Recent Tutoring Session Reviews
"During this first session with the student, we covered a set of review questions that had been assigned ahead of the her first exam for Monday. As we went through the question, we covered the major concepts of isomerism, determination of the acidity and basicity of organic compounds, determination of formal charge, and molecular orbital theory. She was able to pick up most of the concepts very quickly and was able to work easily through most of the questions. I am confident that with more practice, especially via the extra questions that I sent to her, she will be doing very well on the test."
"We began by reviewing the assigned homework on work, energy, and power that did not use integral calculus. From there, we covered integration, prefacing the discussion by showing how to calculate the area under the curve for simple functions using geometry, then showing how reversing the order was akin to taking the differential of the higher-order function. Next, we covered the fundamental theorem of calculus, showing how the limit of summation of rectangles of decreasing width could be used to arrive at the area under a curve. The student quickly picked up on how to integrate polynomial terms. We discussed both indefinite and definite integrals, and I assured him that definite integrals were easier and more applicable to most physics problems. From there, we covered vector multiplication, including both the dot product and the cross product, proving the mathematical basis for both, as well as discussing when to use which product. We also discussed cross products required a prerequisite discussion of unit vectors, tangent lines and normal lines. From there, we redefined the work function as the dot product of force and displacement, generalizing from the geometric definition we had discussed in our previous session. We discussed torque, using it as a FOIL to work in that it was the cross product of force and displacement from the fulcrum. Finally, we briefly covered the definition of power as the change in energy over time. The student is a bright guy. He clearly had internalized the topics we had covered conceptually and in which we reviewed the assigned homework. All the math discussed today was new for him. I assigned him several homework problems which required the application of the new math skills to the same topics we had already covered, excepting power, which was new."
"In our final session, we concluded our work preparing the student for his final exam. We focused our studies on the initial formation of life on earth and earth's early atmosphere. We then discussed different evolutionary theories, including Darwin and Lamarck. We discussed natural selection, how mutations are fundamental to evolution, adaptive radiation, and population genetics. We also spent some time covering the Hardy-Weinberg equation and how to solve problems using this equation. He has been studying and seemed well prepared for his exam. I helped his set up a plan for how he should review all of his content. I think that he will end his semester on a good note!"