Recent Tutoring Session Reviews
"The student wanted to focus on properties of logs, so we did a quick review of trig identities (concentrating on positive and negative values of sin/ cos/ tan on the coordinate plane). We did lots of log problems, in order for the student to feel comfortable and for her to have something to study."
"We started by working on some of the problems the student got incorrect from the homework he'd been assigned. After this I gave him additional problems to work on, on his own, while I graded his other homework problems. After I finished grading, we completed those additional problems together and he did really well during this time. He was focused and could quickly recognize and fix any errors in calculation when I pointed them out. We spent the last part of the session working on a practice problem set. Tomorrow, he will have an exam and the practice set was designed to help him with this."
"In this session, I went over trigonometry and logarithms. I reviewed the student's 2 quizzes with her, and explained to her the problems she did not understand. She needed some clarifications on inverse trigonometric functions and graphs of trigonometric functions."
"Today the student and I went over all the quizzes he's taken in his class to prepare for his upcoming final exam. We focused on factoring and the difference quotient. If he takes the time to check his work he should do fine on the final. We're going to study one more time before he takes it so hopefully he'll be well-prepared."
"Began solving systems of equations through the application of Cramer's Rule to 2x2 matrices. The next two pages are Cramer's Rule applied to 3x3 matrices. This will take some time because finding the determinant of 3x3 matrices takes some time. And in order to solve these 3x3 systems, this involves finding the four 3x3 determinants per problem. I've begun some of the problems (10 of 20) just to save time. 10 problems is sufficient for the student to show he understands."
"Today, we worked on mathematical induction, more binomial theorem, limits (solving by visual inspection, by table, and by direct substitution), continuity, and an introduction to the derivative. These topics went more quickly since they were more calculation-driven, which the student prefers. The student's next test is this Tuesday, her final is Thursday, and we have scheduled two sessions to prep for the final and finish out the coursework, one on Wednesday morning and the other on Thursday afternoon. Almost there!"
"In the previous session, I gave the student a series of polynomial problems. He solved most of them, but had trouble with a few. We reviewed those problems, and it became clear that he had missed a few key insights into the process of factoring. We reviewed those and he was much more comfortable with the process. We worked through practice problems on adding and subtracting rational expressions. The student understands the logic of the problem, but struggles to implement the method independently. We will continue to review this process. We moved on to identifying the order of polynomial equations, which the student picked up very quickly. Then we addressed the distance formula and plotting linear equations. The student is familiar with plotting linear equations but struggles with analysis of those equations. I left him with a series of problems determining the x and y intercepts of various functions, as well as an assessment of the skills he has learned in the polynomial portion."
"Covered more exam topics to prepare the student for his exam tonight. Specific topics we covered were limits, solving two-sided logarithmic and exponential equations, absolute values, and Descartes Rule of Signs, in addition to reviewing topics from last session."
"The student handled most of her limit homework well, but a couple problems had unusual notation which confused her, so we went back over those; she also had trouble with the directions and notation on her sequence and series homework, so we practiced more of those as well, spending most of the session on that topic. However, she showed visible improvement over the course of our time today."
"Covered equations in one variable, in two variables. Did example problems solving and simplifying equations in one and two variables. Covered orders of operation and techniques for solving these types of equations. Will start reviewing functions and graphing next session, as well as some word problems."
"Today we continued looking at functions. We discussed intervals of increasing and decreasing. We also discussed maximums and minimums. I had the student look at a variety of graphs and describe the intervals of increasing/decreasing and identify any maxes and mins. I mentioned to him how we'll use calculus to clearly identify these attributes. We also looked at algebraic properties of 2 functions and composites of 2 functions (i.e. [f+g](x); [f-g](x); [f*g](x); [f/g](x); and f(g(x))). We worked through several problems where he was given 2 functions and had to find each of the combinations. He did well with this. We will look more at composite functions in our next session and start to look at limits."
"Today we started reviewing basic algebra skills and arithmetic concepts as a way to gauge where the student is at in terms of knowledge. From there we started going over concepts and practice problems to help re-familiarize the material. We created a review sheet on exponent laws in preparation for sections on polynomials next week."