Recent Tutoring Session Reviews
"The student had a few questions about the real-life meaning of derivatives, so we spoke about that and practiced a few problems. She had not yet received her math homework, so we completed some physics (mechanics) problems from past homework sets."
"We reviewed compound interest and radioactive decay since the student felt that she got these problems wrong on her recent Pre-Calculus test. She specifically was uncomfortable solving for the rate in these types of problems. She is doing well with setting up the compound interest equations and we worked on familiarizing her with the algebra to isolate the rate that is being raised to a power. For the radioactive decay problems, we went over what the half-life of a material means and how to set up the equation using the half-life. We also covered some of the beginnings of trigonometry, mostly regarding angles, the definition of a radian, how to convert between radians and degrees, and how these topics will relate back to the geometry of triangles."
"The student and I focused primarily on pre-calculus in our session, focusing on the law of sines. She grasped the concept very well, and after the first several problems was able to solve almost every question completely independently, only asking for my input when she needed to double check an answer. She is doing great in her pre-calculus studies, and we will meet again next Tuesday."
"The student has an exam coming up on Thursday. She had questions about testing for discontinuities in functions, graphing functions, and combining functions. I resolved her questions. We also discussed applying to college as a student athlete."
"The student learned of De Moivre's theorem yesterday, so her assignment was on converting coordinates between Cartesian, polar, and the complex number systems. She was also expected to put these into the "polar form" of a complex number, which is really only useful for applying De Moivre's theorem in this limited setting. It was a lot of calculator work as the problems mostly defined hand work. I think her understanding is solid."
"Today we worked on graphing polar equations as well as converting between rectangular and polar coordinates. The student had no problem with this. We also reviewed some law of sines concepts to find the missing parts of a triangle."
"We covered chapters on the law of sines and the law of cosines. We covered solving triangles given by angle-side-angle, and side-side-angle via the law of sines, and triangles given by side-angle-side and side-side-side via the law of cosines. We performed one example for each type of given quantities above. Student had no trouble grasping the concept and numerically executing examples. Strategies for the lesson included picking the right Law for the triangle problem at hand. Extra practice includes proving Heron's theorem, and looking at the area of triangle expressed with all three sides only. Student's confidence in solving precalculus problems seems to have increased. He feels that the exam that he had last week was quite easy."
"The student and I worked through another problem set over graphing trigonometry functions tonight. She has nearly mastered these concepts, needing very little help from me tonight other than to verify her solutions."
"The student was largely on track with what her class had covered so far. We worked on finding where different radian values would fall on the unit circle and then moved up to calculating exact values of trig functions for certain radian measures. She seemed to really get why we were using radians instead of degrees by the end of the session."
"Completed homework on exponential growth and interest compounded continuously and at set intervals. Then reviewed for a test on exponential functions, paying close attention to matching graphs with their equations. The student seemed to have a better command of the material than he had been expecting."
"The student's exam was pushed back to Tuesday-Wednesday, so we continued to prepare. We practiced finding the exact value of trigonometric expressions. He is proficient in the trig aspect of these problems."
"I reviewed with the student trigonometric identities, how to verify that two trigonometric equations were equal to one another, by showing her how to make substitutions on one side or another with other trigonometric identities, algebraic manipulation, etc. to arrive at the same thing on both sides of the equation. I also demonstrated how to solve for trigonometric equations that require use of trigonometric identities -- for example, sin 75 degrees ... by using sin (a+b) = sin a cos b + sin b cos a, and breaking the 75 degrees down to sin (30 + 45) to apply the preceding formula."