Ready for the AP Calculus Exam?
There are two Advanced Placement Calculus courses for high school students, AB and BC, and most schools offer both. This year, both AP Calculus exams are offered on May 9th.
The Nuts and Bolts of the AP Calculus Exams
Before you begin studying for an AP Calculus exam, let’s look at the format of the tests. Both the AB and BC AP Calculus exams are structured the same way:
- A 30-question no-calculator multiple-choice section given over 60 minutes
- A 15-question calculator-allowed multiple-choice section given over 45 minutes
- A 2-question calculator-allowed free-response section given over 30 minutes
- A 4-question no-calculator free-response section given over 60 minutes, where you are allowed to go back to the 2 calculator-allowed free-response questions but without use of the calculator
- Equal weight is given to the multiple-choice and free-response sections (54 points each for a total of 108 points).
- Multiple-choice questions are given 1.2 points if correct, and no points are given or deducted for wrong answers. Free-response questions are scored by trained math teachers, and each question can score between 0 and 9 points depending on a pre-set rubric.
- Though scaling of the AP Calculus exams varies from year to year and the BC scales tend to be slightly more forgiving, a good rule of thumb is to expect a raw score (out of 108) that is above 65 to receive a 5, any score in the 50s or low 60s to receive a 4, any score in the 40s to receive a 3, any score in the 30s to receive a 2, and any score below 30 to receive a 1.
Content Covered on the AP Calculus Exams
The AB Calculus exam covers the concepts of limits and continuity, derivatives and their applications, integration (including u-substitution but not parts or partial fractions) and its applications, slope fields, and simple differential equations. The BC exam covers everything you might see in the AB exam plus Taylor series, convergence tests for series, parametric and polar functions, integration by parts, integration by partial fraction decomposition, improper integrals, and differential equations for logistic growth.
Expert Tips: How to Succeed on the AP Calculus Exams
Since you only need to get about 60% of available points to score a 5 on either AP Calculus exam, and since you have ample time on all sections, you can strategize the exam differently than you would almost any classroom test. Due to the generous scale, students with limited study time can focus their attention on either just the multiple-choice half or just the free-response half of the exam. If you start your preparation early enough, however, you don’t have to choose and can organize a more flexible approach.
Tip #1: Whenever possible, do a problem multiple ways.
With at least two minutes per question (and 15 minutes per free-response question), timing should not be a major concern. Though it is a luxury many students can’t afford on some other tests, the opportunity to do problems two different ways – not the same way twice where you might just repeat the same mistake – will be there for many questions on the AP Calculus exam, and it will allow you to nearly guarantee that you’ve gotten a question correct.
Tip #2: Move around each section nimbly, skipping questions that stump you to put “fresh eyes” on them later.
Often, when a student is struggling with a math question, whatever the student was missing on the first view will be caught when the student returns to the question, even if the second look is just a minute later. For that reason, make a point of allowing yourself to skip questions with the intention of returning to any that you’ve skipped when you reach the end of the page or the end of the section.
Tip #3: Have a plan for the Multiple Choice section that recognizes the purpose of wrong answer choices.
Test writers know all the common errors that students make, so they incorporate those missteps into the wrong answer choices on the exam. If you take the time to examine all the choices, even after you’ve arrived at your answer, you may notice that each of the wrong answer choices represent a path that is born out of a common error. You might even realize that you have fallen into one of those errors, and that will give you the chance to fix it.
Tip #4: Have a plan for the Free Response section that maximizes point allocation.
Though there aren’t that many actual full AP Calculus exams online, you can find free-response questions, and solutions with proper point allocations, from every exam given. This will give you a good sense of what is always tested in those sections. While you are preparing, study how the points are allocated. If rubrics are included, look for the kinds of things that always lead to point deduction, like leaving off units.
Write more when you know more. Your answer should be clear and correct, but elaborating and using full sentences to explain certain steps won’t harm you if you know your stuff.
Tip #5: Value diagrams and graphs, whether they are provided or you have to draw them yourself.
Geometry and function analysis are at the core of calculus, so make use of the visual any time you get the chance. Again, time should not be a major factor, so if a sketch of a graph or diagram will help you round out your understanding of a problem, don’t skimp on your picture.
Tip #6: Use your calculator.
On the AP Calculus exams, there are a total of 17 questions where you’ll be allowed your calculator, two of which are free responses worth nine points each. Usually more than half of the multiple-choice questions on calculator-allowed sections don’t really require a calculator to get to the answer, but you should look for opportunities to use the calculator anyway, especially on questions about functions that can be graphed.
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