All AP Calculus AB Resources
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All AP Calculus AB Resources
For many high school students, an AP course in any subject represents a serious undertaking. The large amount of content it covers, the workload it demands, and the necessary preparation it requires for its corresponding AP exam all combine to make AP classes formidable challenges. AP Calculus (AB) is certainly a demanding class for these reasons; however, by approaching the course in the right way, you can master it and attain your best score on the AP Calculus AB exam. Whether you need top Calculus tutors in Albany, Calculus tutors in Milwaukee, or top Calculus tutors in Albuquerque, working with a pro may take your studies to the next level.
AP Calculus (AB) is essentially divided into two main topics: differentiation and integration. The course usually begins with a discussion of limits and continuity, which then builds up to consider the limit definition of a derivative. From there, rules of differentiation are discussed. So, for this first part of AP Calculus (AB), it is essential to understand not only the limit of differentiation, but the different rules (i.e. the power rule, quotient rule, product rule, and others) for finding a derivative of a given function. Finally, understanding the meaning of derivatives and finding critical points is also crucial to success in the class.
The second half of AP Calculus (AB) focuses on integration. This part starts with the definition of an integral and Riemann Sums (left point, right point, and midpoint) as a lead-in to the concept of an integral being the area under a given function over a specific domain. From there, techniques of integration are introduced, some of which are straightforward (i.e. the power rule of integration), and some of which are more complex (integration by substitution, integration by parts, and trigonometric substitution). The latter category often requires extensive practice, for it can be as much a challenge to know which integration technique to apply to a specific problem as it can be to evaluate the integral.
The second half of AP Calculus (AB) concludes with different applications of integration, which includes finding the volumes of solids generated by revolving a given area around a given axis. These problems also require practice, as different methods are again involved, from the shell method to the disk and washer methods. Again, the challenge is determining which method to use, in addition to actually evaluating the integral. Fortunately, on the AP exam, these types of problems either allow the use of a calculator, or simply ask for the given integral to be set up, but not evaluated. Regardless, one can almost plan on encountering a question on the AP exam that involves the volume of a solid. Varsity Tutors offers resources like a free AP Calculus AB Diagnostic Tests to help with your self-paced study, or you may want to consider an AP Calculus AB tutor.
Speaking of the AP exam, it consists of a multiple-choice section (45 questions in 1 hour and 45 minutes) and a free response section (6 questions in 90 minutes). Both sections have parts where a calculator is allowed, and parts where it is not. The multiple-choice section typically asks for an integral to be evaluated numerically, for a function to be graphed, or for both of these tasks to be accomplished. The free response section involves conceptual questions, where calculations are simple enough so as to not require a calculator. As with all AP exams, time management is essential, particularly on the multiple-choice questions. If a question proves to be too difficult, it is best either to skip it entirely, or take an educated guess (but only after eliminating at least one response). After all, all multiple-choice questions on the AP Calculus (AB) exam are worth the same number of points!
To prepare for the test, be sure to be familiar with the main topics of the course and confident in applying them in problems. Knowledge of the main theorems is also important, including the Fundamental Theorem of Calculus, the Mean Value Theorem, and the Extreme Value Theorem, to name but a few. With mastery of these, and sufficient practice, it is quite possible to score very well on the AP exam and do well in AB calculus!
If you need extra practice with AP Calculus (AB) material or are looking for a good place to start, try taking some free AP Calculus (AB) Practice Tests offered by Varsity Tutors. Each Practice Test consists of 10 to 12 AP Calculus (AB) problems; you can think of Practice Tests as being like little quizzes which you can use to hone your skills. Each question is accompanied by a detailed explanation of how to find its answer, and after finishing each Practice Test, you can compare how you did to the scores that others received, as well as view data about how long you took to answer each question. The more Practice Tests you do, the better idea you will have as to your strengths and weaknesses in AP Calculus (AB), and focusing on the material you understand the least and reviewing the material you understand well will help you prepare for the AP exam! In addition to the AP Calculus AB Practice Tests and Calculus tutoring, you may also want to consider using some of our AP Calculus AB Flashcards.
Another one of Varsity Tutors’ Learning Tools that you can take advantage of are the Full-Length AP Calculus (AB) Practice Tests. It’s not a bad idea to begin your preparation by taking one of the free online practice tests to help you create an individualized study plan. These tests are like the actual exam, giving you an opportunity to get familiar with the test’s length and scope. The results page is just like the one for the concept-specific practice tests, and includes precise explanations and helpful information on each of the relevant concepts. Plus, the complete practice tests provide the perk of streamlining your AP Calculus (AB) review by showing you which skills have you have mastered, and those you have not. Once you know what you’d like to focus on, you can use any of the other Learning Tools to brush up on your skills. To check your progress, just take a Full-Length AP Calculus (AB) Practice Test periodically as you work toward test day!
