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.

I introduced Matthew to geometric sequences and series and told him how to determine whether a sequence is geometric or not. We then used the common ratio to write the rule for a geometric sequence and to find the sum of the geometric series. We did some problems from the homework assignment which left only P.815 # 39 and 48 for him to do.

I introduced Joshua to the sum and difference formulas for the sine, cosine, and tangent functions. We did examples where a trigonometric function of an angle was unknown and the angle was the sum of two angles for which the function was known. I used the examples to show him how to get the unknown functional value. There was no assignment.

Joshua and I worked together to finish problems about solving trigonometric equations. We solved both generic and restricted domain problems to come up with angles that made the equation true. There was no assignment.

I reviewed Matthew's homework and his answers demonstrated mastery
over generic sequences and series. We then began analyzing the properties of arithmetic sequences and series. I explained how to write the rules for arithmetic sequences and how to calculate the sum of an arithmetic series. We worked on some of the assignment which was p. 806 # 3 - 48 multiples of 3.

Matthew finished his test on rational expressions and functions and he scored 100%. We then began to study sequences and series and I explained finite and infinite sequences and series and showed him how to use summation or sigma notation to express different series. I gave him his assignment: p.798 #(3 - 27 and 39 - 54) multiples of 3.

I worked with Joshua during the entire session to correct his homework assignment which was done incorrectly for the most part. We only got halfway through the corrections so we will continue tomorrow. I explained the difference between general solutions and specified domains. There was no assignment.