Recent Tutoring Session Reviews
"Today we went over unit circle values and reviewed functions. There was some difficulty with introducing the concept of radians as an alternative to degrees, but we went through the relevant angles (0, 30, 45, 60, 90) for each quadrant and talked about how the sin and cosine values could be found via the special 45-45-90 or 30-60-90 right triangles. We moved onto an overview of functions, which was mostly review. We covered symmetry, elementary functions, intercepts, the definition of a function, the Cartesian plane, inverse functions, etc."
"Today we started discussing limits. I explained what a limit was and generally how we go about calculating limits. We talked about left and right handed limits (i.e. single sided limits) and about the "overall" limit of a function. I also introduced continuity and explained how we determine if a function is continuous at a given point c. I had the student work through several problems where he had to identify the right and left handed limits at a given value for a graphed function. He also had to then identify the limit (if it existed) of the function and determine if f(c) existed and what the value was. Additionally I had him tell me if the function was continuous at the given value c. The student did very well with the concept. He was a little confused about continuity initially but after a couple of examples he seemed to understand the concept. We will continue limits and continuity in our next session."
"Covered quadratic equations that are perfect binomial squares, and how to factor and solve them. Reviewed completing the square, and solving equations. Did several examples together on these techniques. We will be working on the quadratic equation next session."
"We went over limit theorem and properties of quadratics. Student had little trouble learning the material and breezed through all the examples I presented to him. Left him with some practice problems to go over."
"Went over using Logs and using Exponential functions. Understanding how to solve word problems with exponential functions. Understanding word problems and also how to use negative exponential functions (for decay)."
"We prepared for the student's test today by going over trig identities, simplifying and solving for trig functions. He seemed to understand the topics very well and I'm confident he'll do well in this class."
"Student wanted review for final. This session she wanted to focus on determining the possible triangle solutions for known angles and side lengths. A little bit of work uncovered the need for restructuring her notes as some were not written correctly, but nonetheless identified and corrected. The other weak area she wanted to correct was solving the exact values of angles with certain methods such as double angle and half angle. She seems about as ready and she can be for her final."
"In making sure the student is fully prepared to take a calculus entrance exam, he and I shifted focus away from trigonometry and started looking at some other topics he will likely encounter. This meant looking at logarithms this session. Working with logarithms is largely review for him, and fortunately, he remembers how to evaluate and solve logarithmic and exponential problems for the most part. We mostly had to go over special properties of logarithms, and how to use logarithms and exponents as inverse operations in solving for a variable. I assigned practice problems that focused on these areas."
"Finished going over/through textbook, highlighting important equations and what to expect. From there I answered any questions he had over material covered. After that I answered any questions he had regarding college courses scheduling or planning. Also talked about the importance of outlines for papers."
"We covered functions. Specifically, tests for determining symmetry. Inverse functions: finding, checking horizontal line test, double checking by using composition. The student and I focused on simplifying equations and solving inequalities (including absolute value)."
"Today was our first session. The student explained that she wanted to complete her online course before sending in her transcript for college applications. In this session, we covered problems from the first lesson of her course dealing with analyzing trigonometric identities and equations. She learned the concepts covered in this chapter quickly. I believe she will be able to adapt through more guided practice like we did today."
"This session was spent gauging the student's confidence and comfort in the subject of precalculus. We utilized the time preparing for her upcoming test by reviewing her previous quiz that covered graphing and homework assignment that covered partial fraction decomposition, in addition to her review sheet. She takes to direction well and is very engaged in the tutoring session."