 parts of a free-response question will probably put them at the mean for that question. Remind them not to spend time on something that’s not working out, or that they don’t feel they know how to do.

Directions

Print a copy of the directions for both parts of the exam and go over them with your students. Especially, for the free-response questions explain the need to show their work, explain that they do not have to simplify arithmetic or algebraic expressions, and explain the three-decimal place consideration. Be sure they know what is expected of them.The directions are here can be found on any free-response released exams. Yes, this is boiler plate stuff, but take a few minutes to go over it with your students. They should not have to see the directions for the first time on the day of the exam. Emphasize  the need to clearly show their work and justify their answers, and the three-decimal accuracy rule. This rule and lots of other information is explained in detail in this article: How, not only to survive, but to prevail. Copy this article for you students!

Resources for reviewing

How, Not Only to Survive, but to Prevail… –  Notes and advice for your students. You may copy and duplicate this for your class.

Calculator Use on the AP Exams – hints and instruction.

Ted Gott’s Mujltiple-choice Index – an excel spreadsheet searchable by topic, and referenced to the CED by Learning Objectives (LO) and Essential Knowledge (EK)

Type Analysis 2018 a listing of the questions on both free-response and multiple-choice questions by type, so you can find them easily.

Revised for 2020,

Revised March 12, 2012

# Resources for Reviewing

This is a list of links to some resources for reviewing.

How, Not Only to Survive, but to Prevail… –  Notes and advice for your students. You may copy and duplicate this for your class.

Calculator Use on the AP Exams – hints and instruction.

Ted Gott’s Mujltiple-choice Index – an excel spreadsheet searchable by topic, and referenced to the CED by Learning Objectives (LO) and Essential Knowledge (EK)

Type Analysis 2018 a listing of the questions on both free-response and multiple-choice questions by type, so you can find them easily.

Next Tuesday I will begin a series of posts on the various “type” questions that appear on the AP Calculus exams. The schedule is below.

Schedule of past and future posts for reviewing

• Tuesday February 19, 2019 – AP Exam Review
• Tuesday February 26, 2019 – Resources for reviewing – This post
• Tuesday March 5, 2019 – Type 1 questions – Rate and accumulation questions
• Friday March 8, 2019 – Type 2 questions – Linear motion problems
• Tuesday March 12, 2019 – Type 3 questions – Graph analysis problems
• Friday 15, 2019 – Type 4 questions – Area and volume problems
• Tuesday Match 19, 2019 –  Type 5 questions – Table and Riemann sum questions
• Friday March 22, 2019 – Type 6 questions – Differential equation questions
• Tuesday March 26, 2019 – Type 7 questions – miscellaneous
• Friday March 29, 2019 – Type 8 questions – Parametric and vector questions (BC topic)
• Tuesday April 1, 2019 – Type 9 questions – Polar equations
• Friday April 5 – Type 10 questions – Sequences and Series

Update: April 7, 2018 Ted Gott’s Multiple-choice index added.

Update January 31, 2019

# AP Exam Review

It will soon be time to start reviewing for the AP Calculus Exams. So, it’s time to start planning your review. For the next weeks through the beginning of April I will be posting notes for reviewing. There are not new; versions have been posted for the last few years and these are only slightly revised and updated. A schedule for the dates of the posts appears at the end of this post. My posts are intentionally scheduled before you will probably be needing them, so you can plan ahead. Most people start reviewing around the beginning or middle of April.

Exams for AP Calculus are scheduled for Tuesday May 14, 2019 at 08:00 local time.

Ideas for reviewing for the AP Exam

Part of the purpose of reviewing for the AP calculus exams is to refresh your students’ memory on all the great things you’ve taught them during the rear. The other purpose is to inform them about the format of the exam, the style of the questions, the way they should present their answer, and how the exam is graded and scored.

Using AP questions all year is a good way to accomplish some of this. Look through the released multiple-choice exams and pick questions related to whatever you are doing at the moment. Free-response questions are a little trickier since the parts of the questions come from different units. These may be adapted or used in part.

