WPP #9: Concepts 4-8: Probability with combinations and premutations

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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! 

Fibonacci Haiku: Ariana Grande

Twitter

Singer 

Ariana Grande

I love tweeting

Ariana Grande followed me yesterday 

I was so happy when I saw it 

http://www.thestashed.com/wp-content/uploads/2013/07/Ariana-Grande-The-Way-Ft-Mac-Miller-Video.jpg

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 :(

SV #5: Unit J Concepts 3-4- Solving three-variable systems with Guass-Jordan elimination/ matrices/ row-echlon form/ back-subsitution

In this video I explain DP problem number 3. I explained how to solve a three-variable system with Guassian Elimination and how to check your answer with the rref feature in your calculator. The trickest part in these types of matrix problems is being able to know what row to use. To make my life easier I just use the row on top so I won't get confused. It is really hard when you start mixing up the rows because you will get confused. Another thing that is difficult about these types of problems is making sure you know how to use your matrix feature. This feature is really helpful when checking your answers so if you do not know about it, you should. Other than that matrices are pretty simple if you do Mrs. Kirch's 4 step way of doing. One more thing, ALWAYS ALWAYS ALWAYS show your work. You need to show all your work so if you mess up, you will know where to go back and change something. Thank you for watching.

WPP #6: Unit I Concepts 3-5- Finding compound interest, continuously compounding interest, and investment application problems.

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SV #4: Unit I Concept 2- Graphing logarithmic functions and identifying all parts

In this video, I explained a problem about graphing logarithmic functions. I had to find the x-intercepts, y-intercepts, asymptote, domain, range, 4 key points on the graph, and then the final graph. The hardest part of this problem will have to be finding the y-intercept. I would say this was the trickets part because you have to remember to use the change of base formula. If you do not use it, then there is no way you can find the y-intercept. Another part that was pretty tricky would have to be x-intercept. I would say this was tricky because you have to remember to expotentiate both sides when trying to get rid of the log. Other than that, it was pretty easy. Thank you for watching!

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. 

SV #3: Unit H Concept 7 - Finding logs with given approximations

These types of problems can be kind of tricky. One thing that is tricky about it is that you have to remember that extra clue you have which equals one. Another thing that can bE tricky about this concept is remembering to keep multiplying by 2,3,4, and so on if the numbers can not be matched up with the given clues. Always remember to break down the numbers to numbers that match up to the clues so you can make it into expansion form. Other than that, this concept about finding logs with given approximations was easy.

SV #2: Unit G Concepts 1-7 - Finding all parts and graphing a rational function

In this student video, I was to make up my own ration function and work out each thing. First I found all my factors of the equations and then worked my way into the full equation. Then I had to find my slant asymptotes by using long division. Once I completed long division, everything but my remainder was the equation of the slant asymptote. Next I found the vertical asymptotes by factorinf both the top and bottom of the ration function and canceling any common factors. Then i had to set the denominator equal to zero and solve. After i had to find the holes which were any crossed off commmon factors and set them equal to zero. To find the y-value of the hole, i had i needed to plug in the x value to the simplifeid equation. Then i found the domain which were the horizontal asymptotes and the holes. After i found the x-intercepts by setting the numinator equal to zero. Then there was no y-intercept for my problem. Lastly, i just graphed it by plugging in point and using the trace button.


 

The hardest part of this problem was graphing. The graphing is tough because you have the find the points yourself. Another reason why this is the toughest part is because you need to know the correct way the graphs are going.

SV #1: Unit F Concept 10- Finding all real and imaginary zeroes of a polynomial

In this student video, I was given a polynomails and I was suppose to find the complete factorization and all the zeroes. This problem is about getting a given polynomaial of 4th or 5th degree and finding all the zeroes. In this probelm we had to deal with real and complez First I had to find all the p's and q's. Then I did p/q to find the possible real/rational zeroes. After that I used Descartes Rule of Sign with f(x) and f(-x)to find out how many possible (+) real zeroes there was and how many possible (-) real zeroes there was. Then I used synthetic division to get my polynomail into a quadratic. Lastly I used the quadratic formaula to get the reamainig zeroes. The trickest part of this problem were the complex numbers. Using the quadratic can be hard if you mess up. If you mess up once, it can ruin your whole answer. With the complex numbers, you have to remember to simplify your answer all the way or it will be counted wrong. Other than that, Unit F Concept 10 is easy if you remember all the steps.

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.

WPP #4: Unit E Concept 4- Maximizing Area

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WPP #3: Unit E Concept 2- Path of Football (or other object)

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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.

WPP #2: Unit A Concept 7- Profit, Revenue, Cost

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WPP #1: Unit A Concept 6 - Linear Models

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