Recent Tutoring Session Reviews
"Tonight, the student and I practiced evaluating improper integrals with infinite limits. Although he was apprehensive about the concept at first, he quickly picked up on it, and we were able to finish the assignment rather quickly and smoothly."
"We worked entirely on estimating areas and volumes using infinite sums. When he first looked at it on his own, the concept made no sense to him, but once I explained it, he was able to figure it out very quickly. We went through a few different types of problems that are common with this method, and he seems confident that he can handle it on his exam."
"The student has encountered anti-derivatives, or integrals, for the first time. So tonight, we focused on calculating the integral of exponent functions. We then graphed several functions and interpreted graphically what the integral means. Lastly, we covered a position-velocity problem to apply our concepts to the real world."
"Today's session with the student went really well. We continued with calculus. I taught him the product/quotient rule and the chain rule. He is picking it up really fast. He isn't struggling with anything at this time. He loves to learn new material. We have been focusing on the basics of calculus so that when we go back to the conceptual problems he will have an easier time solving them and internalizing the material. The next time we work on calculus I will be leaving him problems to solve, to prove that he remembers and understands the concepts."
"We continued to apply the rules of differentiation with trig functions. We continued to review product, quotient and chain rules with more complicated problems. The student has a mini-quiz over the general differentiation rules tomorrow, so he should try to write those rules from memory tonight (without his notes) and then check to see if he got them right."
"The student seemed to grasp the material very well. After a short amount of explanation he caught on very quickly. We mostly worked on problems from his homework having to do with finding the volumes of 3-D objects using integrals."
"We went over marginal profit, marginal revenue, and marginal cost problems. He will have a test next week with problems like the ones we did today and yesterday (projectiles). He will study the ones we did for his homework, and by next week he should be ready to do very well."
"We did a final review before the exam later tonight. The focus was on the latter part of the material that would show up, including product rule, quotient rule, and various applications of differential calculus. Some of the harder topics were certain application type problems. Overall, he has a good grasp of the bread and butter questions of this section. After reviewing the previous homework assignments together, he will continue to prepare a bit before he takes his exam."
"The student and I had a very productive tutoring session today leading up to her test Thursday. We covered mostly asymptotes and limits and continuity. She had some review material for us to look at which always helps. I think the biggest takeaways were the ability to just plug in large values to get the horizontal asymptote and x--> infinity. We looked at the powers of the exponents to tell us how these functions will behave as we x increases or decreases. We also talked about some test taking skills. I think she is well prepared for this exam and just needs to relax and go into her test with confidence. Her math foundation is very solid and her interest in the subject will ensure her continued success in math. After this test we'll get into derivatives which is the really applicable part of Calculus. I look forward to our next session."
"We reviewed parentheses, minus signs, and an occasional mis-remembered formula. As for the formulas, that will take a bit of memorization, or extra practice applying the formulas. His class moves pretty quickly and covers pretty sophisticated calc topics, so I think he is keeping up pretty well. In particular, we looked at some integrals that involved trigonometric and rational integrands. We also looked at a few problems on the derivative of an inverse function, in particular, using the formula if g and f are differentiable, and g is the inverse of f, then g'(x) = 1/(f'(g(x)))."
"We reviewed her online 25-question homework covering Riemann sums, definite integrals, "u" substitution, and area approximation using the rectangle and trapezoid methods."
"The student has a big test coming up covering volume by revolution, arc length, and polynomial series. Today we did a quick refresher to review all of the concepts and to go over the fundamental rules/strategies for each topic. I gave some background regarding each subject, going over simple derivations if necessary to help her understand the underlying logic. We made good progress today and we are meeting again on Thursday after she does some practice problems to go over any additional questions she may have. I also met briefly with him regarding his geometry homework. He had one difficult problem that he was unsure of, and I helped him figure out what he had to do to solve the problem."