Recent Tutoring Session Reviews
"The student is completing Module 1, Applications of Integration, Chap 5, homework problems. They use Integration Techniques which are in a later chapter. Though we did a little of this last week, discovering, learning how to use, and using Integration Tables from an Appendix, we did much more of it today. Learning how to use the table requires recognizing that a standard table entry can be matched with some substitution in the problem at hand, e.g.. u=X**2 (X squared), and making the corresponding integration differential, du, equivalent to the original differential, dx, from the presented integration. We did several problems during the two hours. In addition to using integration tables, we did a discrete approximation to the integral with Dx=.5, and Dx=.25, and then verified the convergence by actually evaluating the integral. As Dx became smaller, the approximation was closer to the actual integral value. We also evaluated the corresponding approximation errors to assure ourselves that the approximations were done accurately. The errors were 10% and 5%. We did three arc length integrations, and two surface area integrations. In addition to substitution to match tables, there is also integration by parts, L'Hopital's Rule, trig identities, and others. The student already recognizes that working as many problems as he can exposes him to a wider variety of detailed situations, which allow him to solve new problems more quickly because they are likely to be amenable to similar techniques. This coming week begins two weeks for Module 2, which is Integration Techniques. I recommended the student browse the chapter this weekend to become familiar with it."
"We went over the questions the student was struggling with in her summer assignment from her AP Calculus class."
"We started working on lesson 2, which included solving systems of equations by both graphing and algebraically. We did lots of practice problems, and the student did well by the end."
"We covered fxn behavior. Using only the first derivative, we solved for extrema and asymptotes and determined where fxns are increasing and decreasing. We solved polynomials, exponents, radicals, and logs. The student was quite confused initially, but she now understands the material quite well."
"In today's session, the student and I reviewed his homework. His homework involved coordinates and using the distance formula. He told me that he enjoys doing coordinates, but he had some trouble visualizing the problems. I used my dry erase board and drew an example on there. After a while, he was able to do it on his own. Then, we moved on to the distance formula problems. At first, the formula really seemed to intimidate him. I told him exactly what to do for the first problem and then had him do the next three on his own. Since he had not done square roots before, I had to explain that too, but eventually he was able to do the problems very quickly by himself."
"For our first session, the student and I looked at about three problems from a mock test for the student's math exams. We went over the binomial expansion theorem at some length, and also went over some of the more lengthy and challenging problems involving differential equations. We talked a little bit about problems solving techniques that are useful for the exams."