The AP Calculus Exam will be here before you know it, and hordes of students worldwide will start cramming in the weeks leading up to the test. While that's better than not studying at all for the exam, I've always been a believer in getting ahead during the school year so that AP Exam season isn't such a pain in the Spring. The goal of this post is to lay out a few simple steps students can take all year long so that they're ready for test day when they get there and not scrambling just before a very difficult exam. But before we get started, here's a brief note about what to expect on the AP Exam itself.
The AP Calculus Exam, both AB and BC, consists of two parts: Multiple Choice and Free Response. Both weight equally in your overall exam score, so it's important to be ready for both styles of questions. Multiple Choice questions are shorter and tend to focus purely on whether the student can perform the steps necessary to solve the problem. The problems may be difficult, for sure, but they tend to be straightforward and directly test the student's math ability. The Free Response section, which many students find more challenging, lays out in-depth scenarios and asks the student to select and apply the appropriate skills to the scenario presented. This is an important distinction, because Free Response Questions require that the student not only be able to perform the skill itself, but also understand why it works how it does and what kinds of contexts it might be useful in. This leads us to our first tip for success on test day.
Understand the Meaning, Not Just the Steps
All year long, make sure to understand what different math concepts mean in practice, not just how to do the steps. Students sometimes focus in a given unit on memorizing the correct series of steps to generate a correct response, and while that's helpful, it's only part of what's needed on test day. Free Response Questions, in particular, don't announce what concept they are testing, and students will need to rely on their critical thinking skills to match the math concept to the scenario in the problem. If they didn't understand the meaning of the skill they learned, they often struggle to get these questions right even if they could perform the correct steps if directly asked for them!
Nail the Foundations
Some math courses, such as Precalculus, cover a wide range of somewhat unrelated math topics. In a course like that, struggling in one unit won't necessarily spill over into the next. Unfortunately, Calculus isn't really like that. Calculus builds on itself all year long, and the skills from each unit are almost always needed to understand material later in the course. In addition, there are a couple of key moments in the course that directly lay the foundation for a few months' worth of material. Struggling with those units could be very detrimental because it could interfere with the student understanding the meaning of what they're working on later in the year (and we've already discussed how important that can be!). Students should make sure to nail the units on the Definition of the Derivative and Riemann Sums, which will typically be at the beginning of first and second semester for AB students and at the beginning and end of first semester for BC students.
Review Earlier Units
Beyond just understanding the foundations, it's important to retain how to execute problems related to those early class topics. Ironically, some of the material that I find students struggling with leading up to the AP Exam are not the more advanced topics from the end of the year, but the foundational ones. They might retain a conceptual understanding of what those topics covered, but they might not have executed a problem in several months. It often takes longer to relearn the material at the end of the year than if they had simply periodically done a few problems to keep themselves fresh. The AP Exam will test material from the whole course, though, not just the advanced topics. A little bit of review as the year goes along can keep students from having to cram to recapture early material.
The AP Exam is hard. There's no getting around that, and many students are shocked by the difficulty level when they start directly preparing for the exam toward the end of the school year. Students who have challenged themselves all year long and haven't settled for less than their best can usually rise to the occasion, and the increase in difficulty of the AP Exam doesn't feel quite so overwhelming. So don't let up as the school year progresses or take a unit off. Keep pushing! You'll be glad when you get to test day.
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