Recent Tutoring Session Reviews
"We started with absolute value equations and moved to graphing inequalities, three-variable systems of equations, and square root problems. Drawing out number lines really helped cement the ideas in his mind. Three-variable systems gave him no issue at all and he felt really confident with them. Next session, he wants to work on geometry problems."
"The student got a 94 on his most recent math test and has another test tomorrow which is comprised half of the trigonometric material from the prior test and half of the new trigonometric material. We went over a packet comprised of problems that tested his ability to apply the sine and cosine rules to various, non-right triangles. We also went over some physics problems relating plots of displacement, velocity, and acceleration to time, and how each one is related via differentiation/integration. We also touched a little bit on power."
"We split the 1.5 hour session into two parts: 50 minutes for algebra and 30 minutes for physics, considering that the student has a test for algebra on Thursday and a test for physics on Monday. He did well on both, and only needed an occasional reminder. He should be prepared for the tests."
"Today the student and I went over his online quiz that he will have to submit answers to in class the following day. He says his plan is to go through the quiz with me and then submit them. He just has to get the quizzes done to pass the exam within a month. He definitely can understand the material once he is walked through it and given practice. Since we covered all the material he needed to know to pass the quiz, I gave him no extra practice."
"Since, the student has not had his test in algebra, since the last time we met, I did some additional review with him. We also went over the topics he learned since the last time we met that are going to be on the test, including reciprocal trigonometric functions and Pythagorean identities. While he had issues at first with Pythagorean identities and reciprocal functions, by the end of the session, he was comfortable with the topics. I wrote another summary of items he needs to know by heart for the test, which is tomorrow. I included the latest two topics on it, in order to make sure he reviews it, and remembers it."
"We covered parametric equations t -> (x(t), y(t)) in more detail today, going through a set of worksheets and other examples. At times, we were finding horizontal and vertical asymptotes; e.g. dy/dx = (dy/dt) / (dx/dt) hence dy/dx = 0 when either dy/dt = 0 or dx/dt goes to infinity. There were other questions about finding tangent lines, and I showed him that sometimes you can re-express (dy/dt) / (dx/dt), which is usually a function of t, in terms of x and y (in this case it was something like dy/dx = -2 x^2 y). Because he had to calculate a bunch of tangent lines at (x, y) points, this allowed him to much more easily grab those slopes without actually solving for t in t(x) or t(y) and then substituting it back into the dy/dx expression."
"During this session, we worked on problems about finding volumes using integrals, building off what we had worked on Saturday. The student has a test coming up this week, so we were able to work on making sure her understanding of the material was strong."
"We continued working on integration, especially u-substitution and using integrals to find the areas under curves and breaking an integral into sub-integrals to find the total area between a function and the x-axis."
"We went over the last part of her final exam study guide and the student came prepared to our session with questions on how to apply the fundamental theorem of calculus and how to set up word problems using the formulas on her formula sheet. We attempted and solved a couple of free response questions and were able to synthesize a lot of the concepts covered in this course. Such as consumer and producer surplus, setting up a system of equations and applying calculus to find critical points and setting up 2 dimensional analyses."
"The student and I met for the first time to set up a regular schedule and start working on his first Calculus assignment. We covered functions, domain/range, and some geometric relationships. We have a good rapport and have developed a food schedule."
"She had an exam tomorrow so we reviewed the material that had been covered so far in class in preparation for the exam. We started by going over homework problems that she was not sure about. We then went through a practice exam together that the teacher had provided to the students in order to help them. We covered basics of logs, limits, derivatives, chain rule, quotient rule, product rule, etc."
"We had a productive session today. We reviewed basic derivative rules from last time. We discussed the interpretation of the derivative in more detail and introduced the product and quotient rules. The student understands how to apply the rules very well."