Recent Tutoring Session Reviews
"The student took the test on the derivatives. Although he sometimes got his formulas mixed up and didn't always plug in properly, he understood the concepts and did well on the test. He got an 80%."
"We worked on optimization problems, graphing using the 1st derivative, and limits and asymptotes. I assigned problems from each of these topics. The student expressed interest in another test again and discussed the rest of the summer schedule. We plan on meeting two more times before he has to go back to school."
"For our last day, we looked at the first and second derivative tests for curve sketching and practiced finding critical points and inflection points. We also went over the mean value theorem and Rolle's theorem for continuous functions. Lastly, we did talk a little about how to find the original function if we are only given the derivative as a corollary to the previous theorems. The student is doing well with taking derivatives of various functions and is becoming more confident on using derivatives whether to determine velocity or acceleration from the position function or to analyze a graph by finding specific tangent lines. She has done well this summer connecting techniques we've learned in calculus to long and complicated pre-calculus concepts. She has also strengthened her pre-calculus skills such as simplifying or rewriting functions and working with logarithms and exponentials."
"We went over fractions, negative exponents, and other types of rules involving distribution of exponents to a variable. Many problems were solved in order to differentiate how the rules are to be applied. Ex: common denominators, when to add or multiply denominators/ numerators, etc."
"Today we covered polar graphs and conics. We calculated directrices of ellipses and parabolas. We also looked at foci and vertices of hyperbolas, parabolas, and ellipses. Moreover, we calculated the eccentricities of ellipses. We looked at parametric equations and converted them to equations on a Cartesian plane. We also converted polar graphs to Cartesian equations, using the relationships rcostheta=x, rsintheta=y, and x^2 + y^2 = r^2. We calculated arc lengths and areas of polar graphs. The student was eager to learn the material."
"We studied techniques and applications of differentiation. We did problems using the product rule, quotient rule and chain rule to find the derivatives of functions and then find the slope and equation of the tangent line to the original functions at a given x value. We did very few things with basic algebra, and he really had everything down with the calculus, especially after working through a few problems. The student was very interested and willing to learn the material."