Recent Tutoring Session Reviews
"The student and I continued working on trig. We found amplitude, period, and frequency of sin/ cos curves. We then evaluated the function and graphed by carefully choosing x and y values. We focused on working in radians and memorizing trig values."
"We spent most of our time working on proofs of trig identities. Most of the problems we worked on had solutions provided which were similar to our approach. I did spend some time explaining how proofs of trig identities can often be done different ways. This means that he might find a solution which looks different from his solution manual."
"We worked on vector questions dealing with direction and magnitude. The student understood how to set the questions up and was comfortable with finding magnitude from a vector equation. He has a test tomorrow and is feeling confident in the recent material!"
"In today's session, we continued to review the material for the student's test in precalculus. She took part 1 of the test today and felt confident about it which is great. The confidence definitely carried over into our session today as well because she did much better than she has done in the past. I only had to explain a concept once and she was then able to complete most of the problems on her own. I think this is huge for her and I am hoping this confidence will continue for her exam tomorrow and as we continue with tutoring."
"The student and I reviewed the concepts covered in two sections of his textbook which involved rational functions. The first section covered the methods of determining the characteristics of rational functions and then graphing the functions. The second section covered the methods used to solve rational function equations. I broke down the characteristic/ graphing methods into discrete steps. The beginning of the method involved factoring or dividing (by polynomial long division) the function. Factoring helps one find holes, while the division would shed light on any slant or non-linear asymptotes which aids in graphing attempts. We then practiced determining vertical and horizontal asymptotes by analyzing the denominator and functional end behavior, respectively. We also practiced determining the x and y intercepts of the function by asking ourselves what do all x and y intercepts have in common. With these puzzle pieces, we were able to sketch the graph. Solving the equations proved much simpler. There were fewer steps and the reasons for the steps were more obvious. I highlighted that the steps were not unlike doing operations with fractions which made solving the equations more intuitive. We practiced four steps: find the common denominator and convert all fractions into ones with the common denominator, get rid of the common denominator, solve the resultant equation (usually a quadratic), and determine if resultant solutions are extraneous or not. He seemed pretty comfortable with solving rational function equations but needs a little more time to get comfortable with the graphing methods."
"We practiced writing equations for a given sine/cosine graph and expressions to describe specific points on the graph. The student is doing well determining the period, amplitude, and vertical shift of the graph and converting them into the correct a, b, and d constants, and she is becoming more confident determining the phase shift to describe a graph as either a sine or cosine function. Lastly, we practiced finding the values of various trigonometric functions for angles given by the unit circle. We reviewed angles created by multiple revolutions and negative angles in addition to the standard angles between zero and 2*pi. Once she is able to determine the correct quadrant the angle is in, she is able to find the values of the trig functions very easily."