 Sign In
 Tutor Bios

Test Prep
GRADUATE SCHOOL
Search 50+ Tests
Loading Page

Academic Tutoring
foreign languages
elementary tutoring
Search 350+ Subjects
Loading Page
 About
All AP Calculus BC Resources
Free AP Calculus BC Diagnostic Tests
AP Calculus BC Diagnostic Test 1
All AP Calculus BC Resources
AP Calculus BC: even the name of the course may strike fear into many students; while AP Calculus AB tests easier (“A”) and intermediate (“B”) concepts, AP Calculus BC begins with the intermediate (“B”) concepts and tests the most difficult (“C”) concepts found in an introductory calculus class. If you’re nervous about missing crucial information in your AP Calculus class, need to figure out how the AP Calculus BC exam is structured, or want to find some excellent free resources you can use while studying for AP Calculus BC, you’ve come to the right place. After reading this guide, you’ll feel less apprehensive about AP Calculus BC and ready to take on its most challenging topics.
AP Calculus BC is a course that many high school students take in order to earn college credit. Before taking AP Calculus, students should have successfully completed four years of high school math. In particular, they should have encountered and mastered advanced concepts in basic functions, analytic geometry, trigonometry, and algebra before attempting to take an AP Calculus course. AP Calculus BC courses pertain to singlevariable functions, covering all of the information taught in AP Calculus AB courses in addition to more advanced topics. Because of this, colleges usually grant students credit for whatever course they offer that typically follows their most basic introductory calculus courses. Students thus do the work of two introductory calculus classes in one AP course when taking AP Calculus BC, which makes for a course that is extremely challenging, but potentially very rewarding.
Students who successfully complete AP Calculus BC courses are invited to take the AP Calculus BC exam to demonstrate what they have learned and potentially earn college credit. The AP Calculus exam lasts for three hours and fifteen minutes and consists of a 45question, 105minute multiplechoice section and a sixquestion, 90minute freeresponse section. Each of these sections is weighted equally, and each is divided into two parts. The first part of the multiplechoice section consists of twentyeight questions and lasts for fiftyfive minutes, and during this section, students may not use calculators. The second half of the multiplechoice section lasts for fifty minutes and consists of seventeen questions; during this section, students should use graphing calculators, as some questions will require them. The AP Calculus BC exam assumes that the calculators students use can do four things: graph functions, solve for functions’ zeros, calculate a function’s derivative, and calculate a definite integral’s value. Students’ scores on the multiplechoice section of the AP Calculus BC exam are determined only by the number of correct answers they submit; incorrect answers and skipped problems do not affect their scores. So, guessing is highly encouraged on the AP Calculus BC exam, as it cannot hurt students’ scores.
Like on the exam’s multiplechoice section, the AP Calculus BC exam’s freeresponse section begins by giving students thirty minutes to answer two questions while using a graphing calculator, and concludes by giving students an hour to answer four questions without using a calculator. Students are allowed to continue to work on their answers for the first part of the free response section after the first thirty minutes have elapsed; however, they are not allowed to use calculators when continuing or editing their responses. Showing one’s work is particularly important during the freeresponse sections of the AP Calculus BC exam. After completing the AP Calculus BC exam, students not only receive a score for the exam overall, but also an AP Calculus AB subscore, which is derived from exam questions that ask about topics covered both in AP Calculus AB and in AP Calculus BC.
One of the best places to find free AP Calculus BC resources for free online is at Varsity Tutors’ Learning Tools website. In particular, you can find AP Calculus BC Practice Tests here, each of which function like a little quiz you can use to test your skills. You can focus on particular type of problem, or choose to do problems drawn from various AP Calculus BC topics; the choice is yours. After you complete a free AP Calculus BC Practice Test, you get to see such data as how well you did in comparison to other who answered the same problems, and how much time it took you to complete each problem. You also get to access full explanations for each question, so if you missed a problem, you can figure out where you went wrong and prevent yourself from making the same mistake again.
