Award-Winning Tutors serving East Chicago, IN

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Private Tutoring in East Chicago, IN

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Recent East Chicago Tutoring Session Notes

Tutoring review by Jackson in East Chicago, IN
Today we looked at inverse functions and alternative variables. Essentially we discussed the arbitrary nature of variables. By the end of the session she was doing quite well. Inverse functions followed a similar pattern, once she understood their relationship to functions she did very well.
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Tutoring review by Luke in East Chicago, IN
We primarily addressed the student's test material, although I also gave her a brief rundown of her new material to prepare her for the coming lectures. Regarding her test, the majority of her errors resulted from forgetting two significant processes. First, she forgot how to complete the square; once I reminded her, I think it was definitely familiar to her, and she was completing the square correctly at the end of the session. I showed her exactly how it applied to the solution of each of the problems she missed, so she definitely understands her related mistakes as of this moment. We had gone over completion of the square previously, but it is very forgettable if you don't practice it, especially because it involves reacting to a term that you never really (need to or should as a matter of general practice) write down. During our discussion, I emphasized that the invisible term is inherently forgettable and therefore an abnormally great mental effort is required to internalize the process of "completing the square", relative to simpler, more tangible processes. Second as far as graphing is concerned, she confused the midline of vertically shifted trigonometric functions, and consequently confused the amplitude and the period. She also forgot how she should divide by the factor by which the graph is horizontally stretched or compressed, hopefully acquiring a coefficient greater than one in compression situations (or vice versa for stretching situations) because the input field must grow e.g. 5 times faster in order to horizontally compress a trigonometric function to 1/5 of its original size (because this causes the output function to progress through its loop, and thus arrive at any given destination, 5 times faster [in 1/5 the distance]). Graphing involves abstract application of arithmetic skills, and I think she is still a little nervous regarding her mental math, which, in my estimation, contributes significantly to the difficulty she experiences in intuitively understanding graphs. Thus, I highly recommend she practices mental arithmetic more often while she's doing her math (or simply while going about her day). If she can be encouraged to practice a little more often I think she'll do a whole lot better. The other mistakes she made were certainly evidence of a wandering mind. Once she forgot to include the y-intercept (despite knowing how to calculate the y-intercept) when asked for "the intercepts," and once she simply did a log problem wrong even though she immediately knew she had used the wrong base when I asked her to mentally double-check the numbers. The last point that I haven't addressed involved a question about a "reference angle," which she did not understand to be a special term referring to the "absolute value of the smaller of the two angles formed with the horizontal axis by some ray traveling away from the horizontal axis". E.g., she put 7pi/6, the correct angle in a polar coordinate system, but she was supposed to put pi/6, because 7pi/6 is pi/6 below the horizontal axis.
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Tutoring review by Max in East Chicago, IN
For our last two sessions, the student and I have been beginning our review for his final exam in Algebra 2. Fortunately, he has a couple of weeks of just reviewing all of the various material from the course to prepare. Last week, we worked on a comprehensive review of the conic sections material that comprised his last unit. This included identification of the different sections, transformations of conic functions in their standard forms, simplification/expansion, completing squares to get to standard form, and solving systems of nonlinear functions. The student needed a little reminding of which equations matched with each type, but by the end, he was able to identify them correctly. This week, we went back into some older material, namely exponential/logarithmic functions, rational/irrational root theorems, complex conjugate theorem, and synthetic division. Understanding the inverse relationship between exponents and logarithms is key to being able to solve those types of equations. Reintroducing the rational root theorem is also an invaluable tool to be able to deduce possible roots of any polynomial by the process of synthetic division, which also required a little dusting off for the student. However, once the process is illuminated, the math itself is a cinch for him. I think a good plan of action would be to continue to touch back on what we've reviewed in previous sessions in order to make sure all the ideas are still fresh as we approach the final exam.
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Tutoring review by Saman in East Chicago, IN
The student has final exams coming up. I helped him strategize how he would like to study for the exams, and I helped him finish a paper for English today.
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Tutoring review by Abdul in East Chicago, IN
We covered section 12-4: The Box and Whisker plot. The student learned how to find the 5 important parameters in a data set for graphing the Box and Whisker plot. These parameters are: the minimum, the maximum, the median, the first quartile and the third quartile. We solved several book problems on this subject.
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Tutoring review by Christopher in East Chicago, IN
Tonight, we went over how to calculate the nth coefficient of a binomial expansion using the combinatorial function nCr. After that, we looked at a problem involving fractals. Then, since there was more time left, I helped him with composing his essay on George Orwell's short autobiography, "shooting an elephant."
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