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During this session, a cumulative midterm review sheet was reviewed to completion in preparation for the upcoming final.

Prepared for chemistry test on gas laws: reviewed relationship between variables; how to manipulate the ideal gas law and how it relates to Boyle's, Charles', Gay-Lussac's, and Avogadro's law; completed practice problems on study guide covering each type of problem; discussed how to check/rationalize answers. Also went over Algebra II homework: reviewed finding domains and graphing radical expressions.

We covered derivatives of logarithms and exponential functions. He struggled at first with the chain rule, but after some practice got the hang of it. He seemed to be understanding everything, despite the breakneck speed that I was moving with. I didn't leave him with any extra practice since he seemed extremely solid on most of the material. He's very good at taking derivatives and determining them. We also talked about the second derivative test, as well as the quotient rule, and an introduction to differential equations.

We did the quiz first, and I corrected the students and showed them how they have to do the problems. I am going to help Student 1 learn the concepts during the next session by asking him to solve several problems in front of me. Student 2 is doing well, and she understood the concepts and is able to do problems without any help. We also went through ionic and net ionic equations. I explained the concept and solved some problems to show them how to do them. Then, I asked them to solve some questions for me. I assigned some homework for next session.

Very good session today -- it seemed like the student left the session in a place where she felt very confident about the material. She has mastered concepts from earlier in her semester, such as graphing parabolas, logs, and exponents. We spent time reviewing the technique for graphing a sine or cosine function -- identifying its key points and adjusting those to new coordinates based on the equation. We also practiced verifying trig identities. I emphasized the strategy of persisting and trying out things without being sure if they'll work or not. Since there's a finite number of combinations you can try, the odds are that you'll get it eventually. Lastly, we practiced solving a trig equation -- she was able to identify that it needed factoring and use her skills in that area to solve.

Continuing from yesterday, we covered rational functions and how to find their asymptotes. The entire session was devoted to teaching the student the various cases, so it was more concept based than problem solving based. He insisted that his taking the time to write down basically what's in the book was helpful for him. He did seem to understand everything by the end, as being so methodical really allowed us to drill down and see fine details.