Key Biscayne Tutoring: Tutors in Key Biscayne, FL

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Today, the student and I began on geometry, started on angles, geometric notation, dimensional analysis and area/volume/perimeter. Next, we will discuss difference between postulate and theorem, learn what a proof is, and start on triangles.

The student and I reviewed for a math quiz she is having on Monday. We went through graphing exponential equations without a calculator. She said that she understood most but not all of the process. We went through examples that all involved a transformation of the equation f(x)=1/x. We discussed this basic function and what its graph looks like. We also went over the different types of transformations. The primary reason we discussed this is because the student won't be allowed to use a graphing calculator on her quiz; knowing the basic shape of the graph will help her graph more accurately. In addition to graphing, she needed to find domain, range, intercepts, end behavior, asymptotes, describe end behavior, and also areas of increasing or decreasing for the function. She did well with graphing and plotting what she knew helped her to determine more information about the function. The student had some trouble describing end behavior so we went over that more than some of the other topics. We also did a problem involving real world application and she was able to set up and solve that problem mainly on her own. She works hard during our sessions and is good at asking questions to better understand difficult concepts.

We went over more questions of the student's sample final exam to realize more in depth the meaning of the derivative. I illustrated the derivative from a graphical point of view and then from a calculus point of view using its limit formula. We looked at the derivative of a space-time function and then at the derivative of a velocity-time function. Then, we looked at the derivative of the trigonometric functions and how to draw a sine and cosine from the circle on the x-y plane. I am preparing an online calculus test that he can do before we meet again.

Today we did more practice on integrations with area, changing bounds, and carefully checking over the work of practice problems for understanding.

The student received a 71/75 on the take home quiz, before the curve and the opportunity to get half the points on the corrected problems. So, even though this is a very good grade, it has the potential to be even better. The chapter 3 test was pushed back to tomorrow. So today, we worked on the new review packet for the chapter. We were able to cover all the problems that he hadn't done in class. He did very well today. The only challenge was when he was reading the graph of the first derivative but kept interpreting it as the graph of the function. After about 3 similar problems, he improved quite a bit in recognizing the difference. I feel much more confident in his preparation for this exam, and I feel that he is quite ready for it.

For this session, the student completed his homework including spelling words and math. He did a great job on the math homework which involved determining which items are heavier or lighter. He also completed a couple timed tests including adding by 5s and 6s. He struggled a bit with the 6s and will need to practice those a more to be proficient. Nevertheless, he is trying harder to work with speed and efficiency on the timed tests, which is a huge improvement. He and I also practiced telling time on an analog clock by matching the clock to the digital time and by playing Go Fish. He did a great job with this.

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