Recent Tutoring Session Reviews
"We spent this session preparing for her upcoming test over trig identities/properties. While doing review problems, the concepts that she seemed to struggle the most with were 1) identifying the best method to solve "prove the identity" problems. To address this, I tried to impart some strategic guidelines to match certain techniques to their respective patterns. For example, if you're trying to reduce the number of terms added together, try factorization. 2) sketching graphs of trig functions. For these problems, we had to turn back to a previous chapter and review the concepts of how different manipulations to a y = cos(x) equation impact the graph 3) factoring quadratics. After a few practice problems, she was able to do these on her own without much trouble"
"We covered the trigonometric functions sec, cos, and cot. We talked about how to use a unit circle to identify outputs of the functions for different angles. We also reviewed various mathematical properties of these functions and how to simplify them. She is quickly catching on and has no problem doing the homework problems with a little guidance."
"I taught the student about how to plot a scatter plot of points, construct a "best-fit" line (e.g. linear regression, if you will, the simple way by "eye-balling" the best fit line), and how to construct the model by finding the equation of that line, and using that to interpolate between known points and extrapolate beyond known points. I also reviewed with the student how to sketch graphs of rational functions, finding the x and y intercepts, identifying the vertical asymptotes, how to determine what happens close to the vertical asymptotes, how to identify if there is a hole, and how to identify the horizontal or slant asymptote, if any. We also looked over the basics of log functions and exponential functions, and continue that on Wednesday."
"I met with the student today for our first session of the new semester. She has just begun the trigonometry portion of her pre-calculus class. We reviewed the basics of trig: angles, radians, and the basic functions. We spent a good amount of our time discussing the unit circle for her upcoming quiz. We focused on how to use the unit circle as a tool rather than memorizing specific angle/value combinations. We then considered some of the basic graphical aspects of trig functions and related them to the material we had covered last year, and also to the unit circle."
"Tonight we reviewed graphing conic sections, synthetic division, systems of equations and finding asymptotes and holes on graphs. The majority of the problems came from the student's midterm review packet. When needed, I provided additional problems for her to work on. For tomorrow's midterm, we discussed strategies to help her do her best. For example, she doesn't have to memorize the equations of asymptotes for hyperbolas as long as she remembers how to find the equation of a line. Also, whenever possible, draw a picture of what the problem is talking about to help her visualize what is happening in the problem in case there is an issue with the calculations. She always has a positive attitude towards working on problems that are challenging."
"We started by covering math. We first discussed how to calculate distance or height based on triangle relationship. Then we addressed all the steps in graphing the sinusoid. All the student needs to do is to draw out a sketch so that he will understand the relationships among all the sides and angles so that he can choose which formula in sin, cos, or tan to use. Based on the idea of unknown variable function, he will be able to calculate the answer. For graphing, I taught him how to transfer the graph from a normal sin and cos graph to the required graph. If he follows the steps and does not jump from the first to the last he will be able to finish it."
"This session the student and I spent the session prepping for an upcoming quiz and going over old problems from her last test. She had the most difficulty solving questions involving complex inverse trig functions. Because this section was still a review from last semester, she only needed a quick reminder on how to approach the problems and she was able to complete most of them on her own. She also had some difficulty solving proofs, specifically proving the double angle theorem. Next session I will be bringing a practice quiz to help her prep for her test."
"The student is going over parabolas, hyperbolas, and ellipses in her pre-calculus class. Today we covered the definition of the focus and directrix of a parabola and applied it to a problem from her textbook. We also went over how to find the equation of a parabola using an arbitrarily chosen point, the coordinates of the focal point and the directrix. The textbook problem wasn't easy, as it was not based in the coordinate system, so you had to choose an arbitrary coordinate point for the focal point of the parabola. However, she seemed to understand the concept once I explained it. Next time, we will be covering ellipses and hyperbolas. I will make sure to create practice problems for the next session now that I know what she is covering in class."
"The student showed me where her class was in the book. I choose several fundamental concept problems to start with then moved on to more synthesis type exercises. We covered the fundamental trig ratios in the plane and how to find one ratio given an angle constraint, and the value of another. She was stumped when we ran into dividing by zero, but after a brief review and closely guiding her through one problem of this type she was able to get through more similar ones quite competently. We also, worked a few problems involving arc length and discussed how it relates to circumference and radian angle measure."
"We made more recipe cards and these cards included things like rational zero test, positive zero test, and intermediate value theorem."
"Topics Covered: functions, domains, ranges, graphing functions, function relationships, determining whether a function is even, odd, or neither We reviewed for her upcoming test. The student had significant improvements in evaluating functions, especially evaluating f(x+h)."
"We covered concepts on partial fractions. The student was able to understand the material, and needed very minimal help. She enjoyed this subject very much. I left her to finish the rest of the homework at home. Overall, the session was excellent."