Recent Tutoring Session Reviews
"Today, we were able to prepare for the student's exam again. I'm glad it was postponed, because we definitely covered a lot tonight. We started by working through the exponential growth and logistic problems and Newton's cooling method. He did these very well. We also covered the compounding exponential functions and compared functions that compounded a certain number of times each year and functions that compounded continuously. He also did very well on these! He should to be sure he remembers all of the rules for logarithmic and exponential functions. As long as he remembers the big ones for tomorrow, he'll be able to figure out the problems the rest of the way. Very good work tonight, and I'm excited to start on the new material next time!"
"The student almost got 100% on her last quiz. So close! Her current assignment was some word problems that involved vector addition and using formulas to find angles with a calculator and the inverse cosine. The math isn't that bad for her; the tricky part is just setting up the vector diagram which is what we discussed the most. I think her understanding is solid and hopefully more work on these vector concepts would reinforce it."
"During this session, we focused on series and sequences. We talked about arithmetic and geometric series, and focused on how to find partial sums as well as sums of converging infinite geometric series. We worked on identifying which equations to use in which situation, as well as understanding sigma notation for series. Since there was an upcoming exam, we spent most of our time reviewing the chapter rather than focusing on any specific section."
"The student and I continued to review for her final exam on Thursday. She was able to do some more problems on the review sheet before our session today, which helped her brush up on some more trigonometric problems. We reviewed graphing trigonometric functions, as well as using identities to factor complicated trig functions. We went over the review sheet and made sure she knew how to do all of them before ending our session. The student thinks if she does a few more problems, she'll feel confident for her exam on Thursday."
"In preparation for tomorrow's exam we have covered 2 sections. First, breakup of a rational function into partial fractions. We covered 2 examples, one with second degree polynomial as a denominator, the other a third degree polynomial as a denominator. We have shown how breaking up a rational function into partial fractions can be useful in quickly graphing a function. This is because its asymptotes can be quickly determined. We have motivated the decomposition into partial fractions with the future use for integral calculus. The student was able to use his knowledge of solving a system of 2 or 3 linear equations with 2 or 3 unknowns to his advantage. He will be able to find coefficient of partial fractions that way. The second theme today was systems of inequalities. We have emphasized turning inequalities immediately into equalities to figure out boundaries of regions that satisfy the inequalities. We have shown two examples, one with nonlinear parabola, the other with 4 linear conditions including the 1st quadrant condition. The student was eager to have as many examples as possible to be well prepared for the test. The student is still having trouble with the basic way of adding rational entities - bringing them to the common denominator. We have clarified that for the example at hand. In many regards the student is showing much progress. However, more tutoring will be needed to bring the student to the desired A level of grades."
"We went over vectors in 3 dimensions. The student had no problem understanding the concepts (pretty much the same as last session, just an extra number added in), but needed to practice application of formulas to reduce errors. He was a little confused when it came to solving for vector components, but after a short review, understood and was able to complete problems set out to him. We also reviewed a couple of quizzes/tests he had received from previous weeks. We quickly went over his mistakes. We plan to go over the material in detail next session."