SP #7: Unit Q Concept 2

This SP#7 was made in collaboration with Kelsea Del Campo please visit their awesome blog by clicking here.

Using Identities:

Using SOCAHTOA: 

 In this student problem me and my partner made our own example from Unit Q Concept 2. In this first picture we showed how to find the values using Ratio Identities, Reciprocal Identities, and Pythagorean Identities. In the second picture we showed how to find the values usng SOCAHTOA. As you can see, we can find the values using both ways. In the first picture, using identities, you can see that we found all our values using different Identities and just substituting them into the problem. We used one identity to find another and so on. For the second picture, using SOCAHTOA, we just used the Unit Circle ratios from the previous unit. By doing these two pictures we have proven that identities can be associated with SOCAHTOA. 

SP #6: Unit K Concept 10: Writing a repeating decimal as a rational number using geometric series

In this student problem we had to create a problem form concept 10. First our problem had to have 2 or 3 repeating numbers and a  whole number before the decimal. After that we had to use the formula a sub infinity equals a sub 1 over 1 minus r. We also had to include the proper notation. The trickest part of these types of problems is that we have to be careful with the fractions. You make to make sure you convert you decimals into fractions correctly or the whole thing will be wrong. Lastly you need to watch out for the number before the decimal. Do not forget to add it at the end of your problem. Thank you for viewing! 

SP #5: Unit J Concept 6- Partial Fractions Decompostion with repeated factors

In this problem i did an example of partial fraction decompostion with repeated factors. It is pretty much the same as SP #4 but this time it has repeated factors. After i found the systems i plug in into a matrices box. I used the rref feature in my calculator to find my answer. I checked it by plugging my answer back in to see if it came out the same. The trickest part of this concept is that you have to remember what to do when there is repeated factors. For repeated factos you MUST count up the powers and include the factors as many times as the exponent. Other than that this problem was very similar the concpet 5. You follow all the same stpes except we add that repeated factor step. Thank you for reading!

SP #4: Unit J Concept 5- Partial Fraction decomposition with distinct factors

In this student problem, I had to make up my own example of a partial fraction decomposition with distinct factor. I first had to compose my problem I made. Then i had to decompose it but now with replacing the top with letters according to the amount of facotrs i have on the bottom. Then i had to get a least common denominator for the three fractions by multiplying each part by what is missing. After i grouped them together and set it equal to the numerator that we first started with. Lastly we solve the equations by using matrices and the rref feature in our calculator and plus it back in. The most trickiest part about these types of problems is having so many variables. You can get confused with all of them so keep count on how many you are suppose to have. Another thing that was tricky is knowing how to use matrices because all these problems are related. One thing i found interesting was the rref feature gives us the answer so we know our work is correct. Other than that it was really simple. Thank you for watching! *Sorry i forgot to set it equal to the numinator in the 2nd picture :(

SP #3: Unit I Concept 1- Graphing exponetial functions and identifying x-intercept, y-intercept, asymptotes, domain and range

In this student problem I made my own example of a graphing exponential equation. The first step in these types of problems is finding your a, h, b, and k. 'a' tells you if the graph is above or below the asymptote by the sign. If it is postive then it is above and if it is negative then it is below. B tells you what side, right or left, the graph is. If the absolute value of b is less then one (fraction) then it goes on the right side. If the absolute value of b is greater than 1 then it is on the left side of the asymptote. You find h by setting the exponent equal to zero and this shifts the graph left and right but for this example the key points do the shift. 'k' tells you if the asymptote moves up or down. If it is positive then it moves up units but if it is negative it moves down. You find the key points by adding four numbers to the 3rd key point. You find the asymptote by just looking at k because y=k. You find the x-intercepts by plugging in zero for y and for the y-intercepts you plug in 0 for x. The domain for these probelms will always be (-inf, inf) because an exponential graph has an asymptote of y=k, leading to no restrictions to the domain. The range depends on the asymptote. Lastly for the graph, you just plot in the key points and the intercepts.

The trickets part of these types of problems is probably finding the x-intercept. It was the trickets part for me because you need to make sure you divide by ln correctly and do all your intermediate steps correctly as well. Another tricky part of this problem will have to be the graphing. You need to make sure you do not cross the asymptote, plot each point you find correctly, and go in the right direction. 

SP #2: Unit E Concept 7: Graphing polynomials and identifying all key parts

This student problem I made my own example of a polynomail that I graphed.I included the x-int which were (-2,0), (5,0) and (-3,0). I also included the y-int which was (0,-60). The zeroes were -2M2 (bounce), 5M1(through), and -3M1(through). The steps I needed to do to complete my problem was first make up my own factored equation. After I did that, I was able to get the whole eqaution by factoring them together. Then I was able to find the end behavior, the x-int with multiplicities, the y-int, and was able to graph it. Even though it was a huge y-int i made the y-axis going by tens and the x-axis by ones.

The trickest part of this problem is making sure you only cross the x-axis at the gates. If you do not graph it correctly you do not get it right. You can only go through the x-axis at the gates and makes sure it is with the right multplicity (through, bounce, and curve). Other than the graphing part everything else is pretty easy.

SP #1: Unit E Concept 1- Graphing a quadratic and identifying all key parts

In this studnet problem I made an example of my own quadratic in stand form turining it into parent graph form. I completed the sqaure to accomplish this so I can graph it easier. After I put the quadratic in parent graph form, I was able to find the vertex by getting the oppisite number in parenthesis and the numbr outside. I was alos able to find the y-intercept by plugging in zero into the standard form eqaution. Then i foind the axis of symmentry. Lastly I was able to solve for the x-intercepts by getting x by itself. The trickest part of this problem was completing the sqaure. When I try to complete the sqaure I sometimes forget the steps but other than that it was pretty simple. Solving was kind of tricky too but not that much.