Recent Tutoring Session Reviews
"Today we worked through one of the practice tests on the course's website (covering the same material we had covered in our last two sessions) as an extra practice leading up the course's last test and final exam on Tuesday and Thursday, respectively, of this coming week. We covered half of this test's material today, specifically expansion of binomial expressions, finding specific terms in an expanded binomial expression, and finding the coefficient of a specific term (and I was excited to be able to introduce the student to Pascal's triangle as part of this topic). The other material we intend to cover Saturday and/or Sunday is proof by induction. The student continues to excel in calculations, though small mistakes are still being made when she tries to go too fast. I was able to meet her mother today, and we discussed that while the focus for the next week will be finishing out this course as strongly as possible, our goal for further tutoring this summer before the start of school will be on shoring up the student's foundation, probably with a particular emphasis on graphing as this area seems weaker than others and has been noted by the student herself to be her least favorite part of the subject (but is obviously a critical skill to possess in later courses such as the calculus sequence of courses). She showed great retention from our previous work together. I would recommend continued use of the flashcards to help with maintaining the smaller details of previously covered material from the course, not just for conic sections but also for the first half of the course."
"We reviewed for the final exam, covering the previous exams corresponding to each of the previous weeks. Overall a productive session."
"Today we went over geometric and arithmetic series/sequences. We focused on the formulas that the student struggled with the most."
"We did exercises that applied the Law of Sine to find lengths and angles of a triangle. We also discussed problems to find area of a partial disk (circular shape) using trigonometric functions. Most of these took long calculations to obtain answers."
"The student and I learned an alternate method to measure angles and rotation called the radian. We saw that the radian is a more intuitive measure of angles and is the basis for the formula used to find circumferences. Next, we practiced converting between radians and degrees and vice-versa, using just two forms of the same conversion factor. We focused on certain radian measures (ones whose trig values will soon be memorized). Another topic on which we focused was the conversion between decimal degrees and DMS notation. She picked that skill up rather quickly once she saw that dimensional analysis simplified the process. The last thing we covered was angular velocity and linear speed. We saw that angular velocity is the rate of rotation and that multiplying that with the radius of the rotating object gave us the linear speed. We could therefore link rotation speed with the linear speed (e.g. tire rotation to road speed)."
"We worked on vectors and polynomial equations today. Student 1 was more reserved than Student 2 and mostly listened while Student 2 asked the questions. (I think his class may be a day or two ahead, so he may not have needed as much assistance.) Aside from a few questions about adding vectors and when to regard a polynomial as fully factored, the brothers seemed pretty on top of things today. They hadn't heard of the Golden Ratio or the cubic formula, so we talked about those things for a while."