Recent Tutoring Session Reviews
"We spent today's session working on real world applications of derivatives. The majority of the session was spent using derivatives in optimization problems to find the minimum or maximum in a situation. By the end of our work on this topic, the student was able to identify the equations we needed to model to find the solution and how to manipulate them correctly. We briefly touched on finding rates of change in real world situations and we will continue to work on that subject tomorrow morning before we move on to integrals."
"The primary focus of this study session was on algebra and trigonometry review, and the definition of the derivative. The biggest challenges were working on the algebraic manipulation of functions when applying the definition of the derivative and moving between trig identities to solve some of the problems. A few websites were provided during the session to act as study aids when going through the material. The course is just beginning, so there were no scores or grades to note. The student was very engaged, asking questions, and comparing his work to explanations."
"First, we went over the assigned problems I gave the student on our last session and we continued to go over the Maclaurin series. We then worked on integration and different integration techniques. We covered u-substitution, polynomial integration as well as integration of trigonometric functions. I gave him extra practice problems to do before our next session. We will continue working on integration in our next session and I will give him a short assessment to measure his familiarity with the material. He was again receptive to learning and engaged during our session."
"We looked at derivatives in real life, using functions that model real world quantities (e.g. position, GDP) and what their derivatives measure (velocity, GDP growth rate). Next we talked about second derivatives, which can be thought of as a function's acceleration. We sketched graphs of functions, first derivatives, and second derivatives, and compared how they line up. I think you're grasping the concept of second derivatives, but remember to review notes and study further to really lock it in. We also talked quickly about critical or stationary points. These correspond to places on the graph where the tangent is horizontal (derivative = 0). They can be easily found by setting a derivative function equal to zero and solving for x. For homework, see the email I sent you with practice problems. Be sure to get lots of practice solving equations to find critical points, because we will be building upon this skill in the next session."
"Our last session introduced sign charts, critical points, extrema, etc. Our session today covered hypercritical points, points of inflection, etc. It is a logical extension of our last session, and it isn't any more difficult. As was the case with our last session, the student understands the concept, but can have trouble with the algebra. The problems we do take many steps and require the knowledge of multiple different branches of math, and recalling all of them for each problem is tricky. He is still doing well, but will need to find time to practice."
"The student and I worked on a review sheet of algebra II and precalculus to prepare her when she begins calculus in the coming weeks. We covered things like polynomial division, logarithms, working with radicals and other algebra and precalculus related material."