Recent Tutoring Session Reviews
"The student and I worked on finding area of polar curves today. Once she got the hang of it, she had little issue with the anti-differentiation; however, determining some of the bounds of integration proved difficult. We also practiced finding slopes of polar curves; this went more smoothly."
"Covered several examples of the relationship between surface area and volume using integrals. Derived the volume of a cone, square based pyramid, and sphere using volume of rotation technique. Left the student with a small puzzle."
"We spent a good amount of time at the beginning of this session talking about the properties of exponents and radicals. I gave her some basic formulas and we went through some examples of what expressions with exponents and radicals can be manipulated to look like. We then looked at her next section of homework which dealt with using derivatives to determine when functions are increasing and decreasing. I explained to her what derivatives are and what they tell us, then we worked through one problem together. I wrote a formula for the general rules about taking derivatives, and then we went through the process of solving a similar problem."
"During this session we continued going over derivatives. We focused on the chain rule and derivatives of trig function. The student has trouble remembering the steps for chain rule but with more practice he can master it. Overall this session went well."
"The student and I spent the session catching him up on a few new concepts that he didn't quite have a foothold in. These concepts were inverse trig functions and hyperbolic trig functions. Mostly we just worked through understanding the basic theory behind them, in future sessions I'm sure we will be dealing with more of the calc application but for now we have a good start. This was overall a very productive session without issue."
"Today's session was spend helping the student review and complete out of class assignments. Work focused on finding derivatives and related topics, with special attention to average rate of change, compound functions, and the quotient rule. We also discussed some powerful tools (Wolfram-Alpha, and advanced TI-83+ functions) for calculating and evaluating complex mathematical expressions. I encouraged him to be aware of these tools, but not rely on them to the detriment of his capacity to work problems out by hand."
"The student and I worked on calculus differentiation problems. We covered extrema and first derivatives. We plotted functions and determined extrema. We also covered a complex optimization problem involving different prices for different materials."
"Today's focus was on converting from polar to parametric equations for the purpose of computing the derivative. We also worked on sketching polar coordinates and how to figure out when kind of limacon it is. We also went back and reviewed a bit of arc length and we covered the derivation of the formula, which she had never been shown. It seemed to clear a lot of things up for her, knowing where the formula had come from."
"The student and I covered applications of first derivatives, including finding critical points, as well as using the domain of the first derivative to find where the initial function is increasing or decreasing. He seemed to follow the material quite easily. We had to use the quotient rule for derivatives, as well as the quadratic formula, to solve one of the problems, and he followed very well. He thinks a test may be coming after the break, and that will be a good opportunity to see progress."
"We started a new section on the Mean Value Theorem. The student said she understood my explanation and we were able to use it to look at the definitions of increasing and decreasing functions. Using our new definitions and theorems she was able to solve some problems. We also reviewed logs and solving inequalities."
"The student is studying for her next calculus exam, which will be Friday after she gets back from spring break. During this session we started working on a practice test that she has for her upcoming exam. We went through the first half of the practice test, which included problems asking for analysis of the concavity of functions and whether they are increasing or decreasing. We reviewed first and second derivatives, and how to calculate if a function is increasing or decreasing and concave up or down. We also went over how to check answers using a calculator. I am hopeful that this in particular will help her on her next exam, as timing is not an issue for her and she should have time to check all of her answers. With this method, on the problem that she solved incorrectly, she discovered her error on her own and was successfully able to redo the problem and find the correct solution."
"The student and I discussed concepts in calculus and in his engineering science classes. Specifically, we focused on the first derivative test and matrix algebra used to solve nodal circuit analyses. He is sharp and capable, and I enjoy working with him as he is a great student."