You may also like to take a FullLength AP Calculus BC Practice Test. These test your knowledge of the course content as a whole, and ask you to answer questions spanning the full range of topics you’ll need to know by the end of the year. One great way to start your review is by taking one of the complete practice tests. The results you’ll receive can help you to build an AP Calculus BC study plan that meets your needs. The feedback you’ll get from the free comprehensive online tests include the same valuable statistics you get on the topicfocused practice tests, but have the additional benefit of helping to tailor your study sessions by showing you the areas in which you’ll want to bone up. You can use any of the Learning Tools to review, and once you feel ready, you can take another FullLength AP Calculus BC Practice Test when you’d like to check your progress.
By taking advantage of all of Varsity Tutors’ free AP Calculus BC resources, you can make sure that you don’t miss or misunderstand any AP Calculus BC content, and feel completely prepared for your AP Calculus BC exam!
Free AP Calculus BC Practice Tests
Practice Tests by Concept
Derivatives practice test
ap_calculus_bcderivativesApplications of derivatives practice test
ap_calculus_bcapplicationsofderivativesEuler's method and l'hopital's rule practice test
ap_calculus_bceulersmethodandlhopitalsruleVelocity, speed, acceleration practice test
ap_calculus_bcvelocityspeedaccelerationComputation of derivatives practice test
ap_calculus_bccomputationofderivativesChain rule and implicit differentiation practice test
ap_calculus_bcchainruleandimplicitdifferentiationDerivative rules for sums, products, and quotients practice test
ap_calculus_bcderivativerulesforsumsproductsandquotientsDerivatives of parametric, polar, and vector functions practice test
ap_calculus_bcderivativesofparametricpolarandvectorfunctionsRules of basic functions: power, exponential rule, logarithmic, trigonometric, and inverse trigonometric practice test
ap_calculus_bcrulesofbasicfunctionspowerexponentialrulelogarithmictrigonometricandinversetrigonometricDerivative as a function practice test
ap_calculus_bcderivativeasafunctionEquations involving derivatives practice test
ap_calculus_bcequationsinvolvingderivatives_aaFinding maximums practice test
ap_calculus_bcfindingmaximumsGraphs of f and f' practice test
ap_calculus_bcgraphsoffandf_aaThe mean value theorem practice test
ap_calculus_bcthemeanvaluetheoremDerivative at a point practice test
ap_calculus_bcderivativeatapointDerivative defined as limit of difference quotient practice test
ap_calculus_bcderivativedefinedaslimitofdifferencequotientInstantaneous rate of change, average rate of change, and linear approximation practice test
ap_calculus_bcinstantaneousrateofchangeaveragerateofchangeandlinearapproximationSecond derivatives practice test
ap_calculus_bcsecondderivativesConcavity practice test
ap_calculus_bcconcavityInflection points practice test
ap_calculus_bcinflectionpointsFunctions, graphs, and limits practice test
ap_calculus_bcfunctionsgraphsandlimitsAsymptotic and unbounded behavior practice test
ap_calculus_bcasymptoticandunboundedbehaviorComparing relative magnitudes (exponential growth,logarithmic growth, polynomial growth) practice test
ap_calculus_bccomparingrelativemagnitudesexponentialgrowthlogarithmicgrowthpolynomialgrowthIdentifying asymptotes graphically practice test
ap_calculus_bcidentifyingasymptotesgraphically_aaContinuity practice test
ap_calculus_bccontinuityContinuity in terms of limits practice test
ap_calculus_bccontinuityintermsoflimitsLimits practice test
ap_calculus_bclimitsCalculating limits with algebra (including onesided limits) practice test
ap_calculus_bccalculatinglimitswithalgebraincludingonesidedlimits_aaEstimating limits from graphs and tables practice test
ap_calculus_bcestimatinglimitsfromgraphsandtablesParametric, polar, and vector functions practice test
ap_calculus_bcparametricpolarandvectorfunctionsParametric form practice test
