Award-Winning Test Prep & Academic Tutoring in Matthews, NC

"I continued to work on reducing fractions with the student and we practiced some division as well. He does have a good understanding of the problems and we are going to continue to work on and proceed to addition of fractions next week."

"First we covered factoring quadratic polynomials when the quadratic term has an integral coefficient other than 1. I explained that we begin by preparing two sets of parentheses for the factors and choose the first factor of each parenthesis such that the product of those factors is the quadratic term of the original polynomial. We then label the unknown second factor of each parenthesis with a unique variable identifier. Subsequently, we multiply our factors together, which gives us a system of equations that can be solved using simple algebra. The student is fairly comfortable solving such systems of equations. We then addressed "annual interest compounded quarterly." I explained to her that the terminology here is quite misleading, since "annual interest compounded quarterly" does not equal the "annual interest" on a growing value. Instead, I explained, "annual interest rate compounded quarterly" means "four times the quarterly interest rate." I explained that this is represented algebraically by beginning with our normal annual interest formula and adding a new variable, n, which represents the number of times per year our initial value gains interest. I emphasized that when we are given a rate and the knowledge that interest will be compounded multiple times per year, we can rewrite (n * t) as (nt) and thereby extract the annual interest rate, a = (1 + r/n)n, from the above equation, leaving us with P(t) = P0 * at, which is of the same form as the normal annual interest rate equation. I think she could benefit from a little more practice grasping this concept; I will make sure she gets that practice on Wednesday. After the interest rate question, we solved a quadratic function similar to our first problem using the quadratic equation, and I showed her how she might have applied the methods of our first factoring problem to solve that function without the quadratic equation. We then clarified her understanding of solving and graphic linear inequalities. She grasped this quickly. Finally, we began chapter 6. I helped her more accurately graph points in three dimensions, and I explained how to understand whether she was supposed to be graphing a point or a plane. We practiced solving systems of equations in three dimensions. She correctly solved the given problems. We finished by brushing up on her understanding of logs and exponents. At this point, we had been working for quite awhile and agreed to finish our efforts at a later date. "