Recent Tutoring Session Reviews
"Today we worked on physics and pre-cal. In Physics, we worked on circuits: finding R and I and V. We also talked a little bit about Power. The student did very well with these. I showed her some strategies for simplifying circuits in parallel and series. For pre-cal, we worked on partial fractions. She did very well with these as well - is very good at following procedure. Occasionally, she had a little trouble simplifying algebraic expressions when she had to multiply two quadratics - but she is usually able to catch these mistakes. They're very easy to make on something with so much writing! We also reviewed some log and exponent rules."
"Completed a homework assignment on determining the solutions to periodic functions both when all possible solutions and when just solutions within a given interval are requested. Explored the solutions provided by the calculator and reviewed how find the complementary solution for sines (pi-theta) and cosines (-theta). Also reviewed the unit circle, the pi/6 and pi/4 steps, and strategies to remember the sines and cosines of special angles."
"During this session, we focused on reviewing the parametric equations unit. We talked about how to parametrize the equations for a circle, line, and line segment, and how to switch between the parametrized and standard forms of equations. We also focused on using parametric equations in word problems - in particular, several problems covered the basics behind projectile motion."
"Today we worked on properties of polynomials of higher degrees. The student has had no trouble with quadratic equations, but he was having a bit of trouble with third, fourth, and fifth degree. Mostly, the trouble was because these higher degree polynomials don't factor as easily as the second degree. We went over a few ways to simplify special cases. We were able to make some corrections to his past assignments and complete a pretest for the section."
"The student and I reviewed topics covered in his class during the week. The topics covered involved polynomial functions. We first learned the methods of polynomial long division and synthetic division and learned how to determine when each was appropriate. After this, we used synthetic division to evaluate (remainder theorem) and find factors/zeroes of (factor theorem) polynomial functions. We then learned the rational root theorem which provided us a list of the potential rational roots of polynomials. Using the rational root theorem along with synthetic division (the factor theorem), we learned to factor polynomials of degree 3 or larger. Given a polynomial in linear factored form, we learned to find the zeroes of the functions and if they are x-intercepts or not. We practiced multiplying the factored form to generate the standard form. Next, we learned to generate polynomials, given the zeroes of the functions which he picked up quickly. I stressed that imaginary roots come in pairs so when an imaginary root is present the second must be accounted. By applying the definition of multiplicity, we learned to recognize function graphs given the roots and their multiplicities. To wrap up, we practice factoring functions using the rational root theorem and synthetic division. We found the complex roots by applying the quadratic formula on a quadratic form."
"The student and I reviewed her online homework today. The homework focused on graphing functions. She is able to do most problems, but sometimes she just needs help getting the problems started. She also struggles to remember terms and their definitions, so part of my goal for her is to help her recognize them faster. I do this by using those terms often in our discussions and sometimes asking for her to define the term or explain a problem using the terms. Many of the homework problems could be solved using the graphing calculator, but when possible, we also went over the paper-method. She is better at remembering domain and range than last time. She finished her entire assignment during our session time."