Recent Tutoring Session Reviews
"We went over finding the volume of solids created by rotating a certain area around the x- or y-axis. We covered both the disk and washer methods and how to identify when each method should be used. In addition, we also went over creating a solid by rotating around a horizontal or vertical axis that is not the x- or y-axis and how it changes the equations needed inside the integral. We looked at a practice problem for the AP exam that covered solids created by rotating around an axis so the student could see how this topic might come up especially in the free-response section. Lastly we looked through a practice version of the first section of the exam to see how some of the topics are presented in the multiple choice section and to get a feel for how to approach them. She is doing much better with finding the volumes of solids once we had a chance to go through a couple problems and she could see how the graph helps set up the integral."
"His teacher has finished teaching the textbook and they are reviewing for the rest of the semester. We did practice problems from the AP Calc AB question book. We did questions primarily on integrals and their application."
"The student is working on finding the area and circumference of a circle. They've mostly been finding area and circumference from the diameter or radius but I challenged her to take it a step further by finding the diameter or radius from a given area or circumference. She's starting to get the more advanced problems but could use some more practice. I've given her a worksheet to complete before our next session on Friday."
"The student was given more homework from his workbook which we went over. His teacher is starting to involve the very rudimentary basics of pre-algebra into the homework. He likes the new material, and is just starting to get used to having a "variable" in an equation."
"Today we learned to manipulate complex numbers involving imaginary parts. At first, this was a little confusing for the student, and understandably so; imaginary numbers are slightly abnormal in their treatment. However, managing them requires almost the same rules as any other number, and so he caught on quickly to the manipulation of the complex numbers, and was answering most questions correctly by the end of the session. Certainly, he needs more practice, which he already realizes, but he made significant progress. We also dove into "rationalizing" fractions with complex denominators, which gave him very little trouble, even when we introduced the need for complex conjugates. One of his most regular hang-ups was keeping track of his negative signs, but his skill in that area also improved dramatically over the course of the session. One thing I've noticed is that as soon as he is sure of what he has to do, he has no trouble doing it. I reminded him not to concern himself with whether any given problem is easy or hard, and to simply focus on identifying the precise steps that can be taken toward the solution."
"The student continues to review for the upcoming exam. This session we started with a review of coordinate planes and graphing points with both positive and negative coordinates. In the beginning he was only comfortable working in quadrant 1. So I removed the graphing grid from and just showed him the number line which he was already familiar with to remove the anxiety. He was less intimidated and saw that the points are easy to plot. We then practiced finding the missing point to complete shapes. He caught on right away and no problem finding missing points. From here we transitioned to area and perimeter of irregular shapes. He did very well and was confident in the formulas needed as well as his answers. We played an online area game to reinforce the concept where he aced each round. We then moved onto Science. We reviewed last sessions topics: rock cycle, water cycle, solution vs mixture, and ac vs dc current. He did well with the review and only needed to review his notes for the rock cycle. Next we discussed photosynthesis. He understood the gist of it. We ended the session with an online game covering photosynthesis. He did very well."