Recent Tutoring Session Reviews
"We focused on the student's assigned homework problems. Concepts covered included calculating volumes with using either a disk method or a washer method. An introduction to calculating solids with the shell method was also discussed."
"We went over a few homework problems involving set theory, basic probability theory, and the binomial probability distribution. Throughout the session, I noticed that the student easily grasped the concepts once I showed her a basic example and she seemed to pick up on things very quickly. She was left with a few more homework problems to complete. No concerns."
"We solved homework problems on integration using technique trigonometric substitution. Through this exercise, the student was familiarized with trigonometric rules and was able to make fast and accurate recognition of the substitutions."
"In this session we began talking about graphing trig functions. We started by looking at sine and cosine, and noted how those functions cycle from 1 to 0 to -1, and then looked at their graphs. We went over how to find the amplitude and period of the graph, and how these numbers change if numbers are added to the functions, such as sin2x or 2 sinx. We finished up by looking at tangent graphs, which is a little more difficult because of the asymptotes, so we spent some time looking at why tangent is undefined at certain points. The student had a fairly good understanding of these graphs by the end of our session, and will work out some problems by himself to solidify the concepts."
"I worked with the student to review Partial Fraction Decomposition and Trigonometric Substitution. He had a good understanding of the first so we focused the session on Trig Substitution. We walked through a few proofs so that he could understand the core principle behind the strategy. We then worked through some examples. These problems typically tend to work like a puzzle where there are multiple methods and approaches to arriving at the right answer. Will work on more trig substitution examples next week and begin work on series."
"The student and I first reviewed the test that he took last week, on which he received an 85. Overall, the points he lost were for simple mistakes, but he understood how to do all but one of the questions. I suggested that with a little practice, the incidence of simple mistakes, such as accidentally dropping variables when working equations, would likely decrease. Then, we reviewed for his upcoming quiz on conic sections. He had a good understanding of how to write the equations of ellipses."
"The student and I reviewed what he had learned last week. He's doing well with logarithms and exponential functions. We also reviewed his homework - word problems using exponential equations."
"The student had a test on Ch 9, so we went over the study guides. She needed help converting from standard equations to other types of equations (for circles, parabolas, hyperbolas) but after I walked her through it once, she seemed to really understand everything else."
"The student has a second quiz on probability tomorrow. This test focuses on the probability of multiple events. Three questions on the last quiz were on the addition rule, multiplication rule and conditional probability (bonus question), which is actually in Chapter 12. She worked through her entire homework plus 6 additional textbook problems which focused only on multiple events and got her used to reading 2 x 2 tables. The hardest topic is conditional probability for dependent and mutually exclusive events. Some of the homework problems asked about the probability of one or another event occurring (addition rule); up to this point the questions were mainly on independent events. Now we had to consider how the probability of two events happening was altered by the occurrence of one of them. I asked her to look over problems 18-21 and one problem in Chapter 12 to reinforce her grasp of when to use each equation based on the events independence/dependence and their mutual exclusivity."
"Today we covered indefinite integrals and trigonometric substitution. The student understood the basic process, but we went more in depth about how to complete each step and correctly identify all of the substitution elements for clarity. We also covered homework information, and worked through many example problems. She has a test next week, and will be doing a review session starting on Thursday including more of the information we worked on today."
"In this session with the student we covered his homework for calculus in preparation for his quiz. We mainly discussed finding the area between two functions using integrals. We discussed conceptually what we were actually finding when doing this process. We also went over how to use geometrical shapes to do the same process. Overall a good session."
"We went through a lot of past tests and quizzes and homework problems that the student had completed. For the most part these covered Taylor and MacLaurin series -- finding them and solving problems which contained them. There was a slight conceptual difficulty where the student didn't seem to understand what a Taylor series was, so we practiced that a bit and I showed him some graphs. I tried to clarify how we could make it mathematically rigorous, and did a lot of example problems."