Our completely free AP Calculus AB practice tests are the perfect way to brush up your skills. Take
one of our many AP Calculus AB practice tests for a run-through of commonly asked questions. You
will receive incredibly detailed scoring results at the end of your AP Calculus AB practice test to
help you identify your strengths and weaknesses. Pick one of our AP Calculus AB practice tests now
and begin!
Practice Tests by Concept
ap_calculus_ab-acceleration
Questions: 1
Test Difficulty:
Average Time Spent: 30 secs
ap_calculus_ab-finding-the-derivative-at-a-point
Questions: 3
Test Difficulty:
Average Time Spent: 2 mins 43 secs
ap_calculus_ab-analysis-of-curves-including-the-notions-of-monotonicity-and-concavity_aa
Questions: 1
Test Difficulty:
Average Time Spent: 28 mins
ap_calculus_ab-how-to-find-equation-of-line-by-graphing-functions
Questions: 1
Test Difficulty:
Average Time Spent: 2 mins 40 secs
ap_calculus_ab-interpretation-of-the-derivative-as-a-rate-of-change_aa
Questions: 2
Test Difficulty:
Average Time Spent: 1 mins 49 secs
ap_calculus_ab-modeling-rates-of-change-including-related-rates-problems_aa
Questions: 1
Test Difficulty:
ap_calculus_ab-how-to-find-differentiable-of-rate
Questions: 1
Test Difficulty:
Average Time Spent: 57 secs
ap_calculus_ab-finding-the-second-derivative-of-a-function
Questions: 11
Test Difficulty:
Average Time Spent: 8 mins
ap_calculus_ab-chain-rule-and-implicit-differentiation
Questions: 12
Test Difficulty:
Average Time Spent: 15 mins
ap_calculus_ab-derivative-rules-for-sums-products-and-quotients-of-functions
Questions: 1
Test Difficulty:
Average Time Spent: 1 mins 16 secs
ap_calculus_ab-finding-value
Questions: 8
Test Difficulty:
Average Time Spent: 10 mins
ap_calculus_ab-differentiable-rate
Questions: 1
Test Difficulty:
Average Time Spent: 3 mins
ap_calculus_ab-finding-the-derivative-of-a-function
Questions: 13
Test Difficulty:
Average Time Spent: 1 mins 47 secs
ap_calculus_ab-calculating-limits
Questions: 2
Test Difficulty:
Average Time Spent: 1 mins 3 secs
ap_calculus_ab-relationship-between-differentiability-and-continuity
Questions: 1
Test Difficulty:
Average Time Spent: 2 mins 8 secs
ap_calculus_ab-finding-regions-of-concavity-and-convexity
Questions: 4
Test Difficulty:
Average Time Spent: 2 mins 7 secs
ap_calculus_ab-how-to-find-acceleration
Questions: 1
Test Difficulty:
Average Time Spent: 2 mins 42 secs
ap_calculus_ab-equations-involving-derivatives_aa
Questions: 12
Test Difficulty:
Average Time Spent: 12 mins
ap_calculus_ab-how-to-find-area-of-a-region
Questions: 4
Test Difficulty:
Average Time Spent: 31 mins
ap_calculus_ab-relationship-between-the-increasing-and-decreasing-behavior-of-and-the-sign-of_aa
Questions: 3
Test Difficulty:
ap_calculus_ab-finding-derivatives
Questions: 40
Test Difficulty:
Average Time Spent: 29 mins
ap_calculus_ab-how-to-describe-points-by-graphing-functions
Questions: 1
Test Difficulty:
Average Time Spent: 18 secs
ap_calculus_ab-slope-of-a-curve-at-a-point_aa
Questions: 2
Test Difficulty:
Average Time Spent: 55 secs
ap_calculus_ab-area
Questions: 4
Test Difficulty:
Average Time Spent: 3 mins
ap_calculus_ab-finding-regions-of-increasing-or-decreasing-value
Questions: 5
Test Difficulty:
Average Time Spent: 4 mins
ap_calculus_ab-corresponding-characteristics-of-the-graphs-of-and_aa
Questions: 1
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ap_calculus_ab-how-to-find-continuous-on-the-interval-by-graphing-functions
Questions: 1
Test Difficulty:
