Certified Tutors From Loyola University-Chicago

The student and I went through some review worksheets of the law of sines and law of cosines that she had. For all problems, all 3 angles and all 3 sides needed to be filled in. Given information changed, and first she needed to determine if the law of sines or the law of cosines was needed to solve for the missing information. She is doing well.

The student and I focused on ACT math for the final session before her test on Saturday. We reviewed geometry, probability, percents, and algebraic expressions. We had a broad focus today just to give her a final look at the various kinds of problems she will be seeing, but she did well on the problems and was able to set problems up independently. Even when she was unsure of the "correct" mathematical method for problem solving (which was a focus in prior sessions and this session), she was typically able to reason her way through unfamiliar problems. We also spent about 30 minutes working through some ACT grammar questions and a science passage, and spoke briefly about timing strategies and general tips for each section.

The student and I started with problems requiring her to complete the square to solve. She was initially mixed up by problems in which there was a leading coefficient. She knew that in vertex form you need to have a leading coefficient of one, but she didn't know how to get the coefficient. I told her she couldn't divide because that would change the other side of the equation, but that she could factor the leading coefficient out and then complete the square for the inside of the parentheses. She got this, but she needs to be careful about completing the square. She knows how to find what the c term should be, so I told her to decide what she needs to add or subtract to the number she has to get the new term, and that she just does the opposite outside of the parentheses. She needs to be careful to multiply by any number outside the parentheses too. We did a couple of these problems for practice, then we went on to parabola problems. She completed the square first to find vertex form, then we went over how to find the properties of the parabola once the equation is in vertex form. She wasn't sure about how to find zeroes, but I told her to plug in zero for x and then just use algebra to solve the equation for y. After this we tried some problems with inequalities. We did one word problem to find the maximum width of a rectangle given constraints. She did a good job setting up and solving using the quadratic equation to find the variable for length, then plugging it back into her original equation to get width. She also did a graphing problem with inequalities. I told her to find the zeroes and complete the square to find the vertex, then draw a parabola joining these points. She knew that she had to test a point to decide whether to shade inside or outside of the parabola. Finally she did a problem in which she had to decide which values of x make a quadratic positive. I told her to find the roots, then I showed her how to make a chart and find when each of the factors are positive or negative. When she multiplies the positives and/or negatives together she will get the result of the full equation. When this is positive, the equation as a whole is positive. We wrapped up and she said she felt ready for her quizzes later this week.

We reviewed the previous year's final exam for the student's stats course. We went over each question, using the information as a way to review the key concepts covered. I am in the process of developing a summary sheet for him to use with his open book final exam. We will finish the last question in our next session and also review another year's version of the final exam.

Today we introduced new concepts of direct variation and inverse radiation and solved several problems related. We also solidified older topics such as simplification of rationals, inscribed angles problems, and unit conversions. The student is very confident and capable of quickly solving all posed problems, and is making great progress.

The student is doing a great job. She mentioned that she doesn't enjoy chapter books as much. When I asked her why, she said that it's because they're longer and sometimes harder. After talking with her about it more and ensuring her that with practice reading chapter books will get easier and easier, she seemed much more at ease.