Recent Tutoring Session Reviews
"The student has her final Wednesday. I hope she had time to study before then. We mostly went over differential equations, vector fields and Euler's method."
"This session the student and I worked more on a packet that his class had been provided. The two subjects which we covered the most this session were u substitutions and absolute value of integrals. We started with u-substitution and reviewed our process: 1) choose a "u" 2) take the derivative of it to find du/dx and solve for dx 3) substitute in dx into your integral and hopefully cancel some things out 4) substitute u into your integral and hopefully solve the integral. (If you can't solve the integral at this point, then you have chosen the wrong u and you should try again. 5) reverse substitute and state your answer. And then we practiced it again and again, having just really learned how to evaluate integrals at bounds and solve integrals. By the end of this practice, the student was able to do u substitution by himself, which was a victory. We also got to talk about the integral of the absolute value of a function. I showed John graphically what happens if you take the integral of a function where the function has both positive and negative values. I showed him that he area above the curve and the area below the curve interfere with each other. If you were going to, for example, take the integral of the function sin(x) from x=0 to x = 2(pi) then you would find that the integral is zero. However, if you would take the absolute value of the function over those bounds, you would find that the function is positive from 0 to pi and negative from pi to 2(pi) then, you would do two separate integrals. You would take the integral from 0 to pi and keep that part positive, and then you would take the NEGATIVE integral from pi tp 29(pi) in order to subtract the negative part. But how would you find where the function is positive and negative, if you didn't know what the function looks like the way we know sin(x) well? You need to set the function equal to zero and solve for x. Then, plot these x's on a number line and find if the values of the function are positive or negative ext to those values for which the function is equal to zero. Then, you would be able to tell where the function is positive and negative, and therefore be able to tell which portions of the integrals over what bounds you should negate. This explanation brought us to the end of our class. four out of five stars."
"The student and I worked on the vocabulary workbook, reviewing the vocabulary from chapter 10 and 11. We also continued the psychology review."
"The student was preparing for the midterm and doing some practice questions from the sample exam. We were working on combination of functions, compounding interest and effective rate, percentage change, average rate of change, definition of rate of change, numerical and algebraic methods of finding derivatives, regression models. He is familiar with all the formulas after adequate exercises."
"The student is preparing for a math placement exam that covers every math course between Algebra and Calculus. During our session, we reviewed several concepts covered in Algebra. She had a review sheet with dozens of sample problems. Whenever she had a question about a problem, we would stop and work our way through it. I would also explain the concepts behind the problems. Overall, the session was very productive. We were able to get through all the Algebra problems and get started on the geometry problems."
"This session involved us going over both accounting and calculus. We covered the different type of accounts that you can deal with and how you are supposed to make adjusting entries for loans. In calculus we went over advanced counting and how you can combine different things."