Recent Tutoring Session Reviews
"We covered methods of differentiation specifically the product rule, the chain rule, and the quotient rule. We covered how these rules apply to different functions, then the student completed about 6 practice problems for each rule. I then gave her a problem which combined the application of all 3 rules for differentiating a function. She was able to do this with very little prompting. She has grasped the procedural methods for solving these kinds of problems but will need further practice of application to help retain this knowledge and develop a deeper conceptual understanding."
"In this session, I introduced the student to using the Riemann Sum to estimate the area under a graph. We discussed the purpose of using this method and how to determine if the estimate will be higher or lower than the actual area. She practiced problems using the left, right, and midpoint values of the interval to calculate the Riemann sum."
"The student and I worked on using rectangles to find the area under curves. The areas were found by using the lower and upper bounds for approximations of least and greatest values of the area. We then worked on his semester final review worksheet. After this semester, the student will be working on Calculus on a pass-fail basis instead of for a grade on his own pace and terms."
"We covered material for the Calculus Final Review. The topics were difference quotient, derivatives, product and quotient rules, chain rule, and marginal revenue. The student did pretty well on the concepts but needs to avoid simple errors in algebra and arithmetic."
"We covered the student's homework 5.3. This involved concepts of integration, the fundamental theorem of calculus part 1, understanding graphs, chain rule, concavity and the second derivative test, and trigonometry. The student really needs to slow down and do every step of her work on paper."
"We worked on optimization problems involving related rates and rates of change using derivatives. We were able to complete two assignments and started working on a third assignment that she said she would be able to finish on her own, but would contact me if she needed any help."
"We worked through a hw problem set, about 30 problems. The questions were about the second fundamental theorem of calculus, the relationship between derivatives and integrals. The student got the majority of the problems correct on his own which is a major improvement since we first started meeting. He used to need help and explanation for most of the problems. He definitely knows how to take derivatives and integrals of polynomials."
"In this lesson, we reviewed for the student's upcoming exam. We went through her list of topics on the exam and did a couple practice problems from each topic. We focused more on curve sketching (asymptotes in particular), implicit differentiation and related rates. She has a solid grasp of the concepts."
"The student and I worked with integrals tonight, applying the fundamental theorem of calculus and finding geometric and graphical area as well. We were able to power through the assignment, and he picked up on processes quickly."
"Today was continuation of the graph sketching we had been doing on Sunday (using the graph of a function to construct a possible graph for it's derivative, or vice versa, etc.). We also discussed the automatic process for solving optimization problems (identify equation(s), find substitutions for all but one variable, reconcile equation then differentiate to find critical points). Her next test is early next week."
"We talked about graphing functions by using the first and second derivatives to gather clues regarding where the function was increasing or decreasing and where it was concave down or concave up. We also discussed how to find asymptotes for those functions. We worked through 4 or 5 problems and the student understood them well. She mentioned that she has received some encouraging quiz scores lately (7/8 and 4/4). We will meet twice next week to help her prepare for her final."
"In this session, we covered topics from the first and second exams to reinforce understanding, and reviewed problems from the most recently submitted homework assignment. The student and I will further review graphing discontinuities and limits. The next session will cover final exam prep."