Recent Tutoring Session Reviews
"Today we covered the basics of parametric equations. Specifically converting them into rectangular equations. She quickly caught onto the equations involving trig once we talked about it. I sent her some of her teacher's notes on one of the problems they worked in class."
"The student has been doing a tremendous job in Pre-Calculus. He has worked extremely hard on the material and it has shown on his grades."
"The student got a 97 on her last test and did a great job. Today, we began work on series. We started with plugging in the "n" and finding the nth term of a sequence. This was simpler than she thought. After 2 examples she felt fine. We then discussed the fundamentals of factorial. We discussed it in generalities as well as with specific cases. We saw how (2n + 2)! = (2n+2)(2n+1)(2n)! This is a concept that students in college still struggle to understand. We also worked on finding the rule for a sequence given several terms. She saw that there isn't a "step-by-step" approach - you just have to try it out. We also reviewed the usefulness of (-1)^n. We concluded with how to find the sum of an infinite geometric series (provided that the common ratio, r, has an absolute value less than 1). She also learned why any number to the power of zero is 1, and why .9999...=1. Very good work tonight!"
"This session, we finished up exponential functions. We had only learned the general form of exponential and logistic functions and learned to solve the equations by plugging in and analyzing its graph. This session, we would learn to find explicit exponential equations. Given a rate of growth/decay and an initial value, we practiced generating function equations. We had to focus on converting the rate to a proper form to use in the equation by adding one. Once an equation was produced, we could use the skills learned in last session to determine when a population would be at a certain level or what the population would be after a certain time. We learned two new types of exponential growth and decay equations. The growth had to do with doubling after a certain time while the decay was a half-life decay. We practiced doing these problems, as they have to be dealt with differently than regular exponential equations. I helped the student with his homework to close out the session."
"Most of the work today was on graphing rational functions. We started with the vertical asymptotes, then horizontal asymptotes (including zero and nonzero), as well as non-vertical asymptotes. Then, we simplified rational exponential expressions and calculated sums, products, and ratios of complex numbers. The student is showing great interest and has quick wit and a quick appreciation of simple, yet comprehensive explanations."
"Covered: Domain, End Behavior, Limits, Roots, Turning Points, Synthetic Division, Intercepts, and Increasing/Decreasing Behavior. The student has some trouble remembering which definition goes with what term. I advised him and his mother that he needs to be going over the vocabulary sheet on either a nightly or every other night basis."