Award-Winning Private Geometry Tutoring in Rio Rancho, NM

"Tonight we covered Circles. First I went over an anatomy of circles (center, radius, diameter, circumference and area) Then I went over formulas, pausing to explain the origin of pi. Next, I began exploring the equation of a circle, first centered at the origin, and then at a general center, (h,k). Finally, I re-wrote the general equation of a circle by expanding out the squared binomial terms and simplifying. Next time I will check to see if they can recall information from this night."

"The student had a packet to complete on finding the equations of circles. He also had a multi-step word problem related to common tangent lines in circles. The student did well on this overall, but he was a little rusty on some formulas he needed from earlier in the semester, such as for distance and midpoint. We spent the remainder of the session reviewing for his final. The student said he had a group quiz that he thought went well."

"The student and I covered topics dealing with angular relationships in circles and segment relationships in circles. Various rules and theorems were used to calculate various angles, arc length angles, and secant / tangent lengths inscribed inside, outside, and tangent to circles. We went over two (2) homework sets of problems. The student received a 100% on her last weekly quiz. She seems to grasp the concepts well for these topics."

"During this session, the student and I reviewed for her test on Friday. Her test would cover five sections in her textbook, all of which dealt with circles. The first session discussed different lines/line segments that crossed (secants), touched (tangents), or were contained within (chords) circles. She had a little trouble determining the equation of tangents lines and discerning the differences between certain vocabulary so we focused on these topics. She had no problems understanding the topics contained in the second section which dealt with how arcs are measured (by central angle measure). We talked about the relationship between congruent arc/chord/central angle triples. She was so comfortable with this topic that even the trickiest problems couldn't phase her. The third section focused on arc length and sector/segment area. Using the "part of a whole" analogy, she could derive the formulas for the areas and lengths. We discussed the method of finding segment area to reinforce her understanding. She was comfortable using the trigonometric ratios to find the base and height of the triangle whose area was to be subtracted. The fourth and fifth sections dealt with four theorems regarding angles and the arcs that they inscribed. She could easily determine which theorems should be used when looking at graphs so we gave each theorem a name that made them easier to recall and use. I saw no deficiency in the understanding of the topics. I am confident that she is going to do well. "