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All AP Calculus AB Resources
Free AP Calculus AB Diagnostic Tests
AP Calculus AB Diagnostic Test 1
AP Calculus AB Diagnostic Test 2
AP Calculus AB Diagnostic Test 3
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 leadin 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 selfpaced study, or you may want to consider an AP Calculus AB tutor.
Speaking of the AP exam, it consists of a multiplechoice 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 multiplechoice 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 multiplechoice 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 multiplechoice 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 FullLength 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 conceptspecific 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 FullLength AP Calculus (AB) Practice Test periodically as you work toward test day!
Free AP Calculus AB Practice Tests
Practice Tests by Concept
Acceleration practice test
ap_calculus_abaccelerationFinding the derivative at a point practice test
ap_calculus_abfindingthederivativeatapointAnalysis of curves, including the notions of monotonicity and concavity practice test
ap_calculus_abanalysisofcurvesincludingthenotionsofmonotonicityandconcavity_aaHow to find equation of line by graphing functions practice test
ap_calculus_abhowtofindequationoflinebygraphingfunctionsInterpretation of the derivative as a rate of change practice test
ap_calculus_abinterpretationofthederivativeasarateofchange_aaModeling rates of change, including related rates problems practice test
ap_calculus_abmodelingratesofchangeincludingrelatedratesproblems_aaHow to find differentiable of rate practice test
ap_calculus_abhowtofinddifferentiableofrateFinding the second derivative of a function practice test
ap_calculus_abfindingthesecondderivativeofafunctionChain rule and implicit differentiation practice test
ap_calculus_abchainruleandimplicitdifferentiationDerivative rules for sums, products, and quotients of functions practice test
ap_calculus_abderivativerulesforsumsproductsandquotientsoffunctionsFinding value practice test
ap_calculus_abfindingvalueDifferentiable rate practice test
ap_calculus_abdifferentiablerateFinding the derivative of a function practice test
ap_calculus_abfindingthederivativeofafunctionCalculating limits practice test
ap_calculus_abcalculatinglimitsRelationship between differentiability and continuity practice test
ap_calculus_abrelationshipbetweendifferentiabilityandcontinuityFinding regions of concavity and convexity practice test
ap_calculus_abfindingregionsofconcavityandconvexityHow to find acceleration practice test
ap_calculus_abhowtofindaccelerationEquations involving derivatives practice test
ap_calculus_abequationsinvolvingderivatives_aaHow to find area of a region practice test
ap_calculus_abhowtofindareaofaregionRelationship between the increasing and decreasing behavior of ƒ and the sign of ƒ' practice test
ap_calculus_abrelationshipbetweentheincreasinganddecreasingbehaviorofandthesignof_aaFinding derivatives practice test
ap_calculus_abfindingderivativesHow to describe points by graphing functions practice test
ap_calculus_abhowtodescribepointsbygraphingfunctionsSlope of a curve at a point practice test
ap_calculus_abslopeofacurveatapoint_aaArea practice test
ap_calculus_abareaFinding regions of increasing or decreasing value practice test
ap_calculus_abfindingregionsofincreasingordecreasingvalueCorresponding characteristics of the graphs of ƒ, ƒ', and ƒ'' practice test
ap_calculus_abcorrespondingcharacteristicsofthegraphsofand_aaHow to find continuous on the interval by graphing functions practice test
ap_calculus_abhowtofindcontinuousontheintervalbygraphingfunctionsRelationship between the concavity of ƒ and the sign of ƒ'' practice test
ap_calculus_abrelationshipbetweentheconcavityofandthesignof_aaFunctions practice test
ap_calculus_abfunctionsEquations practice test
ap_calculus_abequationsAsymptotic behavior in terms of limits involving infinity practice test
ap_calculus_abasymptoticbehaviorintermsoflimitsinvolvinginfinityHow to find integral expressions practice test
ap_calculus_abhowtofindintegralexpressionsDifferential equations practice test
ap_calculus_abdifferentialequationsGraphing functions practice test
ap_calculus_abgraphingfunctionsAn intuitive understanding of continuity practice test
ap_calculus_abanintuitiveunderstandingofcontinuity_aaLines practice test
ap_calculus_ablinesUnderstanding continuity in terms of limits practice test
ap_calculus_abunderstandingcontinuityintermsoflimits_aaDifferential functions practice test
ap_calculus_abdifferentialfunctionsCalculating limits using algebra practice test
ap_calculus_abcalculatinglimitsusingalgebra_aaHow to find midpoint riemann sums practice test
ap_calculus_abhowtofindmidpointriemannsumsHow to find differential functions practice test
ap_calculus_abhowtofinddifferentialfunctionsIntegrals practice test
ap_calculus_abintegralsHow to solve for time practice test
ap_calculus_abhowtosolvefortimeFinding specific antiderivatives using initial conditions, including applications to motion along a line practice test
ap_calculus_abfindingspecificantiderivativesusinginitialconditionsincludingapplicationstomotionalongaline_aaHow to find solutions to differential equations practice test
ap_calculus_abhowtofindsolutionstodifferentialequationsHow to find value practice test
ap_calculus_abhowtofindvalueUse of the fundamental theorem to evaluate definite integrals practice test
ap_calculus_abuseofthefundamentaltheoremtoevaluatedefiniteintegrals_aaIntervals practice test
ap_calculus_abintervalsIntegral expressions practice test
ap_calculus_abintegralexpressionsBasic properties of definite integrals (additivity and linearity) practice test
ap_calculus_abbasicpropertiesofdefiniteintegralsadditivityandlinearity_aaHow to find rate of change practice test
ap_calculus_abhowtofindrateofchangeHow to find the meaning of functions practice test
ap_calculus_abhowtofindthemeaningoffunctionsHow to write equations practice test
ap_calculus_abhowtowriteequationsRiemann sums (left, right, and midpoint evaluation points) practice test
ap_calculus_abriemannsumsleftrightandmidpointevaluationpoints_aaTrapezoidal sums practice test
ap_calculus_abtrapezoidalsums_aaHow to find velocity practice test
ap_calculus_abhowtofindvelocityAntiderivatives by substitution of variables practice test
ap_calculus_abantiderivativesbysubstitutionofvariablesHow to find minimum values practice test
ap_calculus_abhowtofindminimumvaluesAll AP Calculus AB Resources
Practice Quizzes
AP Calculus AB Problem Set 120
ap_calculus_ab_120AP Calculus AB Problem Set 119
ap_calculus_ab_119AP Calculus AB Problem Set 118
ap_calculus_ab_118AP Calculus AB Problem Set 117
ap_calculus_ab_117AP Calculus AB Problem Set 116
ap_calculus_ab_116AP Calculus AB Problem Set 115
ap_calculus_ab_115AP Calculus AB Problem Set 113
ap_calculus_ab_113AP Calculus AB Problem Set 112
ap_calculus_ab_112AP Calculus AB Problem Set 111
ap_calculus_ab_111AP Calculus AB Problem Set 110
ap_calculus_ab_110All AP Calculus AB Resources
AP Calculus AB Problem Set 109
ap_calculus_ab_109AP Calculus AB Problem Set 108
ap_calculus_ab_108AP Calculus AB Problem Set 107
ap_calculus_ab_107AP Calculus AB Problem Set 106
ap_calculus_ab_106AP Calculus AB Problem Set 105
ap_calculus_ab_105AP Calculus AB Problem Set 104
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AP Calculus AB Problem Set 99
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AP Calculus AB Problem Set 86
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AP Calculus AB Problem Set 64
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