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Recent Tutoring Session Reviews
"We have covered basics of polar coordinates and plotting functions in polar coordinate systems. We have plotted two graphs.
We have also looked at examples of curves in parametric notation, and the best suggested strategy for drawing such curves would be to express the parameter t in terms of x or y whichever is simpler and then obtain the y as a function of x and then plot that.
We also clarified that, even in parametric notation, the notions of "growing curve," or "concave up," "concave down" really refer to x/y coordinate system. Therefore, the first and second derivatives of y with respect to x need be evaluated.
Student has performed well on tests in the past.
For homework, student is encouraged to solve more specific problems from the text to gain speed of execution."
We have also looked at examples of curves in parametric notation, and the best suggested strategy for drawing such curves would be to express the parameter t in terms of x or y whichever is simpler and then obtain the y as a function of x and then plot that.
We also clarified that, even in parametric notation, the notions of "growing curve," or "concave up," "concave down" really refer to x/y coordinate system. Therefore, the first and second derivatives of y with respect to x need be evaluated.
Student has performed well on tests in the past.
For homework, student is encouraged to solve more specific problems from the text to gain speed of execution."
"During our session, the student and I began working through some calculus assignments from a new section of his textbook covering the derivatives of trigonometric functions. We began by going over some of the definitions of trigonometric functions, such as the relation between tangent, sine, and cosine, and we then introduced the derivatives of these three main trig functions. After reviewing the material, we began working on the problems from the student's assignments. These problems required knowledge of the derivatives of trig functions, as well as the proper application of various rules from earlier in the course, including the power rule, chain rule, product rule, and quotient rule. The student remembered each of these topics very well and applied them to a new type of problem perfectly, using knowledge of concepts from the past, as well as new material learned today to solve each problem and find the derivatives of trigonometric functions."
"As might be expected for a session two days prior to a final exam, we worked on a little bit of everything from the semester. During the review, I tried to reinforce some of the big picture ideas, like the fact that a reference is provided so that you can remove the constant that appears from indefinite integrals, so if you see one given, chances are extremely good that the problem will shape up that way. He had a strong grade in the class going in to today's final, and I'm optimistic about his chances for an A."
"In the first half of today's lesson, we continued practicing usubs for integrals (indefinite, definite, changing limits of integration). The student seems pretty solid at this now, particularly since his class has not moved forward to new material due to AP testing.
In the second half of today's lesson, we reviewed chapter 4 on derivatives (to start a cumulative review for the final). We covered the definition of a derivative (based on secant and tangent lines), how to do a derivative, the product rule, quotient rule, and chain rule. We also went over implicit vs explicit differentiation and conversion rates.
He understands the different differentiation rules pretty well. Now that he understands negative exponents better, he is doing much better on the actual arithmetic. He did have some difficulty conceptually understanding explicit and implicit differentiation, although the metaphor of 'translation' between x and y seemed to help.
Overall, he seems to be doing better each session. I think if we continue reviewing a little each session, he should be very prepared for the final."
In the second half of today's lesson, we reviewed chapter 4 on derivatives (to start a cumulative review for the final). We covered the definition of a derivative (based on secant and tangent lines), how to do a derivative, the product rule, quotient rule, and chain rule. We also went over implicit vs explicit differentiation and conversion rates.
He understands the different differentiation rules pretty well. Now that he understands negative exponents better, he is doing much better on the actual arithmetic. He did have some difficulty conceptually understanding explicit and implicit differentiation, although the metaphor of 'translation' between x and y seemed to help.
Overall, he seems to be doing better each session. I think if we continue reviewing a little each session, he should be very prepared for the final."
"We covered review problems on integration for the exam. I showed her which techniques would be productive for certain problems and when an integral could be solved explicitly with techniques she learned during previous sessions. I advised her to memorize common forms/identities, namely trig identities and trig derivatives. I'm confident she'll be able to solve problems involving sin/cos integrals, sec/tan integrals, and straightforward integrals. Anything involving trig substitution she can set up appropriately."
"The student was on top of her game again today. She was able to make good headway even on the new material. Her attention to detail when writing calculus equations is improving; it is becoming second nature for her to include "small details" like the "dx" symbol at the end of integrals. She catches on so fast that we were able to cover 23 days worth of material in all today. She appears well prepared for any upcoming tests and even preprepped for tomorrow's class topic. Her commitment to completing the homework is beginning to drift, but I encouraged the student to continue completing the book problems that he recommends."
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