Certified Tutors From The Master's College and Seminary

We finished going over the student's world history notes and preparing her for her test this week. She is very confident that she knows the information for her test. We started to review her algebra lesson from this week, and I realized that this is the area we need to focus on at this point. We will begin to go over these concepts from the beginning starting at our next session.

During our session we covered writing inequalities and graphing them, writing equations and graphing them, solving systems of equations and inequalities (algebraically and graphically), and factoring. With factoring and finding solutions we reviewed concepts like greatest common factor and the quadratic formula. The student remembered how to solve most of the problems and had a positive attitude throughout the entire session. Many problems today were in-depth and had a lot of steps, but she still showed her work neatly and thoroughly. Great session!

Today we worked on grammar (suffix, prefix, roots), then we moved on to multiplication and division. The student has a few concepts to grasp in multiplying (carrying). In division, he just needs to understand that it is the inverse of multiplication.

We covered exponential and logistic growth, how to solve the differential equations for each, how to use initial conditions for each, and how to tell them apart. We did several example problems from each, but as I told him, he really didn't need a lot of help. He just needed a nudge in the right direction. He got all the same answers I did, and almost as fast. I told him not to worry about his test tomorrow, so we shall see how he does.

Topics covered: 1 and 2-step algebraic equations and inequalities. The student is becoming more and more enthusiastic about learning math. There are some problem solving skills that need improvement, but she is making steady progress.

We started going over the remainder and factor theorems for polynomials as well as the rational roots theorem. We practiced finding at least one rational root then using polynomial long division to factor out the linear terms unit we are left with a quadratic polynomial that we can use our other techniques to finish factoring the polynomial. We looked at how to create a polynomial of least degree from a set of given zeros. We looked at how using synthetic division to test a possible rational root can give us the coefficients of the reduced polynomial when we do have a root. Lastly, we talked through sketching the graph of a polynomial by finding any real roots and understanding the end behavior. The student is getting better using the rational roots theorem and synthetic division to find roots of a polynomial and he has a better understanding of what the roots of a function mean both graphically and as linear factors of the function.