Recent Tutoring Session Reviews
"The student and I worked on his calculus homework which covered ordinary differential equations and initial value problems. The problems were based on exponential growth and he knew how to solve the problems once the calculus was done. He has a pretty good grasp of the material."
"The student and I met this morning to work on trigonometric substitution, improper integrals, and L'Hopital's Rule. She understood the procedures for improper integrals or L'Hopital's. Our practice today helped, and I have also advised her to look back over her old trig notes on her own."
"I gave a lesson/lecture covering implicit differentiation. I introduced the concept by demonstrating how to find the derivative at any point on the unit circle (x^2+y^2=1), which is not a function. This could be achieved by splitting the circle into two function (top and bottom half of circle). However, we worked through how to use implicit differentiation, which is really just an application of the chain rule, to find the slope at any point along the circle. We then worked through 2 or 3 more examples of complex relations that aren't easily described as functions. She quickly picked up on how to implement implicit differentiation. We went over how to then rearrange the equation using algebraic manipulations to get an expression for dy/dx. After this we looked over the homework assignment due this Friday."
"The student and I covered chapter 2.1, the derivative for his calc class. We went over the definition, which he knew part of and we worked through one problem and most of our time was spent sorting through the algebra of the problem, not the calculus. We discussed several techniques regarding when to substitute a new variable into a function, or the variable for a number, ways to multiply and expand polynomials, and how to show work. He understood the steps very well. I expect our next session we will cover much more material; it will be over chapter 3. He intends to go over this problem again on his own and the homework we will go over Saturday during our next session."
"The student was able to successfully complete all but 3 problems on the practice exam he was to have finished for the session today. We reviewed the concepts for each problem, and I gave him additional practice problems over each concept, which he was able to do fluently. We talked about how he felt going int o this exam, and that he is prepared for the exam. We will be meeting on Sunday to begin studying Related Rates problems to get him a head start into the next part of the curriculum."
"The student showed great improvement in her understanding and confidence about the product rule and the quotient rule. She still needs to memorize the equations associated with these rules, but overall I thought she showed much more understanding and skill this week. She has a test next week, and as I told her today, she needs to focus on memorizing the rules and breaking the problems down into smaller segments to more easily solve them."
"Today we went over new material. The student had independently looked through implicit differentiation and derivatives of inverse trigonometric functions. We first went through derivatives of logarithmic functions and also logarithmic differentiation. Next we went through the current homework assignment. Some of the chain rule questions posed issues when chain rule had to be applied multiple times or the chain rule was used in conjunction with other rules. We then moved on to working on questions covering implicit differentiation, which he seemed to have a good grasp on. We discussed certain tricks with these problems, such as looking for back-substitutions. He will continue to work on this homework set before next time."
"The student has a test coming up so we spent the session review concepts. He had taken an online exam that acted as a practice test and wanted to go over a few of the problems he had trouble with. For most of the problems he knew the steps to do them. He has a good understanding of the material and will be able to do well on the exam."
"We worked on integrals and derivatives involving exponentials and natural logarithms. For the most part, the student needed a review of some of the rules of dealing with exponentials and logarithms, which make the problems far easier to solve. After doing a few of the problems, he began to see the patterns of how these often appear and the kinds of manipulations and substitutions necessary to solve the problems."
"To prepare for the student's upcoming midterm, we went over the list of topics provided by the professor. We went through the practice test, paying close attention to problems with these topics and also reviewed how to sketch a graph of a function by using the derivatives and sign lines. He voiced he felt much more ready for this test and was happy to realize that he understood the concepts."
"The student had her exams the past two days. She wanted to use her time to review the old calc material. By the end she was starting to understand related rates. I gave her the assignment to do all the worked problems in her textbook on related rates."
"We went over review practice for test tomorrow. We covered integrals, but basic integrals both definite and indefinite. She has improved the most when evaluating trig functions like cscx, secx, cotx at specific x values."