Recent Tutoring Session Reviews
"Today's session with this student consisted of going over integral approximations, namely the left and right Riemann sums, the trapezoidal rule, and triangular area approximations. She was initially having trouble differentiating between the different area approximations and what each one entailed, but I went from the very beginning and broke it down from its most basic components in a graphical and algebraic way. She responded well to my instruction and had little trouble completing the problems that were thrown at her. She ensured me that she had a much clearer understanding of the different approximation methods and what it meant to have an overestimation and an underestimation depending on what graph/ function was given and which approximation we would use. The goal is to meet again with her before her final exams so that we can work out any more kinks in her understanding of cumulative material."
"We reviewed the student's trigonometry homework, which involved graphing trig functions (review) and applying trig laws. She had a bit of trouble with simplifying trig expressions with her trig laws simply because she could not figure out which ones to use in certain situations, so she would get stuck. After a few examples, she was able to do the whole assignment herself."
"In this session we attempted to work on a worksheet that the student had which focused on particle motion. She mentioned that her teacher would review the worksheet in class. Afterwards, we reviewed logarithms. There were some questions that she struggled with, so I would encourage her to avoid using the calculator to condense and expand logarithm problems. We would review more of these problems in our next session."
"Tonight, the student and I worked on another previous exam to practice for his final. This included a pretty wide variety of problems, including complex numbers, sequences and series, combinations/permutations, and conic sections. He seemed to remember more of this material better than the trigonometry from yesterday. He definitely gets the basics of complex numbers, sequences, and probability. In a few cases, he just needed a little help setting up the problem and getting it started. I've definitely noticed improvement compared to the beginning of the semester, so here's hoping he does well on the final!"
"We reviewed vectors and complex numbers. We reviewed how to find the x- and y-components for a vector between two points as well as how to write a vector as a sum of unit vectors. We practiced finding the sum of two vectors, both graphically using the tip-to-tail method and algebraically by adding the components. We reviewed how to find the magnitude and direction of a vector from the x- and y-components using the Pythagorean Theorem and the tangent function. We practiced converting complex numbers between rectangular and polar form. We also went through multiplying and dividing complex numbers in polar form as well as DeMoivre's Theorem. We talked a little about finding the roots of a complex number and multiplying complex numbers in rectangular form. Lastly, we talked about the dot product of two vectors and how to find the angle between two vectors. The student is doing better working with vectors in component form and converting between the two forms for complex numbers."
"We covered parameterized curves and surfaces. The student had been able to do most of the homework himself, so we just reviewed the problems to make sure he had any questions clarified. He was doing well with the material."