Calculus 1 Pdf Questions And Answers

[Floriana Grundy]

Calculus Questions with solutions are given here, along with a brief concept explanation. Calculus is a branch of mathematics that deals with the continuous change in infinitesimals (differential calculus) and the integration of infinitesimals which constitutes a whole (integral calculus). It is a vast field of study; hence in this article, we will look into solving questions based on basic calculus concepts, such as limits, continuity, differentiation of functions, maxima and minima, integrals and application of derivatives and integrals.

Hence, to prove that any function is continuous, we need to show that the function satisfies the above two conditions. If the above conditions are not satisfied, then the function is discontinuous at the given point.

I find calculus to be a really interesting topic to study, and from what I've experienced it simply boils down to applying algebra to more complicated concepts. I understand calculus and can easily formulate proofs for myself as refreshers for things I don't quite remember.

However, when it comes to actually solving calculus problems, I really struggle in terms of accuracy. No matter what problem I approach, I always end up making stupid mistakes or miscalculations. For example, today I was doing a practice problem that involved applying integrals to a distance/velocity problem to find the total distance a particle traveled, given the s(t) function that represents position versus time. It took me three lengthy attempts to solve the problem before I got the correct answer, and EACH attempt paradoxically yielded three different answers (the last being the correct).

So the one solution I read in another post on Stack Exchange -- to take things slowly -- does not help, because when I solve calculus problems like a snail, I (mostly) do things correctly, but at the cost of time. This means that on timed exams, I may get more than half the questions correct, but I won't have enough time to finish the rest.

Others suggest practicing over and over to hone my skills so that I don't trip up and make these mistakes...but that doesn't help either. In fact, I've been practicing what I learned in my AP Calculus AB course for about a year now, and yet I still continue to frequently make miscalculations.

Again, what frustrates me is that I fully comprehend introductory calculus topics; it's not the application of calculus concepts or the use of formulas that gives me trouble, but rather it's maintaining accuracy while working quickly and efficiently.

Does anyone have suggestions on how I can alleviate my problem? I'm about to take a 2nd semester Calculus course in college when the Fall starts and I'm afraid that my grade will suffer if I continue to make these careless mistakes.

Documentation. Write out each step carefully, using consistent and precise notation. Don't skip steps and don't be sloppy. Each step should be understandable and justifiable, as if you were explaining to a reader what you are doing.

Double-checking your computations. This means you should always go back and review your work. It doesn't mean that you just redo the same computations. Rather, you should look at your work critically, as if you are attempting to determine whether what you wrote is in fact correct.

Reasonableness. See if your answer makes sense. If the answer must be positive, is it positive? If it must have a particular unit of measurement, does it? Another aspect to this is to try to see if there is another way to obtain a solution. If so, try an alternative computation and compare the results.

The reality is that accuracy is not a talent, but a skill that is developed through persistence and good habits; it isn't something you can suddenly develop overnight. Accuracy is a result of experience.

Take comfort in the fact that real mathematics is not done under timed conditions like the examinations. When I was an undergraduate, I too found the introductory calculus and linear algebra courses one of the hardest, simply because I could not do computations as fast as other people. But mathematics is ultimately about theorems and proofs, not computation (that's now all doable by computers anyway). I then went into pure mathematics where almost all the higher-level courses involved mostly proofs and little computation.

If the methods are different enough, it's unlikely that you'll repeat the same mistake both ways, so comparing the answers gives you a way to check. And if there's a difference, you can often use what you learned from one method to validate your intermediate results from the other and find out exactly where the mistake is.

Try to find the pattern of your mistakes. You can even write your mistakes down to get a bright image of what your mistakes are. After a while, you will find out on which part you make lots of mistakes. Thus, when you are dealing with problems, you will be wary of not redoing your mistakes.

Read the question carefully, word by word. Sometimes you go a long way to find a suitable answer to a question while the question, in fact, has wanted you to get another aspect of the problem. So, answer what question has asked you, not anything else.

Be doubtful about math questions as if they are your enemies wanting to deceive you. That is to say, when you calculated your answer, check it again, before choosing it as the final answer. Do not trust questions, some of them seem really easy that you can find the answer in second, however, they use tricky methods to deceive you to reach the wrong answer.

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:

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.

I tend to download testbanks for Pearson's TestGen application (requires instructor account at Pearson, available 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.

Though not nearly as good as some of the other suggestions here, the practice exams for AP Calculus contain decent problems. The sample multiple choice ones are buried inside the "AP Calculus Course Description" pdf.

I am looking for away to give a Calculus exam in Canvas next week and I have no idea how to do this in Canvas. I use Webassign for their homework but Webassign only has a lockdown browser. Any ideas or suggestions?

I've decided to still issue paper and pencil tests to my classes. WebAssign has allowed free access and 4 of my 7 differential equations students have used it in calculus, but the other 3 have not and I didn't want to switch over to online.

I'm making several versions of a PDF exam available as a question group inside a Canvas quiz. Once the students start the quiz in Canvas, they will get a link with a PDF. They can print it if they have a printer or write their answers on paper if they do not. It's timed and at the end of the time, they scan their work with Adobe Scan and upload it into Canvas.

I toyed with the idea of having a quiz question that was a file upload so it was all there in one spot, but it had some severe drawbacks for me. I had to do download the submissions, individually, open them with Acrobat Reader (I've got the full version), mark them up, save them, and then attach them as a submission comment to the students. They would need to have Acrobat Reader (or another reader that supports comments) to read the comments I left.

Instead, I opted for creating a separate assignment where they could submit the actual exam as a PDF. Then I get to use DocViewer to mark on the exam directly and they students don't need any special tools to read it. I also created a rubric with a criterion for each question that has the number of points that question is worth. I grade mine on a uniform scale using awesome, good, okay, fair, poor, none and so I can mark up the points and let Canvas total it. The students get to see how they did on each question, even if I don't write something on their exam with DocViewer. Then, I use a tool that I'm writing that downloads the rubric results so I have a record of how each student did.

I know that they are going to cheat. Well, I guess it depends on what you call cheating. I know if you let students be at home (which we must) in front of a computer (which we must) that has internet access (which it must), that you cannot expect them to not use resources available to them. I'm not going to use some proctoring software because there are typically ways around that as well and it puts some of our students at a disadvantage. They may not have had a webcam available and they can't go get one now and we don't want to throw that cost on them.

I'm going to put in an honor statement basically saying it's okay to use non-human resources and then make the questions the kind that students won't be able to do in the time allowed if they don't already know what they're doing. Yeah, they may pull up Maxima to do some simplification, but I do that in class as well - I don't want to spend 50 minutes doing algebra on a power series solution when we're already spending 20 minutes doing the differential equations portion. If I'm assessing (in differential equations) something that requires partial fractions or integration by parts, am I really concerned that they can do that by memory or do I want to focus on the content of the course we're on?

c80f0f1006