Calculus 2 multiple choice questions

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Calculus 2 multiple choice questions

Calculus Diagnostic and Placement Exams, with Solutions Tests to determine whether you are ready to take calculus, and at what level. SUNY Buffalo has online quizzes that test you on the algebra needed for calculus. University of Colorado Calculus diagnostic test for advanced, multiple variable calculus, with solutions. University of Manitoba Calculus diagnostic test. Self scored. SMU has a sample precalculus placement exam to indicate whether you have the background to take precalculus.

Generates a multiple choice diagnostic exam, then immediately grades it and shows you the answers. From James A. Sethian, Theodore A. Slaman and W. Hugh Woodin. See also a previous calculus placement exam. University of Utah Calculus diagnostic test. Solutions are here. Vanderbilt U. Possibly some matrix theory and more advanced topics.

Kansas State University Math Trigonometry old exam archive, some with solutions. Text: Fundamentals of Trigonometry, by Swokowski and Cole. See also the Math College Algebra old exam archive, From Manitoba provincial examinations. University of Washington has an extensive archive of precalculus Math exams with solutions. Textbook: Precalculus by Collingwood and Prince. The text PDF is available free online. East Tennesse State University sample precalc exam. Georgia Tech final exam with solutions.

Textbook: Larson and Hostetler. Indiana Southeast University practice precalc final exam problems with solutions. Middle Tennesse State University sample precalculus exam. Washington University in St. Louis has a large collection of Math exams with solutions, including precalculus.

Organized by topic.

calculus 2 multiple choice questions

Also precalc 2 Mathematical Radical collection of precalculus exams with solutions. Thirty years of AP exam problems with solutions. AP free response : More AP exam problems,with solutions. Math Large collection of exams sorted by topics.These are split up into a calculator and no-calculator section.

Overall you have minutes for both of those sections, so that translates to over 2 minutes per question. Each MC question has four answer choices below it. The following tips include general advice that could apply to any test, as well as help for the AP Calculus specifically. Shaun earned his Ph. In addition, Shaun earned a B.

Shaun still loves music -- almost as much as math! Shaun has taught and tutored students in mathematics for about a decade, and hopes his experience can help you to succeed!

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High School Blog. About Shaun Ault Shaun earned his Ph. Leave a Reply Click here to cancel reply.Part A. Directions: Answer these questions without using your calculator. Which of the following statements about the graph of is not true? Then p must:. If equals. The area of the largest such rectangle is. The value of x for which the ring of largest area is obtained is. The general solution of the differential equation is a family of. Estimate dx using the Left Rectangular Rule and two subintervals of equal width.

The volume generated equals. Solutions of the differential equation whose slope field is shown here are most likely to be. The graph of g, shown below, consists of the arcs of two quarter-circles and two straight-line segments. The value of is. Which of these could be a particular solution of the differential equation whose slope field is shown here? The speed of the particle when it is at position 2, 1 is equal to. When rewritten as partial fractions, includes which of the following?

Using two terms of an appropriate Maclaurin series, estimate. Part B. Directions: Some of these questions require the use of a graphing calculator. The graph of function h is shown here. Which of these statements is are true? Graphs of functions f xg xand h x are shown below. At what point in the interval [1, 1. Over which interval s is the graph of f both increasing and concave up? Which of the following statements is true about the graph of f x in Question 62? Suppose where k is a constant.By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service.

Mathematics Educators Stack Exchange is a question and answer site for those involved in the field of teaching mathematics. It only takes a minute to sign up. I'd like to give my Calculus 1 class periodic multiple choice questions that really test conceptual understanding.

Ideally, I'd like these questions to require very little computation. I know that a lot of textbooks have true false questions, which I like, but I'm hoping to find a source of questions with more than two possible answers. Something along the following lines:. Which of the following statements must be true?

For a student who understands the derivative well, this question could be answered in under one minute with absolutely no computations.

calculus 2 multiple choice questions

Anyone know of a good source to find a bank of such questions? It would be ideal if the TeX code was available too, or if the problems were already encoded into WeBWorK or some other online homework system. Cornell's Good Questions Project has a great question bank for conceptual questions.

