Award-Winning Test Prep & Academic Tutoring in North Park, UT

We first discussed how to graph f'(x) when given a graph of f(x). This can be a bit tricky at first. I first demonstrated how to identify points on f(x) that have a derivative of 0, or horizontal tangent lines. Between any 0-derivative points, we approximated the value of tangent line slope and graphed those values. This allowed us to roughly graph f'(x) on the same set of axes as f(x). This process took a few examples for the student to start picking it up. I told the student that we would spend more time on this concept again at our next session. We again did some review problems that covered derivatives. They progressed in difficulty before I gave her a very complex problem that incorporated power rule, chain rule, product rule, and quotient rule, trig functions, e^x, and ln(x) all into one. It was meant to be intimidating, but we talked through how to break it down into smaller components and solve each one. We also talked about how to find the derivatives of rarer trig functions, such as sec, csc, cot(x), when you can't memorize them. We were able to finally reach the correct derivative solution to this extremely complex question. Afterward, the student breathed a sigh of relief and I congratulated her on solving something more complex than she'll likely see on her exam. I then covered some new topics with the student that introduced some applications of derivatives. This included finding extrema values, the extrema value theorem, concavity, and inflection points. We did one or two examples that required the student to find extreme values, the concavity, and any inflection points within a given range. We then used the last 15-20 minutes of our session to get a head start on the next homework assignment due later in the week.

Today we covered Box and Whisker Plots. This included finding quartile 1, 2, 3 by using the median of the data set and the median of the two halves of the data set. We then worked on some test problems that included probability, finding volume, and solving word problems.

The student felt he did well on his quiz last week. We worked from the book on possible future topics. We started with a review of sin and cos graph transformations. We then moved on to csc and sec graph transformations. He did well with the csc and sec graphs and seemed to have little trouble transferring his knowledge of cos and sin graphs to the new topic. Next, we covered tan and cot graphs with vertical & horizontal shifts as well as changes in period. After reviewing these graphs, he and I talked about how these functions (specifically sin and cos) are used to model 'real world' systems (springs, Ferris wheels, etc.). The final topic we worked through was inverse trig functions, i.e.. Arcsin, Arccos, Arctan, etc. Overall he seemed to understand the new material. He will continue to work through these topics over the course of next week during school.

We started by covering radicals. The student had seen some of this material before, so it wasn't difficult for him to learn the radical operation rules and their applications. Afterwards, we went over exponential functions. He picked up on this topic readily, and understands how to apply the general formula for an exponential function. The only issue that came up was that sometimes the student would rely too much on mental math; the few minor errors he made were due to this. When he writes his work out, however, those errors go away entirely. We ended by doing 11 multiple choice questions from a practice Algebra I state exam. The questions we did covered a broad range of topics, but the student was able to answer almost all of the questions entirely on his own. At this rate, I have no doubt that the student will be more than ready for the exam when he takes it.

Today, the student and I worked on a handful of problems, mostly dealing with momentum, and conservation of momentum in collisions. She did well overall; she didn't really appear to have any problems in understanding the material.

Today we played the vocab dice game and practiced the words ambiance, memento, sympathize, encumber, subtle, instigate, retort, elation, candid, animosity, engaging and gracious. The student also practiced mean, median, mode and range. We also started working on finding points on a coordinate plane and finding numbers on a number line. He is doing very well learning this concept. He also worked on the order of operations and he got all of those questions correct. He also worked on synonyms, reading comprehension and analogies which he did well on.