Recent Tutoring Session Reviews
"The student and I reviewed log and exp functions as well as their properties. We then proceeded to solve integrals involving logs and rational polynomial fractions. I emphasized the difference between coefficients and variables as well as strategies for approaching integrals. He is proficient at integrating but needs work on some of the fundamentals of algebra two."
"We covered a basic review of concepts that have been covered in class regarding continuity. We went through specific examples of how/when functions are continuous and how to graph general functions given just information about its continuity. We then reviewed the Intermediate Value Theorem and went through two examples to determine understanding."
"The student and I spent the session today reviewing for a test he has on Friday. Most of what we covered had to do with the exponential and log functions, with a focus on differentiation and integration. We talked about the relationship between the chain rule for differentiation and u-substitutions for integrals. For differentiation, we looked at a problem that involved doing the chain rule twice to find a derivative for a complicated function. For chain rule problems, you want to break the function into a composition of functions that you can differentiate with other tools. For U-substitutions, we talked about dealing with the du and dx terms and how that often can introduce constants that need to be dealt with appropriately. We also talked about a principled approach to solving integrals. First, you look for any algebraic manipulations that can be applied to the integrand, like factoring or separating sums. Then you check to see if you need to do a substitution. Usually, the denominator of a rational function makes a good choice for a substitution, though not always. The student has a good handle on the material but occasionally mixes up differentiation and integration techniques. We talked about staying organized and taking time to check our work when we do complicated problems. The student still has plenty of practice problems from his review sheet to work on. I told him I'd be available to answer any questions he may have via email."
"The student has a test on Friday so we focused on reviewing material. I made up a short quiz covering the algebraic techniques that we had covered in our last session. She did well, but was a little unsure of techniques involving conjugates of square root functions. I used the rest of the session to reinforce the idea of the conjugate and why it can be used with derivative expressions that involve square roots."
"I helped the student with a worksheet on the chain rule. She understood the basics for her homework. I gave her a more advanced problem from the book that combined the chain rule and finding maximums (from the previous week) which she was able to do."
"Today the student and I went over some simple antidifferentiation problems as well as natural log derivation. We also did some practice problems involving the product and quotient rules. He seems to have a solid understanding of these topics now."