I tend to download testbanks for Pearson's TestGen application requires instructor account at Pearsonavailable for almost any text they produce and hunt through them for conceptual questions for this purpose. Sometimes it's a bit slim pickings in this regard, but it at least gets me started for a first semester, and then more ideas occur to me as I teach the course, and I personalize the quizzes more over time.

Sorry this is not a free online resource, but I hope it helps. Though not nearly as good as some of the other suggestions here, the practice exams for AP Calculus contain decent problems.

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Sign up to join this community. The best answers are voted up and rise to the top. Home Questions Tags Users Unanswered. Source of conceptual, multiple choice calculus questions Ask Question. Asked 4 years, 7 months ago.

Active 1 year ago. Viewed 2k times. Jared Jared 1, 11 11 silver badges 24 24 bronze badges.

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Active Oldest Votes. Collins Feb 28 '16 at Here are a set of practice problems for the Calculus II notes. Click on the " Solution " link for each problem to go to the page containing the solution.

Note that some sections will have more problems than others and some will have more or less of a variety of problems. Most sections should have a range of difficulty levels in the problems although this will vary from section to section.

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Here is a listing of sections for which practice problems have been written as well as a brief description of the material covered in the notes for that particular section. Practice Quick Nav Download. You appear to be on a device with a "narrow" screen width i.

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Due to the nature of the mathematics on this site it is best views in landscape mode. If your device is not in landscape mode many of the equations will run off the side of your device should be able to scroll to see them and some of the menu items will be cut off due to the narrow screen width. Integration by Parts — In this section we will be looking at Integration by Parts.

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We also give a derivation of the integration by parts formula. Integrals Involving Trig Functions — In this section we look at integrals that involve trig functions.

In particular we concentrate integrating products of sines and cosines as well as products of secants and tangents. We will also briefly look at how to modify the work for products of these trig functions for some quotients of trig functions. Trig Substitutions — In this section we will look at integrals both indefinite and definite that require the use of a substitutions involving trig functions and how they can be used to simplify certain integrals. Partial Fractions — In this section we will use partial fractions to rewrite integrands into a form that will allow us to do integrals involving some rational functions.

Integrals Involving Roots — In this section we will take a look at a substitution that can, on occasion, be used with integrals involving roots. In some cases, manipulation of the quadratic needs to be done before we can do the integral.

We will see several cases where this is needed in this section. Integration Strategy — In this section we give a general set of guidelines for determining how to evaluate an integral.

The guidelines give here involve a mix of both Calculus I and Calculus II techniques to be as general as possible. Improper Integrals — In this section we will look at integrals with infinite intervals of integration and integrals with discontinuous integrands in this section. Collectively, they are called improper integrals and as we will see they may or may not have a finite i. Determining if they have finite values will, in fact, be one of the major topics of this section.

Comparison Test for Improper Integrals — It will not always be possible to evaluate improper integrals and yet we still need to determine if they converge or diverge i.If you're seeing this message, it means we're having trouble loading external resources on our website. To log in and use all the features of Khan Academy, please enable JavaScript in your browser. Donate Login Sign up Search for courses, skills, and videos. Course summary.

Calculus II

Integrals review. Accumulations of change introduction : Integrals review Approximation with Riemann sums : Integrals review Summation notation review : Integrals review Riemann sums in summation notation : Integrals review Defining integrals with Riemann sums : Integrals review Fundamental theorem of calculus and accumulation functions : Integrals review.

Interpreting the behavior of accumulation functions : Integrals review Properties of definite integrals : Integrals review Fundamental theorem of calculus and definite integrals : Integrals review Reverse power rule : Integrals review Indefinite integrals of common functions : Integrals review Definite integrals of common functions : Integrals review Proof videos : Integrals review. Integration techniques.

Integrating with u-substitution : Integration techniques Integrating using long division and completing the square : Integration techniques Integrating using trigonometric identities : Integration techniques. Trigonometric substitution : Integration techniques Integration by parts : Integration techniques Integrating using linear partial fractions : Integration techniques Improper integrals : Integration techniques.

Differential equations. Differential equations introduction : Differential equations Verifying solutions for differential equations : Differential equations Sketching slope fields : Differential equations Reasoning using slope fields : Differential equations.

