Certified Tutors From Loras College

The student wanted to get one last session in before her final the next day. She has made marked improvement in her fundamental understanding of calculus concepts. We practiced several related rates problems, some of them very difficult. She had to use her own reasoning to come up with relationships between different changing variables, identify the independent variable, what that means for implicit differentiation, and how to check her reasoning using units. I was very impressed with her problem-solving skills. We then spent quite a bit of time on the definition of limits and how to calculate them, finishing with tips on graphing functions by hand.

We discussed what the student is learning in Chemistry. He said they were covering hydrogen bonding and dipole-dipole dispersion. He told me he felt comfortable with the material. For Alg. 2, we looked at his next assignment that involved solving a set of equations with 3-4 equations and unknowns. He expressed some confusion with the multiple steps but did a good job working the steps and finding a solution.

The student had a test on Friday, so our session on Thursday was a chapter review of her exam. Her test involved conic sections equations and graphing. We reviewed how to graph a parabola, ellipse, and hyperbola. She needed practice and help remembering how to find a directrix and focus for a parabola through the equation. For ellipses, she needed to remember how to find vertices and what constituted the major or minor axes, as well as how to find the foci for an ellipse. For the hyperbola, it was similar to the ellipse, but she needed a way to remember which one was added and which one was subtracted, so I gave her an image on how to do that (2 halves of the ellipse come together = +, and hyperbola points away = -). Also, she needed help finding the equation of asymptotes. Lastly, we went over how to take the given info above and finding the equations of the conic sections.

This session the student and I went over prisms, cylinders, pyramids, and cones. Last session, we discussed the surface areas of the four shape types but we calculated each area on a shape by shape basis. We had broken the shapes into its components shapes and calculated the area of each before finding the total surface area. This week, we learned general formulas for the surface areas and volume of the four shape types. These formulas could be applied to all prisms, cylinders, pyramids, and cones. For surface areas, we recognized that all the shapes were comprised of its base areas (2 for prisms/ cylinders, 1 for pyramids/ cones) and is lateral area. So calculating SA was broken down into two steps. Finding the base areas were simple because they were basic shapes whose areas were previously covered. We derived the formulas for the lateral area by recognizing that it was the base's perimeter scanned over the length of the prism/cylinder. Surface area calculations regarding pyramids and cones required some memorization. Like with prisms/ cylinders, the base area was easily calculated. We derived the formulas for the lateral areas to show from where the formulas came. He had no trouble find SA's after he memorized the formulas. Volumes of the four shapes proved easier to find than surface area. We recognized that volume of prisms and cylinders were just the bases' area scanned through its height and saw that the volume formulas reflected that (Base x h). Volumes of cones/ pyramids were less intuitive but easy to memorize (volume is 1/3 of the volume of its corresponding prism/ cylinder). He had no trouble applying these principles either. We talked about Euler's rule for polyhedrons as well as Cavalieri's principle.

Today the student and I went over his classwork and homework on box plots and frequency tables. We also went through some 6th grade math sample state test questions. The questions had covered several topics that he and I had worked on and with some encouragement, he tackled the questions and did well. I was very pleased with how well he did.

The student did well today! She got an A on both her individual and group exam for the last chapter! :) This improved her overall grade, but I want her to get an A in the course. We're going to work on different tactics/test taking skills so she's getting A's on her quizzes (since they're timed). Today, we went over the material that will be in the upcoming chapter. It's not too hard and I think she will do well. For Tuesday, we'll go over homework she had and start learning some test-taking skills/practice for her upcoming quizzes.