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Private In-Home and Online Calculus Tutoring in Mission Viejo, CA

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Session Summaries by Calculus Tutors

Mission Viejo, CA Calculus tutoring
We continued with volumes of revolution from last week. The student completed her homework problem and then we looked at several more problems using both the disc method and the washer method. I then showed her how to use her calculator to evaluate these integrals and to check her answers from the long hand method. We then looked at differential equations first solving the differential equation as an exercise in algebra and determining anti-derivatives (abstract). We then applied this to some practical examples: time of death of a murder victim and population growth of bacteria. This made more sense to the student and she was able to complete the second problem on her own. We will finish off integration next week and then we will review PreCalc as this is her first college math course for her freshman college year.
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Mission Viejo, CA Calculus tutoring
Today we covered four sections of the recent materials. Topics included derivatives of trigonometric functions, proof by mathematical induction, and derivatives of composite functions. We also investigated problems related to rate of change of a dependent quantity when an independent quantity is changing. Example, rate of change of area of square when side is changing. Another example, rate of change of displacement with time in physics. The student is showing confidence and increased ability to solve problems on her own. She is encouraged to solve additional sample problems from the sections covered on her own.
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Mission Viejo, CA Calculus tutoring
The student had a number of old exams with practice problems for her upcoming exam on Tuesday. We went through a bunch of multiple choice questions first. Then we switched to free response questions. We had some time at the end to go back to more multiple choice questions in the calculator portion. She felt good about the problems we did today.
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Mission Viejo, CA Calculus tutoring
The student and I began by reviewing the chain rule again in more detail and practiced on some example problems from his textbook. After walking through a few problems we reviewed the formal definition of the rule to set up a step-by-step approach to chain rule problems. It has become apparent that he gets a lot of value from setting up organized step-by-step approaches to problems in general, so in the future we will make sure to include those for each type of problem. The rest of the session was dedicated to reviewing and practicing implicit differentiation. I introduced him to the rules and "commandments" for those types of problems and identified the most common mistakes students make (primarily forgetting about the product rule).
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Mission Viejo, CA Calculus tutoring
In this lesson, we continued to review for the final exam. We reviewed volumes obtained by revolving regions around axes and lines. We went over both washer/discs and cylindrical shells. In many examples, following a general procedure gets the job done, but some of the trickier questions require examining and figuring out the specific scenario of the problem. I focused on having her understand where each component fits into the formula and why. She now has a solid grasp.
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Mission Viejo, CA Calculus tutoring
I gave the student two sets of practice tests for the AP exam, and we covered a good part of part I. I identify the concepts and skills that the student may need some brushing, so that she can be totally prepared for her test on Tuesday.
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