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Private In-Home and Online Pre-Calculus Tutoring in Pomona, CA

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Session Summaries by Pre-Calculus Tutors

Pomona, CA Pre-Calculus tutoring
The student was very responsive and willing to learn. We covered mainly trig functions and Pythagorean theorem. The student got extra practice. Mainly just preparation for tomorrow's test.
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Pomona, CA Pre-Calculus tutoring
We worked on multiplying and dividing radicals. The student was awesome with this stuff! It is usually really difficult for students, but she completed most of the assignment independently.
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Pomona, CA Pre-Calculus tutoring
The student and I went over both his algebra 2 and geometry homework and class notes. The homework for geometry was based around using both the Pythagorean theorem and proportionality to figure out the given sides or variables in a triangle. We also used induction in order to figure out a general rule of thumb for the 30-60-90 triangle and the 45-45-90 triangle. Two special cases where certain particular proportionality occur. The student already understood how to properly use the 45-45-90 triangle proportionality to figure out a given side, so we focused primarily on the 30-60-90 to get a better understanding. The student made the observation and was able to recite the information after we had concluded the lesson entirely. I was very pleased when his brain was also able to register some of the information when we switched over to graphing on the Cartesian Plane and figured out where the 3rd point of a triangle lies. This involved using the distance formula and deducing that since the 3rd point (what we were solving for) lies in the 3rd quadrant, then the short side was already given to us. I was very impressed as this is a more advanced observation one must make in mathematics to complete this problem. When we switched over to algebra II we were focusing on solving inequalities involving radicals. The thing I had to instruct the student the most on in this section was that the number in the radical had to be a number such that when subtracted, squared, or whatever operation performed on it was done, the number under the radical had to BE AT LEAST zero. This is crucial as any other number would result in an imaginary number which did not apply since we were dealing only with real numbers. The student understood this and even wrote down the note so that he will remember. After that, a check needed to be done to see if that solution worked. Usually it didn't or wasn't the entire solution, so I had to explain to the student that this was a close approximation of what our number should be around. The student grasped this after a few examples and walkthroughs, and all that was left was to solve the inequality in its entirety. I am proud to say that the student excelled at this, and eventually he was able to do these problems on his own. The tricky part of these problems is that after you had gathered the given information your answers would be combined to either eliminate one possibility or combine them into one big one. The premise of this exercise was to understand the domain of a function and the restrictions a given function can have, where certain numbers will not exist because of characteristics of the function. The student really did grasp the material and was able to perform it on his own. I was quite pleased with his ability to do this, and it showed that he was indeed understanding the material. I know that the student is very bright in mathematics and, without a doubt in my mind, he has a promising future in the subject. Next time, I will show him how to use his calculator to double check his answers along with a few other procedures/"tools." All of this will involve higher mathematical concepts and logical understanding that will only advance his ability in the class.
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Pomona, CA Pre-Calculus tutoring
We had one more day to review for the Pre-Calculus exam. She was feeling pretty good about it because she had been able to solve many of the problems they had covered in class. Primarily, we focused on use and meaning of the remainder theorem, solving limits at a point and at infinity, and use of the IVT.
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Pomona, CA Pre-Calculus tutoring
Since the previous session, the student has been taking better notes and it seems to be helping a lot more. In the session, he and I covered trigonometric identities, vectors, and the laws of Sine and Cosine. He struggled a bit with the vectors, but after a little bit of clarification to explain about i and j (the x and y values to show direction), he seemed to be able to do the work without any issues. With regards to the trigonometric identities and manipulating one side to be the other, that will take some time for him to master, but he understood the overall process. Those are tricky problems to work with and require a lot of practice, so I believe working on a few more problems on his own should suffice. With regards to the laws of sine and cosine, he breezed through those topics and showed a grasp of the concept. Leaving the session, he was able to summarize what we worked on in his own words.
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Pomona, CA Pre-Calculus tutoring
The student and I began to cover a new unit on Trigonometry functions and the Unit Circle. He did not have her class materials with him for this session, but did have some practice problems given to him by the teacher. He was able to grasp the fundamental principles at work in this unit well, and responded well to my explanations. He will need to do some memorization for this chapter of some basic facts (which functions are which signs in each quadrant; the length of legs in the two special triangles, how many radians in 180/360 degrees), but I think he should not have too much trouble once he has more practice with these components.
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