At the end of the year I suggest you review the free-response questions by type – table questions, differential equations, area/volume, rate/accumulation, graph, etc. More detailed notes on what students needed to know about each of the ten types will be the topic of future posts. For a list of the types see the posting schedule at the end of this post. Plan to spend a few days doing a selection of questions of one type so that student can see how that type question can be used to test a variety of topics. Then go onto the next type. Many teachers keep a collection of past free-response questions filed by type rather than year. This makes it easy to study them by type.

Student Goals

During the exam review period the students’ goal is to MAKE MISTAKES!  This is how you and they can know what they don’t know and learn or relearn it. Encourage mistakes.

Simulated Exam

Plan to give a simulated (mock) exam. Each year the College Board makes a full exam available. The exams for 1998, 2003, 2008, and 2012 are available at AP Central  and the secure 2013 – 2017 exams are available through your audit website. If possible, find a time when your students can take an entire exam in one sitting (3.25 hours). Teachers often do this on a weekend day or in the evening. This will give your students a feel for what it is like to work calculus problems under test conditions. If you cannot get 3.25 hours to do this give the sections in class using the prescribed time. Some teachers schedule several simulated exams. Of course, you need to correct them and go over the most common mistakes.

Be aware that all the exams (yes, including the secure exams unfortunately) are avail online. Students can find them easily. For suggestions on how to handle this see Practice Exams – A Modest Proposal.

Explain the scoring

There are 108 points available on the exam; each half (free-response and multiple-choice) is worth the same – 54 points. The number of points required for each score is set after the exams are graded.

For the AB exam, the minimum points required for each score out of 108 point are, very approximately:

• for a 5 – 69 points,
• for a 4 – 52 points,
• for a 3 – 40 points,
• for a 2 – 28 points.

The numbers are similar for the BC exams are again very approximately:

• for a 5 – 68 points,
• for a 4 – 58 points,
• for a 3 – 42 points,
• for a 2 – 34 points.

The actual numbers are not what is important. What is important is that students to know is that they can omit or get wrong many questions and still earn a good score. Students may not be used to this (since they skip or get so few questions wrong on your tests!). They should not panic or feel they are doing poorly if they miss a number of questions. If they understand and accept this in advance they will calm down and do better on the exams. Help them understand they should gather as many points as they can, and not be too concerned if they cannot get them all. Doing only the first 2 parts of a free-response question will probably put them at the mean for that question. Remind them not to spend time on something that’s not working out, or that they don’t feel they know how to do.

Directions

Print a copy of the directions for both parts of the exam and go over them with your students. Especially, for the free-response questions explain the need to show their work, explain that they do not have to simplify arithmetic or algebraic expressions, and explain the three-decimal place consideration. Be sure they know what is expected of them.The directions are here: AB Directions and BC Directions. Yes, this is boiler plate stuff, but take a few minutes to go over it with your students. They should not have to see the directions for the first time on the day of the exam. Emphasize  the need to clearly show their work and justify their answers, and the three-decimal accuracy rule. This rule and lots of other information is explained in detail in this article: How, not only to survive, but to prevail. Copy this article for you students!

Schedule of future posts for reviewing for the 2019 Exams

Exams for AP Calculus are Tuesday May 14, 2019 at 08:00 local time

• Tuesday February 26, 2019 – Resources for reviewing
• Tuesday March 5, 2019 – Type 1 questions – Rate and accumulation questions
• Friday March 8, 2019 – Type 2 questions – Linear motion problems
• Tuesday March 12, 2019 – Type 3 questions – Graph analysis problems
• Friday 15, 2019 – Type 4 questions – Area and volume problems
• Tuesday Match 19, 2019 –  Type 5 questions – Table and Riemann sum questions
• Friday March 22, 2019 – Type 6 questions – Differential equation questions
• Tuesday March 26, 2019 – Type 7 questions – miscellaneous
• Friday March 29, 2019 – Type 8 questions – Parametric and vector questions (BC topic)
• Tuesday April 1, 2019 – Type 9 questions – Polar equations
• Friday April 5 – Type 10 questions – Sequences and Series

Revised for 2019