Recent Tutoring Session Reviews
"The student and I covered vectors and scalars and applications. We calculated the force exerted on a sled on an incline. We also addressed problems with boats and speed."
"We covered a lot in this two-hour session. The student began by listing the topics that will appear on tomorrow's test, including graphing parametrized and polar equations, converting points and equations from one to another coordinate systems, analyzing chromosome and rose curves, and analyzing projectile motions. We began with these topics in order. He made very limited mistakes when it came to graphing parametrized equations. He knew exactly what he was doing. I gave him three problems on this and he did it very quickly. We then moved to plotting polar coordinate points, which proceeded fluently as well. Now it went to the more advanced topics: converting points between polar and rectangular coordinate systems. He did a good job of converting from polar to rectangular. I spent some time showing him that there are infinitely many correct ways to express a point, using polar coordinates. This took a while because it led me to introduce what "reference angles" were. We then jumped to convert the equations, and I told him that things ran into the other way- converting from rectangular to polar was much more easier than its opposite way. I gave him some of the problems. After I hinted up once on the most complicated problems, or even without a hint, he got the topic. After all of these, we proceeded to analyzing rose curve and chromosome curve. He did a very good job analyzing the graph without a calculator. I showed him how to find symmetries, and he got it right away. Due to the lack of time, I only gave him two problems, but he did the problems fairly quickly. The last topic we did was the projectile motion. I pulled out an example from the book. The set up of the problem is okay to him, and he managed to plug the known info in quickly. We discussed evaluating the quadratic equation with coefficients. I showed him how to do this on calculator. Throughout the session, I recommended some effective ways to check the answers. For problems that require to convert a point between coordinate systems, I suggested him to graph that point first, so his answer would be in the right quadrant (right polarity). It was a very intense session."
"We spent nearly all of our time discussing how to find anti-derivatives. He was a bit uncomfortable with recognizing the derivative formulas, which was the main source of his difficulty. I encouraged him to put in extra practice so he would start to recognize the types of integrals he'll see on homework and tests later on."
"We continued our discussion of trigonometric functions and vectors. Today, we focused on squared functions and examined their inverse and multiplicative inverse. We also examined a vector word problem involving air speed, wind speed and ground speed. The student has a good understanding of the material. On occasion, he needs a little guidance on how to approach a few of the steps in solving, particularly when finding algebraically the intersections of two functions. Overall, he feels very comfortable with the material and should perform in outstanding fashion on his exam this week."
"I helped the student prepare for his upcoming quiz. We worked on questions dealing with partial fractions and conversion between linear speed to angular speed. The student did great!"
"Today we reviewed trig functions, their graphs, and trig inverses. We focused on drawing vectors and finding the angles between the two vectors."