Recent Tutoring Session Reviews
"We worked on graphing shifts in functions. So she graphed the parent function (like f(x)=x^2) and then graphed the new function with a shift (like f(x)= 2x^2 + 1). We went over how each change to the function would alter the graph."
"The student and I practiced graphing asymptotic equations. We also worked on finding end behavior of those equations. In our last twenty minutes, we practiced SAT Math problems."
"Tonight, we reviewed an old test on factoring and graphing trinomials. Then, we covered polynomial inequalities. We're meeting at least one more time before his test on Monday."
"Today we worked on packets 14-16. We have moved up from linear and quadratic equations to general polynomials. Our main goal today was to go over how to factor and graph polynomials. First we discussed how to do division of polynomials. This was already something he was familiar with. We then talked about the multiplicity of a zero, and talked about how that will affect the shape of the graph. After that we learned about the remainder theorem and the factoring theorem. Together, those two theorems let us factor any polynomial by making a list of all its possible zeros, and the factoring out that zero using synthetic division. This was a long process, but the student was able to grasp it in the end; however, I recommend looking over the examples again. We then worked on how to graph a quotient function (a quotient of two polynomials). We were able to find the x intercepts, the y intercepts, the vertical asymptotes, and we will work on horizontal asymptotes next time."
"Tonight we continued reviewing his text, covering the rules of differentiation for polynomials and utilizing product and quotient rules. The student was a little uncomfortable with the notation at first, but after reviewing the notes and explaining the different notation for derivatives and what each rule meant, he was able to apply them to the practice problems with little to no help. He understands the applications. The last few practice problems were word problems, and the remaining concept came up to explain how to take the derivative of a multivariable function with respect to only one variable. After explaining the method to just treat all variables like constants, the student was able to solve the problem on his own. We plan to meet again tomorrow as this concept is a relatively foreign mathematical concept when seeing it for the first time. The student would like to cover the next few lessons ahead of time to prepare for his end-of-the-year tests."
"We reviewed for the student's free-response final. We looked over the packet we completed last week, which covers trigonometry and series. We went over every formula that he should place on his allowed piece of paper including the unit circle, equation of a sin or cos curve (understanding amplitude or radius, period with relationship to b, the phase angle or horizontal shift and, the center line or vertical shift), trig identities to solve proofs, solving equations using the unit circle or calculator, geometric series having a common ratio, finding infinite sum of a series, performing summations on the calculator, and understanding drug dosing problems as related to a series."