Average Time Spent: 41 secs
ap_calculus_ab-relationship-between-the-concavity-of-and-the-sign-of_aa
Questions: 1
Test Difficulty:
ap_calculus_ab-functions
Questions: 40
Test Difficulty:
Average Time Spent: 21 mins
ap_calculus_ab-equations
Questions: 40
Test Difficulty:
Average Time Spent: 26 mins
ap_calculus_ab-asymptotic-behavior-in-terms-of-limits-involving-infinity
Questions: 1
Test Difficulty:
ap_calculus_ab-how-to-find-integral-expressions
Questions: 35
Test Difficulty:
Average Time Spent: 30 mins
ap_calculus_ab-differential-equations
Questions: 8
Test Difficulty:
Average Time Spent: 17 mins
ap_calculus_ab-graphing-functions
Questions: 4
Test Difficulty:
Average Time Spent: 4 mins
ap_calculus_ab-an-intuitive-understanding-of-continuity_aa
Questions: 2
Test Difficulty:
Average Time Spent: 7 mins
ap_calculus_ab-lines
Questions: 1
Test Difficulty:
Average Time Spent: 1 mins 49 secs
ap_calculus_ab-understanding-continuity-in-terms-of-limits_aa
Questions: 1
Test Difficulty:
Average Time Spent: 26 secs
ap_calculus_ab-differential-functions
Questions: 14
Test Difficulty:
Average Time Spent: 7 mins
ap_calculus_ab-calculating-limits-using-algebra_aa
Questions: 4
Test Difficulty:
Average Time Spent: 2 mins 7 secs
ap_calculus_ab-how-to-find-midpoint-riemann-sums
Questions: 1
Test Difficulty:
ap_calculus_ab-how-to-find-differential-functions
Questions: 14
Test Difficulty:
Average Time Spent: 7 mins
ap_calculus_ab-integrals
Questions: 40
Test Difficulty:
Average Time Spent: 19 mins
ap_calculus_ab-how-to-solve-for-time
Questions: 2
Test Difficulty:
Average Time Spent: 1 mins 21 secs
ap_calculus_ab-finding-specific-antiderivatives-using-initial-conditions-including-applications-to-motion-along-a-line_aa
Questions: 1
Test Difficulty:
ap_calculus_ab-how-to-find-solutions-to-differential-equations
Questions: 8
Test Difficulty:
Average Time Spent: 6 mins
ap_calculus_ab-how-to-find-value
Questions: 8
Test Difficulty:
Average Time Spent: 1 mins 46 secs
ap_calculus_ab-use-of-the-fundamental-theorem-to-evaluate-definite-integrals_aa
Questions: 4
Test Difficulty:
Average Time Spent: 2 mins 9 secs
ap_calculus_ab-intervals
Questions: 1
Test Difficulty:
Average Time Spent: 28 secs
ap_calculus_ab-integral-expressions
Questions: 35
Test Difficulty:
Average Time Spent: 17 mins
ap_calculus_ab-basic-properties-of-definite-integrals-additivity-and-linearity_aa
Questions: 12
Test Difficulty:
Average Time Spent: 8 mins
ap_calculus_ab-how-to-find-rate-of-change
Questions: 5
Test Difficulty:
Average Time Spent: 2 mins 53 secs
ap_calculus_ab-how-to-find-the-meaning-of-functions
Questions: 11
Test Difficulty:
Average Time Spent: 5 mins
ap_calculus_ab-how-to-write-equations
Questions: 15
Test Difficulty:
Average Time Spent: 6 mins
ap_calculus_ab-riemann-sums-left-right-and-midpoint-evaluation-points_aa
Questions: 24
Test Difficulty:
Average Time Spent: 8 mins
ap_calculus_ab-trapezoidal-sums_aa
Questions: 12
Test Difficulty:
Average Time Spent: 7 mins
ap_calculus_ab-how-to-find-velocity
Questions: 3
Test Difficulty:
Average Time Spent: 3 mins
ap_calculus_ab-antiderivatives-by-substitution-of-variables
Questions: 1
Test Difficulty:
Average Time Spent: 1 hrs 16 mins
ap_calculus_ab-how-to-find-minimum-values
Questions: 1
Test Difficulty:
Average Time Spent: 26 secs
All AP Calculus AB Resources
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All AP Calculus AB Resources
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All AP Calculus AB Resources