Award-Winning Test Prep & Academic Tutoring in Lockport, NY

"We reviewed inverse trig functions and finding both angles described by an arc function. We talked about why the answer would be in two quadrants and how to determine which ones, then we practiced finding angles from reference angles. For her chemistry class, we reviewed converting between moles, molecules, and grams. We then practiced some percent composition problems."

"We covered section 10.2 of the student's textbook and went through the homework that was assigned for the day. The section covered arc segments of circles and how to describe and measure them (central angles, minor and major arcs, semicircles). We discussed the conditions to determine the congruence of circles (by radius) and arcs (same measure and of the same or congruent circles). He had no problems comprehending the material discussed. He just required a bit of reinforcement regarding the vocabulary. He stated that he had difficulty with "proofs" so I tried to frame each problem we covered in a way where he had to justify each step of the problem's solution (with theories/postulates). It was a good first session. "

"Today we covered the geometric series. The student started the lesson by bringing up some problems regarding to evaluating finite geometric series. I showed him the most direct approach: write down the general formula S = a + ar + ar^2 + ar^3 + ... + ar^(n-1) = a[(1 - r^n)/(1-r)], where a is the leading term and r is the common ratio. Then substitute the values into the formula S = a[(1 - r^n)/(1-r)]. He was on the right approach, but made some minor mistakes such as subtracting fractions and dividing fractions, but he managed to correct them quickly once I pointed them out. After watching him doing two or three problems and correcting his occasional minor mistakes, he was confused on how to find n. I told him that n stands for the number of terms, and that made a lot of sense to him. Therefore, he finished with the finite geometric series. We then moved onto the infinite geometric series, which he liked more because he did not have to worry about determining what n was--it was infinity. I showed him that there were only two cases, either |r|<1 (converges to S = a/(1-r)) or |r|>1 (diverges). I showed him why these statements were true. The comments I gave him were to organize his work more effectively. This would allow him to do problems far quickly: write down the general formula, and plug the variables with the known numbers, then compute directly. I always let him do problems himself. In cases when he made a minor mistake, I would cue him and let him discover and correct them. After he finished each problem, I showed him my solution (even though his answers were correct), just to give him a faster approach, without confusing him. He understood this topic conceptually, which greatly pleased me. Next time I will emphasize more on organizing his work more effectively. In this way he will minimize the likelihood of making minor errors."