Recent Tutoring Session Reviews
"We discussed antiderivatives, finite sums to determine areas under curves, Riemann sums, the limits of infinite sums, and the definite integral."
"Today we worked on many topics, the largest of which was particle motion. These problems can go one of three different ways. Sometimes, you are provided with an equation for position, and you have to take derivatives of it to get the equation for velocity and then take the derivative of the velocity to find the equation for acceleration. Another question topic in particle motion is when you are given an equation for acceleration, and then integrate it in order to find the equation for velocity. When you do this, you end up with a constant +C which you then need to find using a constraint. A constraint tells you the value of the function given a specific input. The question will say something like: "the velocity at t = 10s is 40 m/s" Once you plug in this point, you get a numerical value for C. Then you can re-write your velocity equation and then integrate that in order to find the equation for particle motion +C. You then need to solve for that =C using a different initial condition, this time for position. The final question type in particle motion is if you are asked to find the total displacement VS total distance traveled. To find displacement, simply find the integral of the velocity function. If you are asked to find the total distance traveled, then you should find the integral of the absolute value of the velocity function. To do this, the first step is to find for which values of t your velocity function is positive and which values of t yield negative value for velocity. Do this by setting your velocity equation equal to 0 and solving for t. Then graph your end points, and each zero point on a number line and determine whether your function is positive or negative in between each of these points which you have marked on your number line. Then, you need to evaluate the integral of the velocity for each sub-section interval which you've just created. The trick is to negate the terms which are going to give you a negative distance, to make it a positive distance. In this way, instead of getting the displacement, you get the total distance traveled. This brought us to the end of the session."
"The student and I covered all the materials that we have previously covered in all our sessions. She was getting ready to take her final test in her calculus class. In order to note progress, I made sure I checked all her quizzes and tests, so that I could know what she needed support with and what she already understood. Recalling and practicing how to take derivatives definitely helped her to know the difference between derivatives and integrals. It was such a pleasure to work with her; she has been a hardworking student who gave 100% in every tutoring session. I have seen a lot of progress in her! She took her final test and sent me an email to let me know how she not only got an A on her final calculus tests, but that she got an A in the class!"
"We went through her new packet - it had graphing rational functions, which we have worked on previously, although with the added difficulty of polynomials of varying degrees and finding holes. Then we moved into simplifying, adding, and solving rational equations. Some of these were fairly simple, but others were more difficult. Having steps written down will help on complex problems like this. She has a test on Monday so we are going to meet on Sunday for an extra review session."
"The student's have started learning converting percents into decimals and converting percents into fractions. They took a pretest on these subjects and they told me they did well on the pretest. Gave them both practice problems on converting percents into decimals, converting percents into fractions, converting decimals into percents and converting fractions into percents. I had to explain to student 1 how to convert percentages to fractions and how to convert decimals to percentages. I left him with some problems on converting fractions to percents. I had to explain to student 2 how to convert percentages to decimals. I gave him review problems on missing dimensions. They both handled the problems I gave them very well. They both had good attitudes toward the material being reviewed."
"Today, the student had an assignment about variability and statistics. She had been unsure how the two were related, and I used one of the questions she had previously answered to show her that variability was necessary for a situation to be statistical. Afterward, she was able to complete the assignment with no difficulty. With the remainder of our time, she brought up an assignment from her social studies class about Hinduism. She had answered most of the questions, but there were a few that she had been unable to find the answers for in the article she had been given with it. We discussed the material in the article until she was able to come to the answers on her own."