Recent Tutoring Session Reviews
"We discussed integration by parts and then looked at a sample free response problem from the AB exam. This was the first time the student has seen integration by parts in detail, and he did well on the problems we looked at. He struggled a little with a few small parts of the free response question that we looked at, but the answers he gave would've been enough to get a decent amount of points on the AP test."
"We covered product rule, quotient rule, and chain rule. We also finished reviewing for her exam tomorrow and completed some of her make-up quizzes from when she was sick. I left her with a study plan for the rest of the night before her exam in the morning. I would like to meet with her more regularly so we do not have to cram before her next test!"
"Today, the student was studying inverse functions, with a special focus on derivatives of inverse trig functions. We worked on how he interprets the directions; once he knew what to do, he had very little trouble doing it. We also briefly practiced finding definite integrals on the graphing calculator."
"The student has a test coming up on the first few concepts of integration (finding anti-derivatives, using rectangle approximations, properties to combine integrals, etc.). We worked through several of the suggested problems her teacher gave her on these topics. She was great at finding anti-derivatives and evaluating, but she had a little trouble visualizing the rectangle approximations. I showed her the pictures of what's going on and how the approximation is related to the exact area under the curve. I also showed her how to use her calculator to calculate all of the heights at once in a table, which she found very helpful. I looked ahead and suggested that she focus on the 1st Fundamental Theorem questions, since that can be a difficult concept at first, but the questions are pretty quick once you get it."
"Today we began our journey into Calculus. We started with solving the derivative by using the definition of a derivative, and finished by analyzing the graph behaviors associated by a function and its derivative."
"The student and I went over his test corrections and covered topics like partial fractions, trig substitutions, and u substitution where you need to use the u substitution to get x in terms of u. It was a very productive first session!"
"The student has an exam tomorrow, so we did a variety of practice problems from each section. The hardest part for him was logarithms. There are a few properties of logs for simplifying and manipulating expressions, and they haven't stuck with him. We went over it many times. Relatedly, we did derivative questions involving logarithms and chain rule, and while he knows both individually, he was struggling to combine them. I simplified it and broke it down as much as possible. Aside from those types of problems, he showed significant improvement and was solving those types of problems much better than he used to."
"Today, the student and I reviewed differentiation of exponential functions and tools to graph these functions. We discussed the preferred methods of graphing these functions, which is the use of limits (especially in the absence of identifying factors such as relative extrema and points of inflection), rather than the usual input-output chart. I provided a sheet of detailed notes for her to keep, and I will also send her additional notes in the near future. She should familiarize herself with the properties of natural logarithms, the exponential function, and the use of limits to determine the behavior of these functions. Overall, she is a bright student and able to understand things very quickly, but she will need to carefully review the information that we covered today."
"Practiced definite integral word problems with the student. I showed him an example of a basic fluid mechanics problem that uses implicit differentiation and definite integrals, that puts together these two seemingly disparate calculus concepts. We then briefly explored how to use definite integrals to solve kinematics problems."
"We went over some additional Logarithmic properties problems and began going over L'Hopital's Rule. We went through some problems in the textbook and discussed strategies on identifying when you can use L'Hopital's Rule and when you should just use simple algebra. The student seems to have a better understanding of negative exponents and is more comfortable converting them, which is a large improvement from the last couple weeks. Towards the end of the lesson we went over how to find local and absolute maximums and minimums. We also touched on how you can use the second derivative to determine concavity, which is a topic that is likely on his midterm. He has a midterm next Wednesday and should have finished a practice test by our next session so we can go over the practice exam together."
"The student has a big test coming up on volumes by revolution, arc length in Cartesian and polar coordinates, and divergence/convergence of series. In this session, we did a lot of practice problems to help her turn some of the skills to automaticity. Since working with her, I have found that giving her explanations and derivations is very beneficial for her understanding, so I also went over some of the derivations of the formulas and series convergence/divergence tests. She has a great work ethic and has strong mathematical reasoning."
"The student is very positive about the course work, which makes her a pleasure to work with. Mostly, I would say that she was totally prepared for her test and did a very good job studying the information and making herself knowledgeable about all the subject matter. We continued to discuss the limit definition of a derivative, briefly reviewed some derivative rules, function graphing, completing the square, and economics concepts. Apart from a few hiccups and a review of how to do some of these processes, she showed great skill with solving the problems and explaining her methods. I left her with a few reminders to check her answers and simplify equations before solving derivatives or graphing the functions."