Quick Review of Topics in Calculus: Application of Derivatives (Quick Review Notes)

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A standard scientific calculator has everything you need. The on-line exercises correspond to these exercises in the text. In previous years we had regular evening times where students could walk in to get help. There wasn't enough demand and on many evenings no students showed up, so we're trying something different this year. There are currently 8 upperclass students who you may contact to set up one or more tutoring lessons. Their names and email addresses will be sent to you by email.

The department will pay these students by the hours they work, so please contact them for help. That comes to about five to nine hours outside of class on average per week, the actual amount varying from week to week. Here's a summary of a typical semester's hours Regular class meetings, 14 weeks, 42 hours Two evening midterms and final exam, 6 hours Reading the text and preparing for class, 4 hours per week, 56 hours Doing 28 daily homework assignments, 56 hours Meeting with tutors or in study groups, variable 4 to 12 hours Reviewing for midterms and finals, 12 hours For more detail about how to study mathematics, see About studying mathematics in general, and Calculus in particular.

Tests and final exam There will be two tests during the semester and a final examination during finals week in December. The final is cumulative, but post-midterm material will be emphasized. The tests are closed book, no calculators, and no notes allowed. You can leave your answers in terms as algebraic expressions on tests.

There may also be short quizzes given periodically throughout the semester.

Dates for the midterms and finals are tentative. First midterm. Third week in September. On chapter 2 on limits and continuity Second midterm. Fourth week in October. On chapter 3 on derivatives Final exam during finals week. Choice of two days, times to be determined. The instructors reserve the right to make changes to any information contained in this syllabus at any time during the semester. Changes will be announced, and an updated version of the syllabus will be posted here.

Calculus 1

Calculus is about the relation between a quantity and its rate of change. For an example, if the quantity is the distance from the initial position on a line at a given time, then its rate of change is velocity. If the velocity is constant, then calculus is not required: the distance travelled is the product of the elapsed time and the velocity.

Nonetheless, the distance and velocity are intimately related. If the distance at all times is known, then the velocity at any given time can be determined; and if the velocity at all times is known, then the distance at any given time can be determined. These two operations are called differentiation and integration.

Much of calculus involves analyzing and developing these concepts and their applications. Proofs are going to used throughout the course. Notes: Changing quantities The origins of calculus Chapter 1. Review of functions.


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There are a slew of things in the first chapter that you should already know. Chapter 2.

Limits and Continuity. We first must clarify the concept of derivative. In some ways it is intuitively clear that a travelling body has a velocity, or more generally, any changing quantity has a rate of change. But just what is the rate of change? The answer is that the rate of change at an instant is the limit of the average rates of change near that instant.

Remember that the AP exam is prepared by a committee that likely uses multiple resources to create the problems. You should also diversify your portfolio, so to speak, and use the internet or other good textbooks on Calculus.

Math Calculus I

There are scores of websites devoted to sample Calculus problems. I would visit as many as possible without over doing it of course. Ask for help: If you are having difficulty with certain types of problems then it would be a good idea to seek help. You might want to schedule some time with your teacher at school or perhaps look into hiring a good Calculus tutor. Help other students: Besides just getting together with other students or friends for a Calculus studying session, it would be good for you to help other students that may be having problems with understanding Calculus.

If you are very comfortable with having an above average understanding and knowledge of Calculus, it would be great for you to help someone else out. This would be a win-win situation for both of you since teaching a subject matter always reinforces the concepts with yourself. You will gain additional confidence and understanding of the basic principles of Calculus by teaching someone else. Learn from students that have taken the test before: You may already know some people that have taken the AP Calculus exam before.

If so, speak with them about their experience in taking the exam. They may have some tips for you as well. You may also ask them if they thought the test was easy or difficult. Try to get as much information from them as you can. Make sure that you are serious about preparing for the exam way in advance and start doing problems on a daily or otherwise frequent basis.

It is important that you stick to a plan and execute it properly. If you do that, it will definitely ensure that you will not be fully prepared for the exam. Always remember that practice makes perfect and just make sure that you do a lot of practicing. Again, like I said before, the more you practice, the better are your chances of getting a 4 or 5 on the AP Calculus exam.

Answer all questions: When you are finished with the exam, make sure that all questions have an answer. If you leave a question blank you will not get any points for that question. This could make the difference between a 4 or a 5 score if you leave too many questions unanswered. Wear a watch: Although there may be a clock on the wall in the room, there is no guarantee. If you feel overwhelmed or your hand cramps, take a short break. Taking thirty seconds to shake out your wrist after all that writing and look up from your paper will not be harmful.

Taking short breaks when you feel confused allow you to clear your head and relax. The AP Calculus test is supposed to be difficult.

A Gentle Introduction To Learning Calculus

While you might have done very well on unit tests in your Calculus class, most people do not score nearly as well on the AP test. This is how it is designed. This is not a test to ensure you know everything, but to measure what you do.

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Once you have turned in your exam, there is nothing more you can do for a couple of months. Do not worry too much about your results until they come out. You have worked hard all year to earn college credit, and now your studying and practice has paid off!

Calculus: Derivatives 1 - Taking derivatives - Differential Calculus - Khan Academy

We review by chapter, the day before or after each test. Thanks for the tip from Ms.

About the Test

Gisella C. Pull together the ideas of what you DO know and good things will happen. Thanks for the tip from Aaron P. Be sure to label all work correctly. For instance, it you taking the derivative be sure to label f prime x. Setting up an integral use the integral symbol etc. As a reader it is amazing how many students work a problem with no labeling or worse mix f and f prime.


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Thanks for the tip from Mr. Review all formulas the night before the exam and then go to sleep. Well, that and to learn every little detail about every little Calculus theorem there is. Thanks for the tip from Pamela L. Fike High.

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