ap_calculus_bcparametricformPolar form practice test
ap_calculus_bcpolarformVector form practice test
ap_calculus_bcvectorformIntegrals practice test
ap_calculus_bcintegralsApplication of integrals practice test
ap_calculus_bcapplicationofintegralsInitial conditions practice test
ap_calculus_bcinitialconditionsLength of curve, distance traveled, accumulated change, motion of curve practice test
ap_calculus_bclengthofcurvedistancetraveledaccumulatedchangemotionofcurveModeling by solving separable differential equations practice test
ap_calculus_bcmodelingbysolvingseparabledifferentialequations_aaVolume of cross sections and area of region practice test
ap_calculus_bcvolumeofcrosssectionsandareaofregionFundamental theorem of calculus and techniques of antidifferentiation practice test
ap_calculus_bcfundamentaltheoremofcalculusandtechniquesofantidifferentiationFundamental theorem of calculus with definite integrals practice test
ap_calculus_bcfundamentaltheoremofcalculuswithdefiniteintegralsImproper integrals practice test
ap_calculus_bcimproperintegralsSubstitution of variables (by parts and simple partial fractions) practice test
ap_calculus_bcsubstitutionofvariablesbypartsandsimplepartialfractionsNumerical approximations to definite integrals practice test
ap_calculus_bcnumericalapproximationstodefiniteintegralsRiemann sum: left evaluation practice test
ap_calculus_bcriemannsumleftevaluationRiemann sum: midpoint evaluation practice test
ap_calculus_bcriemannsummidpointevaluationRiemann sum: right evaluation practice test
ap_calculus_bcriemannsumrightevaluationTrapezoidal sums practice test
ap_calculus_bctrapezoidalsumsPolynomial approximations and series practice test
ap_calculus_bcpolynomialapproximationsandseriesSeries of constants practice test
ap_calculus_bcseriesofconstantsAlternating series with error bound practice test
ap_calculus_bcalternatingserieswitherrorboundGeometric series practice test
ap_calculus_bcgeometricseriesPseries practice test
ap_calculus_bcpseriesRatio test and comparing series practice test
ap_calculus_bcratiotestandcomparingseriesTaylor series practice test
ap_calculus_bctaylorseriesLagrange error bound for taylor polynomials practice test
ap_calculus_bclagrangeerrorboundfortaylorpolynomialsMaclaurin series practice test
ap_calculus_bcmaclaurinseriesMaclaurin series for exponential and trigonometric functions practice test
ap_calculus_bcmaclaurinseriesforexponentialandtrigonometricfunctionsRadius and interval of convergence of power series practice test
ap_calculus_bcradiusandintervalofconvergenceofpowerseriesTaylor polynomial approximation practice test
ap_calculus_bctaylorpolynomialapproximation_aaAll AP Calculus BC Resources
Practice Quizzes
AP Calculus BC Problem Set 29
ap_calculus_bc_29AP Calculus BC Problem Set 28
ap_calculus_bc_28AP Calculus BC Problem Set 26
ap_calculus_bc_26AP Calculus BC Problem Set 25
ap_calculus_bc_25AP Calculus BC Problem Set 22
ap_calculus_bc_22AP Calculus BC Problem Set 21
ap_calculus_bc_21AP Calculus BC Problem Set 20
ap_calculus_bc_20AP Calculus BC Problem Set 19
ap_calculus_bc_19AP Calculus BC Problem Set 18
ap_calculus_bc_18AP Calculus BC Problem Set 17
ap_calculus_bc_17All AP Calculus BC Resources
AP Calculus BC Problem Set 16
ap_calculus_bc_16AP Calculus BC Problem Set 15
ap_calculus_bc_15AP Calculus BC Problem Set 14
ap_calculus_bc_14AP Calculus BC Problem Set 13
ap_calculus_bc_13AP Calculus BC Problem Set 12
ap_calculus_bc_12AP Calculus BC Problem Set 11
ap_calculus_bc_11AP Calculus BC Problem Set 10
ap_calculus_bc_10AP Calculus BC Problem Set 9
ap_calculus_bc_9AP Calculus BC Problem Set 8
ap_calculus_bc_8AP Calculus BC Problem Set 7
ap_calculus_bc_7All AP Calculus BC Resources
AP Calculus BC Problem Set 6
ap_calculus_bc_6AP Calculus BC Problem Set 5
ap_calculus_bc_5AP Calculus BC Problem Set 4
ap_calculus_bc_4AP Calculus BC Problem Set 3
ap_calculus_bc_3AP Calculus BC Problem Set 2
ap_calculus_bc_2AP Calculus BC Problem Set 1
ap_calculus_bc_1Certified Tutor
Certified Tutor