Award-Winning Test Prep & Academic Tutoring in Guttenberg, NJ

"Today we did reviews on conic sections, to prepare for the student's test tomorrow. We went through one type of problem in detail--give a long equation and organize into the form of one conic section, then do analysis. She was a little confused with the parabolas, ellipses, and hyperbolas. I mentioned that in parabola, she needed to find 3 things: focus, vertex, and the directrix. In ellipses, she needs to find center, foci, vertices, and the endpoints of the minor axis. In hyperbola, she needs to find center, foci, vertices, asymptotes. In ellipse and hyperbola, finding a, b, and c will help her--but be careful that in ellipse, a^2 - b^2 = c^2, but in hyperbola, c^2 = a^2 + b^2. She got a little confused, but finally overcame these difficulties. She made some minor mistakes in organizing the equations at first, but I told her about the Great Wall of Equal Sign--whatever she does on one side she must do the same thing on the other side. At the end she finally did three problems in a row (organizing equation part) without making a mistake. Then she gets better every time on the analysis: finding foci, vertices, center for both ellipse and hyperbola. I wish her success on tomorrow's test. Great work. Great student :-)"

"We covered inequalities with absolute value functions by going through the student's previous homework sheets. First, we did problems where we solved for x in an absolute value inequality function. This involved first isolating the absolute value part, if necessary, and then "breaking" the absolute value by splitting the inequality into two separate equations that solve for x. She learned that problems with "greater than (>)" or "greater than or equal to", had solutions for x with ranges that were exclusive. So, "or" is needed to describe the solutions: x > a OR x < -a. For problems with "less than (<)" or less than or equal to", the solutions for x had ranges that overlapped and create a bounded range. So, "and" is needed to describe the solutions, and these can be rewritten in a form that is easier to comprehend: -a < x < a (for example). The student seemed to catch onto how to solve these very quickly after a few practice problems, and by the end was solving them perfectly. In the beginning, I gave a quick reminder that dividing by a negative number switches the direction of the inequality (< become >, or vice versa). After this, she remembered to do this for all her subsequent math problems. Then, we did problems involving using the vertex form of the absolute value function to perform translations on the absolute value function and find its slope. I explained that this was somewhat of a review from one of our previous tutoring sessions and she seemed to grasp how to do these quickly. "

"For the first session, I began reviewing with the student the basic parts of speech in order to determine our starting point. After that, I helped him finish and edit his rough draft paper on black bears. We ended our session with beginning research on his state history assignment."

"The student has been doing a great job. I have been focusing on math with him. We have been working on groups of 10, regrouping, addition, money, and time. He has been doing well, with me going over the first half of the problems on a sheet with him and then letting him do the rest on his own. We are also working on adding without using fingers and using more than 1 strategy to do the same problem."

"I assisted the student with her math and vocabulary. For vocabulary, I quizzed her on the words and helped her to understand the definitions of them, as well as their pronunciations. Overall, she did a great job!"

"The student was a pleasure to work with! We covered the three chi-Squared tests: goodness of fit, association, and homogeneity. We also touched on two sample proportion Z tests and confidence intervals, all in preparation for her tests tomorrow and Wednesday. She really seemed to have a good grasp of everything we covered! After we briefly went over the differences between the chi-Squared tests, we jumped into practice problems. She worked quickly and got all of them right, and I gave her some advice on how to best phrase the explanation part of her answers. She is going to do well on her tests, and I look forward to working with her again!"

"Today, the student and I worked on graphing strategies for parabolas. She managed to complete her weekend homework during the session. I explained to her how to easily solve the quadratic equation by looking at pieces and solving them individually, then estimate if needed with the calculator. I did suggest that she pick up a scientific calculator because the math that she is doing now is specific to the order of operations and this type of calculator allows her to use the parenthesis indicating the order of operations. I am very proud of the 79% she got on her last test because she is slowly evolving from a C student into a B student. I see no reason that she cannot end the class with a B for the semester. There is a test before spring break at the end of the month and so we are aiming to get a B on that one. Overall, she is putting the work in and seeing strong results."

"We practiced creating Taylor and Maclaurin polynomials and using them to approximate the value of a function. We also went through finding the Lagrange error bound for a Taylor polynomial using the n+1 term and the maximum value of the n+1 derivative on the interval between the center and the approximated value. The student is doing better generating the Taylor polynomial for a function as well as using knowledge of the coefficients of the terms to determine properties about the original function. He is also doing better finding the Lagrange error of a Taylor polynomial and we talked about how to find it for both calculator and non-calculator problems."

"We discussed acid/base reactions and discussed the methods of solving for the pH of weak acid/weak base solutions. We discussed the theory behind ICE tables and how they can be used in conjunction with acid dissociation constants to solve for pH. We then discussed buffer solutions in terms of how they work and why they maintain pH when small amounts of acid or base are added. "

"Today, we continued covering sampling proportions to prepare for the student's quiz tomorrow. We went over the sample questions provided by the teacher. I gave a sample quiz and we reviewed the problems together. The student seems to grasps the concept of sampling proportions and had no trouble with the quiz. It is clear how hard the student has been working. The student has no problem explaining concepts and answering given questions. Great job!"