Recent Tutoring Session Reviews
"The student has a quiz on conics tomorrow, so we worked on studying for that. We worked on finding standard equations of ellipses, using the eccentricity to find the foci and the vertices of an ellipse and rearranging equations algebraically so that it would resemble ellipses' standard equation."
"Today we started by working on writing absolute value functions as piecewise functions and then graphing them. The first step was to break the absolute value up into two equations: the positive and the negative. The student was able to do this step easily. She initially had difficulty finding the vertex of the absolute value graphs, but once we talked through how to do so, she was able to find it on her own. The second step we covered was finding the domain of a function. The student saw where the x values would be limited and was able to express the domain in inequalities. We finished by looking at how various changes to a function change a graph, i.e., shifting left and right, up and down, and reflecting across the x or y axis."
"We covered two topics for a quiz the student has tomorrow. One is mathematical induction. I covered the steps involved, breaking it down into four basic steps for the types of induction problems she is likely to encounter, the simplest kind. Induction requires at one stage a little creativity, and multiple methods of proving the P(k+1) statement are sometimes possible, so we went over two examples step by step, and she took notes on the steps as I broke them down. Second, I was presented with an example problem in her notes which asked to "find the explicit formula". The example examined the difference of the difference, which was a constant, and then assumed the formula to be quadratic and went on to solve it through a system of three equations with three unknowns. I sent by email some links to an online tool pertaining to arithmetic and geometry with sequences that are very well laid out with explanations which are very to the point and easy to understand. Those pages also provide examples problems to solve."
"Today we continued looking through the student's review packet on complex numbers. There were some fundamentals that were skipped over in class, so we started there. As we moved through the packet, we came across some problems that the student struggled with, but as a rule our time was spent strengthening his understanding. He is on the verge of being very comfortable with this. It should be noted, however, that there are many equations to keep straight for this test. We can work on that in future sessions."
"We practiced trig identities and briefly started problems with inverses. The student is doing well. She needs to practice a few more identities problems on her own to build her comfort level, but she knows how to do them."
"Today's lesson focused on logarithms. We worked through several example problems, highlighting the various properties of logs. The student was able to follow along with the material."