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.
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.
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.
Make it an incentive not to be concerned about a grade.
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
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Thank you Lin