Recent Tutoring Session Reviews
"Tonight, the student learned how to use the unit circle to compute sines, cosines and tangents of angles--provided that they are a multiple of 30 or 45. This procedure is far from automatic, but memorizing how to perform this it rapidly is an absolutely essential skill that will give her a leg up on her classmates. As it is never too soon to master this art, I emailed her some worksheets to practice on. The other main topic of discussion was the new unit which we adumbrated last week: the radian. The justification for this unfamiliar unit system is often overlooked, so I took some pains to explain how it is useful when calculating arc lengths--and therefore can be used to (for instance) relate the distance traveled by a wheel to the number of rotations, or its speed to its RPMs."
"Today we reviewed the quadratic formula. The key things for her to remember are to keep enough decimal places and round the final answer, and to get no solution if the number under the radical is negative."
"We covered exponential, linear, and parabolic equations. He has a good grasp of the content, but stumbled a bit when trying to work with them when only given a set of coordinates. While he always has the option of graphing them to see what they are, we went through just recognizing the pattern of what linear/exponential/parabolic equations through just the numbers and I wrote up a couple extra problems that he was able to do pretty easily by the end of the session."
"The student is preparing for the exam coming up in June. She started to fall behind when working with powers and exponents and factoring, so that is the areas we are focusing on right now. We pick a few problems from each section and work them out. She tells me that it is clear and I believe it is with the proper amount of time. I suggested that she do the odd problems from sections 8-6, 8-7, 8-8, and 8-9 because the odd problems have the answers in the back so she can check her answers. We worked out a problem from each section as a guide. Factoring out common terms, using the foil method, and recognizing the special cases of a squared binomial and conjugate binomials are the techniques she needs to focus on. Unfortunately, becoming confident with material like this can only happen with time and practice. I asked her to do some of the odd problems from these sections, then afterward we can discuss problems she was having and move on."
"I emailed the student's teacher earlier in the week. She asked me to cover solving systems of equations by adding and subtracting. After two or three examples, he did very well with these problems, so we moved on to solving with multiplication. I also tried to get him to show more work as per the teachers instructions."
"We focused on mathematical modeling of exponential growth and decay, with special attention to the amount of compounding interest earned in savings accounts in practice problems compared to today's meager .01% interest."