Recent Tutoring Session Reviews
"Although today is a holiday, I wanted to have a session before the students class began working on the next chapter. They had just finished rational expressions and are moving on to exponents and logarithms; since this concept can involve some of the most complicated word problems in Algebra 2, I thought we should get a head start. Luckily, logs are not new to the student. A brief introduction and a few simple practice problems were enough to make the topic seem completely familiar to her. I also brought a few advanced exponent problems, which we solved together. Finally, we discussed the topic of compound interest and exponential growth. The session served as a useful introduction to this concept, and I'm sure the student will understand the next few classes with little trouble."
"The student had compiled a list of topics she specifically wanted to review. I placed them in an appropriate order, and then we went through mini-lessons and practice problems. We began with maximums and minimums and the connection between y, y', and y" in terms of graphs and equations. We review the first and second derivative test. Second, we covered related rates. Third we covered trapezoidal sums and midpoint Riemann sums. We ended the session with average value and special integrals, specifically, integration by parts and u-substitution. We did not get to volume, but she hopes to review that individually, and if necessary, we will review it next time."
"We began the session by working on the current homework, a review of all conic sections. This went well, and left us time to begin the review for the student's upcoming final. For the review, we worked on an earlier section of parabolas, which allowed us to see how the earlier work prepared the student for the later work on conic sections."
"We covered asymptotes and finding intercepts. I did not see any scores/grades. She was catching up with material she missed. I did not leave her with extra practice since she did not have any of her books and worksheets."
"The student had started working through his Algebra II workbook, trying about half of the questions, of which he answered maybe two-thirds. None of the concepts were really new, but he had some trouble with radicals, exponential functions, real number properties, and sequences/series. He had forgotten again the rule about when factors cancel out, so we looked at it another way. After a moment's thought he then noticed a difference of squares, factored it correctly, and correctly canceled out factors in the numerator and denominator. He can absolutely understand everything needed on the test, or even to get an A in the class! It only takes practice. No new material has been introduced at school for a little while, with spring break and everything. The teacher will be presenting logarithms early next week."
"The student and I spent more time on infinite series and polar coordinates. She had been struggling a bit with polar coordinates and finding area bounded by two curves. We made progress in figuring out how to handle such problems. We also went over position, velocity, and acceleration vectors and how to calculate the magnitude of such vectors."
"This was the first time we met since his spring break. In school they have been going over solving systems of equations using conics. I was really impressed by his ability to solve them with substitution. It seems like he got some extra help from his teacher in a good method step by step to solve them."
"The student and I continued working on her problems for the first week of the algebra class. This included going through problems involving commutative property, associative property, combining like terms, and order of operations. She has a great grasp of these early concepts, and we will continue working on next week's assignments during our next session. We finished with a quiz and she made a 100%."
"Test tomorrow, so did comprehensive review. Quick question checks: linear graphing, parametric graphing, basic algebra inequalities. Worked through problems on linear and parametric modeling (supply/demand and other word problems), harder polynomials and factoring, 3d modeling (folding up a box w/ volume= V= l*w*h find area in term of x) transformations. We attempted to do or look over a problem of every possible type and he's been studying hard. Good luck"
"We decided to do a general math review. We went over the equations for sector area and arc length. We also went over the basics of lines and the three ways to write an equation (point-slope, slope intercept, and standard). We also went over the basics of trigonometry."
"We spent the first hour or so of this session exploring the logic behind and application of the unit circle. We discussed the structure of the unit circle and how to use the unit circle to evaluate trigonometric functions. Then we continued with our work on arcs and segments in circles from geometry."
"To prepare for the student's test tonight, we covered the final section of new material from this unit, addressing parametric region transformations and Jacobian determinants in two and three variables. He was briefly confused on a couple of problems, but I was able to alleviate that."