Applications of integrals. Average value of a function : Applications of integrals Straight-line motion : Applications of integrals Non-motion applications of integrals : Applications of integrals Area: vertical area between curves : Applications of integrals Area: horizontal area between curves : Applications of integrals Area: curves that intersect at more than two points : Applications of integrals Volume: squares and rectangles cross sections : Applications of integrals.

Volume: triangles and semicircles cross sections : Applications of integrals Volume: disc method revolving around x- and y-axes : Applications of integrals Volume: disc method revolving around other axes : Applications of integrals Volume: washer method revolving around x- and y-axes : Applications of integrals Volume: washer method revolving around other axes : Applications of integrals Arc length : Applications of integrals Calculator-active practice : Applications of integrals.

Parametric equations, polar coordinates, and vector-valued functions.

calculus 2 multiple choice questions

Parametric equations intro : Parametric equations, polar coordinates, and vector-valued functions Second derivatives of parametric equations : Parametric equations, polar coordinates, and vector-valued functions Arc length: parametric curves : Parametric equations, polar coordinates, and vector-valued functions Vector-valued functions : Parametric equations, polar coordinates, and vector-valued functions Planar motion : Parametric equations, polar coordinates, and vector-valued functions.

Polar functions : Parametric equations, polar coordinates, and vector-valued functions Area: polar regions single curve : Parametric equations, polar coordinates, and vector-valued functions Area: polar regions two curves : Parametric equations, polar coordinates, and vector-valued functions Arc length: polar curves : Parametric equations, polar coordinates, and vector-valued functions Calculator-active practice : Parametric equations, polar coordinates, and vector-valued functions.

Convergent and divergent infinite series : Series Infinite geometric series : Series nth-term test : Series Integral test : Series Harmonic series and p-series : Series Comparison tests : Series Alternating series test : Series Ratio test : Series Absolute and conditional convergence : Series.

Course challenge. Community questions.The multiple-choice section consists of two parts: Part A contains 30 multiple-choice questions for which you are not allowed to use your graphing calculator, and Part B contains 15 multiple-choice questions for which you may and in fact, will most likely need to use your calculator. A stand-alone question covers a specific topic and is not part of a set; the question that follows it covers a different topic.

Tough questions are scattered between easy and moderately difficult questions. The two-pass system, discussed next, should be used here.

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You can tweak the general idea of the two-pass system and apply it specifically to the AP Calculus exam. Picking out questions with graphs is not an especially critical way to analyze the exam questions, but some students do no more than that. You should realize that the more advanced your pacing system is, the more time you might have at the end of Section I to answer the questions that you find difficult.

To further refine your two-pass approach before Test Day, draw up two lists of exam topics. When you get ready to begin the multiple-choice section, keep these two lists in mind. On your first pass through the section, answer all the questions that deal with concepts you like and know a lot about. The overarching goal is to use the time available to answer the maximum number of questions correctly.

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This refinement of the basic two-pass system should give you a clear idea about how to approach the multiple-choice section of the AP Calculus exam. Some tests are sneakier than others. Students taking a sneaky test often have the proper facts, but get many questions wrong because of traps in the questions themselves.

The AP Calculus exam is not a sneaky test. It aims to see how much calculus knowledge you have. To do this, it asks a wide range of questions from an even wider range of calculus topics. The exam tries to cover as many different calculus facts as it can, which is why the questions jump from topic to topic. The test makers work hard to design the test so that it is comprehensive, which means that students who only know one or two calculus topics will soon find themselves struggling.

Understanding these facts about how the test is designed can help you to answer its questions. The AP Calculus exam is comprehensive, not sneaky; it makes questions hard by asking about hard subjects, not by using rhetorical tricks to create hard questions. Trust your instincts when guessing.

If you think you know the right answer, chances are that you dimly remember the topic being discussed in your AP course. The test is about knowledge, not traps, so trusting your instincts will help more often than not. Some of your educated guesses are likely to be incorrect, but again, the point is not to get a perfect score. A perfect score would certainly be nice, but most people are going to lose at least some points on the AP exam and may still get a 5. Your basic goal should be to get as good a score as you can; surviving hard questions by going with your gut feelings can help you to achieve this aim.

On other questions, though, you might have no inkling of what the correct answer should be. In that case, turn to the following key idea.


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