Award-Winning Test Prep & Academic Tutoring in Forest Grove, OR

Today we covered quadratic equations and application. The student seemed enthusiastic about the material. I see her becoming more comfortable with the material once she has some more practice. We went over several of her homework problems. I stressed memorizing the quadratic equation, and doing so with a song that helped me back when I was in high school.

I helped the student work through a number of Algebra problems from a packet he was given in class. During solving problems, I asked the student questions to challenge him to answer the question on his own. I also would have him repeat a problem and explain to me how to solve it to make sure he fully grasped the concept.

The student had begun a new unit in his math class, so we spent our time working on a packet which covered some of the new topics. I began with a brief discussion of rational expression (the theme for the new unit), what they are, how their graphs look, and how we can manipulate them. We then began working through the packet together. The first set of questions dealt with filling out a table, developing a formula, and graphing the derived equation. After the first example, he was more or less able to construct the rest of the equations and graphs following a similar process. There were only a few points where we had to talk about determining the stretch factor (a) which we could do both based on the graph, and algebraically.

The student and I discussed studying for her upcoming exit exam next week. We discussed the types of questions that she had struggled with on the practice exam earlier this week. We then reviewed a homework worksheet on solving for variables in various types of equations. Finally, we worked on determining from the equation of a line whether a given coordinate point lies on that line.

Today, we focused on reviewing probability for her Algebra 2 class, specifically sections 10.1 through 10.4 of her textbook. We started off with basic probability and discussed the meaning of the numbers themselves. We compared theoretical and experimental probabilities and how each of them are used. The student and I then reviewed complementary probabilities [1-P(A)] and how it can be used to make some problems easier. Next, we went over dependence and independence of variables. They each have their respective equations to prove or disprove independence and we practiced using both equations. I also gave her the hint as to how to usually find dependence. When the problem states that items are chosen "without replacement," that typically leads to a dependent problem. The verbose word problems can sometimes get confusing, so it is important to break down the word problem into key facts so she knows what each number within the word problem is referring to. She needs to remember that the second term in this type of probability means that she is restricted to finding the probability only if that variable is certain. It usually becomes the denominator of the fraction to find the probability itself. This becomes easier when there is a chart of variables instead of word problems. The individual numbers are known are the joint variables while the sums are the marginal variables. Finally, we worked on determining union, intersection, or disjoint variables and how to spot them. We worked on using charts and word problems for these types of problems. For union and intersection (where there is overlap between two groups), it is important to remember to subtract the overlap since it is being counted twice. Before we ended the session, we reviewed a few more word problems and chart problems to practice. We also went over a quiz on sections 10.1 to 10.3 to fix some mistakes and clarify misunderstandings she had. Her exam on probability is next Friday, so we plan to meet the Thursday beforehand to prepare for the test.

The student and I worked through a critical reasoning and two math sections in our time together. Despite the lapse in time since he and I last met, he retained a good amount of the strategies we discussed - his skills showed minimal atrophy. His reading score was very high, and would have placed him in an elite level. Math was also strong, but not quite as stellar. I have asked him to review several concepts, particularly the properties of exponents, in order to ensure adequate familiarity on test day.