Recent Tutoring Session Reviews
"This was our last session, as the student's final for this class is on 12/19. We did an amazing amount of material in this class which would take a long time to summarize using a normal amount of accuracy. Therefore, here is an abbreviated list of things that we went over: Approximations of functions using polynomials of a finite degree: Take as many derivatives of your function as you want in your polynomial, and plug in the value of the point you want to estimate into each of these derivative functions. That real number answer is the coefficient for a term in the polynomial. The overall polynomial will be of the form a sub zero plus a sub one times x plus a sub two times x squared over two factorial plus a sub three times x cubed over three factorial and so on. Taylor Polynomials and Maclaurin Polynomials: These are Polynomials of a finite degree of the form described above, except they are centered about a point c, so in place of each x listed above should instead be x minus c. In an Maclaurin polynomial, c is always 0. Power Series: A function can be represented EXACTLY as a power series, because it uses an infinite amount of terms to 'approximate' the function. The rule for convergence of a power series is that only one of the following can be true: Either the series converges only at the center, it converges for all x, or is converges for a distance from c equal to what's called the radius of convergence. The interval of convergence is (c-R, c+R). The ratio test is used to calculate the radius of convergence, and then the answer to the ratio test is compared with the form "the absolute value of x minus c is less than R in order to determine what R is equal to." We did many examples of how to do this. Integration by parts: We reviewed the idea of IBP and how to do it. We then chose the hardest example in which two integrals have to be combined. The student did the hard example with only a couple of snags, and then did an easier version of the problem with ease! He showed great progress. I also went through a review packet and he did some integrals from the packet before time was up. It was a fine ending to our time together."
"Today the student and I went over remaining questions that she had regarding BC calculus topics. We spent the majority of the lesson going over old test problems. We went over continuity, limits, integrals, theorems and derivatives. She seemed to have ironed out all her questions by the end of the lesson and was excited to have problems reworked correctly!"
"I met with Student A first, as he has a math unit test tomorrow. It is on integers, equations, order of operations, and exponents. We went over the first 3 topics last week and he was pretty confident about them. He had just had an exponent test earlier this week, which he did decently well on. He had gone over and studied all of his mistakes already. I brought him a handful of challenging test problems, which occupied us for a while. He definitely benefited from them. Student B was struggling a little with logs. She showed me a few of her notes that she needed help with and I explained them to her. Logs are tricky. We will have to go over them some more next session."
"We covered equations of tangent and normal lines to a curve, increasing and decreasing intervals in a function using first derivative theorem, concavity and point of inflection using the second derivative theorem, implicit differentiation, kinematics problems involving calculus, graphing and transformation."
"The student is working on logarithm functions and properties. She picked up stuff fast and response immediately after the questions. We went through the definition and derived the properties from there. Also a list of homework problems were covered."
"We went over practice problems in the student's homework covering definite integrals, the first and second fundamental theorems of calculus, and limit method. The student is doing well and should continue to do practice problems. I recommended that she read the textbook and additional materials and memorize key equations. I shouldn't be feeding her answers but rather facilitating her thought process to the right answer. I will also follow up with her on 2 problems."