Award-Winning Test Prep & Academic Tutoring in East Amherst, NY

"The student scored 90% on his last Algebra 2 quiz, which is a fantastic improvement. This week we moved on from complex numbers and continued with our study of quadratic equations. Over the course of the last few weeks the student's class has been working with various methods of simplifying and solving for variables within quadratic equations. More recently, he has been factoring quadratic equations and using the zero-product property in order to solve for the variable. This week, we moved on to situations where factoring the equation isn't a possibility- which happens to be a lot of the time. In order to do this, an equation referred to as the "quadratic formula" can be derived from the model ax^2 + bx + c = 0, which uses the values of a, b, and c in order to solve for values of x. What we covered first are the requirements and indications of the use of the quadratic formula. First, our quadratic equation must be equal to 0, and if it isn't, it must first be manipulated so that it does. Second, we have to ask ourselves, "Can this quadratic equation be factored?" If the answer is no, or if it would take a substantial amount of time to compute the answer, then we continue on to the quadratic formula. This formula is stated as follows: x = (-b +/- sqrt (b^2 - 4ac)/2a. When a, b and c are plugged in from the quadratic equation in form ax^2 + bx + c = 0, then you will receive 1 or 2 possible solutions for x. The student's homework that we reviewed during this session covered 12 problems that tested the use of the quadratic formula. In many cases the objective was to simply plug in values, but there were several that required some initial manipulation to get our equations into our ideal a/b/c format. The student realized how to maneuver through these problems quickly and the homework soon became a game of repetition. He had very little difficulty with setting up the problems and also little difficulty executing their solutions. The one thing we need to work to improve is his more general understanding of the purpose of the quadratic formula and of solving quadratic equations for their variables at all. His class has moved through these techniques in a very logical fashion, so we will continue to move forward and review at the same time to make sure that he is grasping the "why?" of quadratic equation solving as well as the graphical implications of what he is doing. He is doing very, very well now and has improved greatly since the first session. "

"We went back to looking at the student's study sheets. I had him rework the ones he missed, and we went over a few concepts, like multiplying vs adding polynomials, and the distributive property. He still has several of the worksheets yet to do, and he will be missing the next couple of sessions, so I told him to finish the worksheets during the time we miss. We will evaluate them next week, when we meet again."

"In our session last night, the student and I began studying for his upcoming map quiz in history. We made a template map together with potential regions, empires, and cities located and labeled, and talked about areas of significance and overlap. For our next session, he is going to practice finding and labeling the locations on blank maps, and continue his English reading in the novel "The Catcher in the Rye.""

"We went over more partial credit questions dealing with the Arrhenius equation, etc. We moved onto the practice final questions the student wanted to go over. He had a difficult time with rate laws and determining the rate of a reaction since they are not straightforward. I think that he remembers the concepts well and needs to be aware of what information he is given and what information he can gain with additional steps."

"Our first session here: we blazed thru my "easy bucket", and I believe the student already has many tools necessary to evaluate 600 level word problems and more abstract algebra. Please do review the problems we did today on Saturday or Sunday."

"We reviewed for the student's upcoming test on determining the equation of the line given information pertaining to points and slope in addition to obtaining the equation of a circle. He picked up on the information quickly, and he will do well if he remembers the necessary equations and the key fact of math to do to one side of the equation what you do to the other. I expect he will do well if he does the practice I assigned him and doesn't attempt to do too much in his head. Overall, the session was a success, and I was happy to see him have a firm understanding of the methodology required to solve each problem. He is a smart kid and will do well, especially if he does the practice I assigned. "

"We worked on problem sets. We solved equations for x-squared, practiced FOIL, converted quadratics to vertex form by completing the square, converted vertex form to standard form, discussed translations and scaling of parabolas and cusps, and graphed quadratic and absolute-value equations."

"We continued our work on convergence today, going over the geometric series in considerable depth, as well as its application in real-world problems such as the damped bouncing ball. We also covered how to use several tests in conjunction to find interval of convergence."

"The student and I covered trig substitution and Taylor Polynomials for our session. We went over the theory for each concept and covered several example problems for each concept using several different approaches. I am sending him the notes from the session, as well as additional material to review for extra practice."

"The student has a test in calculus on the integration of velocity, and finding the area between two curves. He also had some basic questions with differential equations. We went over a handful of problems in the textbook, most of which he was able to answer by himself!"