Recent Tutoring Session Reviews
"We went over various topics in preparation for his final exam: Roman numerals, changing the base of a number, linear programming, area/volume and probability."
"The student was preparing for his exam tomorrow. We went over his exam review looking over problems he was unable to answer or struggled with. Most of the problems he struggled with were not core ideas, but rather word problems that incorporated problem solving skills."
"This session we discussed the final two tests for convergence and divergence of infinite series: the root test and the ratio test. We began with the ratio test, which is a test which compares the absolute value of the ratio between the following term in a series and the current term. If the ratio is less than one strictly, the series converges. If the ratio is greater than one, the series diverges, and if it is equal to one, then the test is inconclusive. We did several examples using this test. There were no conditions that we needed to check for like we needed to do with the integral test or the limit comparison test. We then moved on to the root test. The root test asks you to compare the n-th root of the series with one. If the nth root of the series is less than one, the series converges. If it is larger than one, the series diverges, and if it is equal to one, then the test is listed as inconclusive, and you have to choose another test to determine convergence or divergence. We then did a few examples of using the root test, but we didn't need to do many examples, which was a great sign. The student really got a good handle of these tests as time went on. We then looked at all of the tests together and looked at the index cards for each test that we had created. We looked at a list of series in the textbook and we determined which test could be used in each case. In some cases we found that more than one test could be used. We used this opportunity to review these tests and we discovered that the nth term test is to determine divergence only. If the limit as n goes to infinity of the series is equal to a non-zero number, then the series diverges. Therefore, if the series is known to converge, then the limit as n goes to infinity is equal to zero. This test does not determine if the series converges or not. This brought us up to the end of the class."
"In preparation for his cumulative physics final, we worked through practice problems related to centripetal force (in the horizontal/vertical), force body diagrams, static equilibrium, Newtonian gravity, and torque. He is able to recall all of the relevant equations and is able to work through most problems fairly independently."
"We continued to work with Chapter 6, which is on properties of exponential and log functions. He struggled to understand the structure of logarithmic expressions but is improving at manipulating them. We reviewed how to move back and forth between addition and multiplication, subtraction and division with logs. He will print out the review for his next exam in advance of our next session."
"The student had a Pre-calculus test coming up the next day, so we spent most of this session preparing her for it. To help her prepare, we did problems from a study guide that covered series and sequences, permutations/combinations, and probabilities. After looking through Pre-calculus, we looked through the physics study guide. She had troubles understanding electrostatics. To help her, I clarified some key points about electrostatic such as conductors, insulators, how electrons move when charging an object, etc."