Rachel and I reviewed together the midterm review that was put together by her teacher.

I asked her to determine the order in which we proceeded so as to give priority to the items she deemed most appropriate.

One theme of this session was to review the algebra required to perform the given mathematical task, but to also provide simple effective ways to check her work. This time I showed her how to check graphically using her calculator. Another theme was pausing to understand what the question was actually asking us. A third theme was going back to basics specifically, multiplying two sets of parentheses (aka foiling or the box method). We also reviewed factoring. I highly recommend that she visit these core skills with frequency in the new year.

We were able to cover every topic that she wanted to review except for imaginary numbers. We ran out of time for this topic. She is to go and speak with her teacher about this prior to the exam for this review.

I gave Matthew his test to finish. The test contained problems on trigonometric functions, inverse trigonometric functions, areas of triangles, the law of sines, and trigonometric functions of inverse trigonometric functions. He finished the 16-problem test and I scored it. He made a perfect 100%.
Matthew has made major gains this school year in terms of his student skills and his math knowledge and understanding.

I went over the homework assignment with Matthew and I introduced the topic of inverse trigonometric functions. The task is to find the angle within a given domain that satisfies the desired function and value. We went through some guided practice and Matthew worked on his assignment which was Guided Practice # 2 - 12 evens, and Exercises p. 878 # 12 - 28 evens, except # 26. When Matthew finished his homework assignment, I gave him the test and he started taking it.

I explained to Matthew how to determine the trigonometric functions on the positive and negative x and y axes. We then worked with coordinate
points located on a circle to calculate the angle between the positive x-axis and the terminal line. This allowed us to determine the reference angle and to use the coordinates to find the six trigonometric functions. We did some guided practice problems followed by working together on the assignment which is: Guided practice # 2,4,6,8 and P.870 # 3 - 33 multiples of 3. Matthew finished all but 3 problems in the assignment.

Matthew and I reviewed the homework assignment and then began our topic for today. I introduced coterminal angles. I showed him how both positive and negative angles can have the same terminal side. We then did some guided practice problems on the topic. I next showed him how to convert from degrees to radians and vice versa. The assignment was the guided practice # 2,4, 6,8 and Exercises p. 862 # 3 -39 multiples of 3 which he completed in class.

I explained how to solve a triangle by providing all sides when two are known. We continued to use the definition for all six trigonometric functions for several triangles. I then explored with him the 45 degree, 30 degree, and 60 degree right triangles. I showed him how cofunctions of complementary angles are congruent. I reminded Matthew of how the angle of elevation and the angle of depression are used. The homework assignment I gave was Guided Practice # 2,4,6,8 and P. 856 # 2-24 evens. I worked with Matthew to start his assignment.

I gave Matthew the test on sequences and series. We covered operations on arithmetic and geometric sequences, sums of finite arithmetic and geometric sequences, and recursive sequences. Matthew scored a 100% on the test and we briefly started the chapter on trigonometric functions. There was no assignment.

I continued to work with Joshua on calculating trigonometric functions of sums and differences of angles. We applied the formulas to find the trigonometric functions of given pairs of angles. Since this was our last session of the school year, there was no assignment.

Joshua was taking an AP exam today and was not available for my session. His last math class with me will be tomorrow and I will repeat my lesson. There was no assignment.

I developed the topic of finding the sum of an infinite series with Matthew by referring to a graph of the sum of the series of one-half, one-quarter, one-eighth,... to show him that the sum approaches 1 as the number of terms approaches infinity. I then showed him the formula and explained how to use it and the conditions for it to have an answer. We also explored non-terminating decimals. I gave him a homework assignment of exercises p.823 # 9 - 33 multiples of 3.