Recent Tutoring Session Reviews
"The student did some practice problems similar to those on his recent chapter 7 test. Then he worked on some extra problems I selected from chapter 7. I left him with a homework assignment reviewing chapters 1-3."
"The student's next algebra test is Friday, so we focused on preparing for that. The test covers sections 5-1 and 5-2 in the textbook, which includes standard form, vertex form, factored (binomial) form for quadratic functions, as well as solving quadratic equations. In addition to finishing homework questions, I encouraged her to complete questions in the book that could be double-checked in the back. It would be a good strategy to know if she was completing questions correctly. This way, she can identify what concepts might need more work. We clarified the differences between the three forms - standard, vertex, and factored - and how each can be used with respect to graphing and understanding the direction and width of a parabola. I also introduced a song to remember the quadratic formula that goes to the tune "Pop Goes the Weasel." In addition, we discussed the importance of the discriminant in understanding the roots of the parabola. For instance, if the discriminant is negative, then there will be an imaginary value and therefore two complex conjugate roots. A positive discriminant indicates two real roots, and a zero discriminant indicates one real root. There were questions we needed to finish, so we decided to have a follow-up session tomorrow night."
"Today, we reviewed questions in a practice test. The topics included (but were not limited to) integration by parts, derivatives, reading graphs and word problems."
"For today's session we focused on properties of logarithms. We worked through examples of the change of base formula and graphing logarithms using a graphing calculator as well as discussing briefly the natural number e and how a graphing calculator will fail to show the logarithm's vertical asymptote. We spent additional time working on expanding and contracting logarithms as well as some strategies for quickly contracting a logarithm. By the end of the session, the student seemed comfortable with the properties of logarithms and how to apply them."
"The student finished her homework. This was a review of some geometry concepts with scale factors, angles of polygons and calculating areas and volumes. We also worked on completing the square to put the equation in vertex form. We also talked briefly about circles as they'd just been introduced in her class."
"The student and I had a very productive session. We discussed solving exponential and logarithmic equations, involving converting back and forth between exponents and logarithms, simplifying expressions by combining logs, applying change of base for calculation, substituting complex expression by a single term to facilitate the solving process, and factoring quadratics and applying the quadratic formula. She absorbed these new materials well. We spent the last 30 minutes to discuss exponential and logarithmic graphs, their domain and range, vertical and horizontal asymptote. We did several examples involving graph transformation (vertical/horizontal shift, stretch/compression, and reflection). I assigned a worksheet for more practice."