Anyone who has prepared for any major exam, whether it be an AP exam, SAT, or ACT, knows the cliche multiple choice tips every review book provides. “Use process of elimination,” “Read the passage first,” or “read the questions first” (for English questions), “plug and chug,” or “trial and error.” Certainly, some of these strategies are useful on the multiple choice part of the AP Calculus AB exam. If you can eliminate an answer choice or two, the odds of you picking the right answer increase. For questions that involve plugging into functions, if you cannot find a simple way to obtain the correct answer, plugging and chugging will help. This post is not meant to discount these methods, but rather provide some techniques that are somewhat specific to the AP Calculus AB (or BC for that matter) exam.
I’ll enumerate certain tips specific to AP Calculus AB.
- Be fluent with your calculator: There’s really no other way around it: you must know how to use your calculator for success on the AP exam. For the multiple choice section, there will be certain definite integration questions that will require calculator usage for a numerical answer. In addition to differentiation and integration on the home page, know how to fully utilize the graphing part of your graphing calculator. Graphing functions in questions will give you a better understanding of the questions. Moreover, there are certain functionalities in graphs you should maximize:
- Integration: On the TI-89, you can easily find the area under a curve between two points on a graph (F5 –> 7 –> enter bounds).
- Differentiation: The TI-89 also gives you the ability to find the derivative of a graph at a certain point (F5 –> 6 –> enter point).
- Intersections: Some questions may involve finding the area between curves. Finding the bounds for integration may not be as simple as you think. As a result, you should practice graphing both functions and then finding the intersection points (which are the bounds). Then, you can proceed with integration via the graph or the home page on the calculator.
- Maxima, Minima, and Inflection Points: There are commands in the graphing setting that allow you to easily find maxima, minima, and inflection points. On the TI-89, for finding maxima in a graph: F5 –> 4 –> enter bounds (the interval where you are looking for a maxima). For minima: F5 –> 3 –> enter bounds. Finally, for inflection points: F5 –> 8 –> enter bounds (the graph will notify you if there is no inflection point).
- Zeros: You should know how to find zeros on graphs since this will be significant in applications like the first and second derivative test (F5 –> 2 –> enter bounds). Note that if you are using this functionality for the first derivative test, you should graph the first derivative.
- Maxima, Minima, and Inflection Points: Both the calculator and non-calculator section will have a good amount of questions on maxima, minima, and inflection points. You should develop a strong association with these terms and the first and second derivative tests. Then, as you take the exam, when you see terms like ‘extrema’ or ‘maxima’ (or slight variations on them), you will know that you need the first derivative test to find any critical points and then either the first or second derivative test to classify any extrema. If you see the term ‘points of inflection,’ you should know to set the second derivative of the function equal to zero and then verify that the second derivative changes its sign at this point.
- For applications, know what you are looking for: The AP Calculus AB MC exam will contain several word problems with applications of differentiation and integration. In these questions, you should identify what you are to solve for. For example, if a question considers a rocket’s velocity and asks for the maximum height the rocket attains, taking the derivative of the velocity is not important. Instead, you should identify the time when the rocket changes direction from up to down. Then, you can integrate the velocity function and plug in the obtained time value to find the maximum height.
- Volumes of Solids of Revolution: Volumes of Solids of Revolution is arguably the hardest topic in AP Calculus AB. For these MC questions, you should identify the axis of rotation first. Then, you can rewrite the function (if necessary). Next, identify your bounds and write the integral. Double check what you have written and if you have taken into account the position of the axis of rotation. Finally, integrate and pick the correct answer.
- Know continuity conditions: There will be 1-2 questions that require you to find certain constants for a piecewise function to make the function continuous. Always remember that the left hand limit must equal the right hand limit. Then, write expressions for the left and right hand limits at all border points. Finally, solve for the constants and double check your answers with the continuity conditions.
- Riemann sums: Some questions will require you to approximate the area under a curve using a certain type of Riemann sum. Whether the function is provided in the form of a table or a function, identify which endpoints are important. Note the difference between a midpoint sum and a trapezoidal sum (revisit the Integration module of the AP Calculus AB course for an explanation of this concept). For some functions, there will be no difference between the two approximations but for others, the difference could be significant.
- Know your theorems: Before going into the exam, you should be comfortable with theorems such as the Mean Value Theorem, Intermediate Value Theorem, and Average Value Theorem. Then, during the exam, key words like ‘average value’ should direct you to which theorem to use.
All of these tips will help you on the AP exam. If you walk into the exam having thoroughly prepared, you should do fine. A high stress exam can become less stressful if you have done a lot of practice. Ultimately, this can be the difference between a 5 and a 4 or a 4 and a 3: PRACTICE.