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

       In order to understand the viewer must pay attention to making sure they account for the zeroes when writing out the sequence. Remember to turn your first term into a fraction so it is easier to work with, as well as your common ratio; after you do so, set up your geometric formula needed for the summation notation. Don't forget to get rid of the double fraction division by multiplying by the reciprocal of the denominator. Also, keep in mind the whole number that was ignored in the beginning. Add it to your final fraction and that will be your final answer. You can check the answer by plugging it into a calculator. Hope this helped! 

Thank You

Fibonacci Beauty Ratio

         After measuring 5 of my friends, Alexis T seemed to be the most mathematically beautiful based on the beauty ratio. I measured some of their distances from body parts to body parts and then took the ratio of those distance measurements. After finding 3 ratios, I found the average for each. When I was done finding the average for all 5 friends, I compared it with the value of phi, which represents the golden ratio, which is 1.6180339887..... Alexis T had an average of 1.542, the difference between her average and phi is .076, which was the closest out of all. I think the beauty ratio is incredibly mind-boggling because it comes up in so many things that are actually considered beautiful by us humans. That leads me to accept the validity of the beauty ratio. Also, I do consider Alexis T to be good-looking so it re-asserts my opinion about the validity of the golden ratio.

Fibonacci Haiku: Under the Water

Water

Polo

Toughest sport

Six on six

Egg beating through the water 

The crowd fills with excitement as you shoot

Your friends around you scream for you to make it, and you do

Six months of hard work, payed off by the sweet taste of victory, no longer the underdogs, prepare to witness triumph

http://www.dallasaquatics.org/wp-content/uploads/WaterVolleyball-362x174.jpg

SP#5: Unit J Concept 6 - Partial Fraction Decomposition with repeated factors

In order to understand the viewer must pay special attention to separating the initial denominator factors into separate fractions. Make sure to count up your powers and stay consistent. When multiplying by the factors make sure your work is correct or the system will be wrong. Because our answers are fractions, checking your work on the calculator with reduced row-echelon form will be hard, so another method must be used. For this method we combined rows and multiplied to get rid of variables in order to back-substitute and find the rest. Remember to reduce your fractions at the end.

SV#5: Unit J Concepts 3-4 - Solving Matrices

Hello my name is Ivan and in this video we will be solving one of our Doctor Prescription problems. The viewer must pay special attention to the type of solution we have. As seen in the video (and as seen in your work) this problem is an example of a consistent dependent solution, which means there are infinite amount of solutions. However, one must find the restrictions (which come in the form of equations) that make this statement true. To find these, we set an arbitrary value for z and used this so solve for the rest of the variables. Be careful to plug it into your calculator correctly and don't forget to keep your negative values negative. Be sure to identify the type of solution we have an highlight your zero rows to keep your work organized. Thank you and good luck!

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

In order to understand, the viewer must pay attention to both parts separately. In Composition, remember to get a common denominator and multiply the denominator by whatever you had to multiply your fraction by to get that common denominator. Double check your work or else your combination of terms will be incorrect. Use a reliable method such as box or foil. In decomposition part, make sure you set a variable on top of each of the factors and stick with it. Same idea with the common denominator but remember to keep your work organized and correct. After combining like terms, get rid of the common terms of x^2 and x. Set them equal to the original equation to find your final answer and double check your work on the graphing calculator. Good luck and thank you!

WPP#6: Unit I Concepts 3-5 - Interest and Investments

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SV#4: Unit I Concept 2 - Graphing logarithmic equations and finding their properties

    Hello, my name is Ivan and for this video we will be graphing a logarithmic equation and finding its properties. In order to understand, the viewer must pay special attention to the conversion of "h"'s sign and how to identify the vertical asymptote (x=h). To solve for x-intercept you have to use unit H skills, including exponentiating. Remember that the domain must correlate with the asymptote. Also, when plugging into your calculator, make sure the change of base is done properly, including the paranthesis. When choosing points, remember to choose the correct values to obtain an adequate graph. Lastly, don't forget to add the arrows to indicate this function continues forever.

   THANK YOU!

SP#3: Unit I Concept 1 - Graphing exponential functions and identifying their properties

In order to understand the viewer needs to pay special attention as to why we have no x-intercept. We know by observations that is not possible since "a" is positive the graph will be above our asymptote, which is y=3, it is above the x-intercept and therefor nothing falls below the asymptote. Algebraically,  when you try to find x-intercept by setting y=0, you will find yourself with an undefined answer, as you cannot take log of a negative number. Understanding this is crucial. Note that an asymptote of an exponential equation is y=k. Which means the range will be limited to whatever the asymptote is and whether the graph falls below or above that asymptote. When choosing key points, make sure you include "h" as your third value and subbing plugging in x- intercepts that help in plotting your line (nearby numbers that you can plot in your window, etc.) Make sure you note arrows that show the graph goes on infinitely on both sides (since there are no restrictions on the domain).

My name is Ivan and THANK YOU!

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

         



           In order to understand, the viewer needs to pay special attention to their clues. These clues are what guide you to the rest of the problem and what start you off. When trying to expand the numerator and denominator of the log by using the factor tree, you can only use the clues in the factor tree. The "branches" in your factor tree should all be a number that is found in the clues. Make sure all your branches are or your problem answer will be incorrect. Before you check your branches make sure the clues you already know (refer to the video if you don't know what I'm talking about). If a branch is not one of the numbers found in the clue, you must keep factoring until they are. If no further factorization is possible and your factor tree branches are still not numbers found in the clue then you must multiply by 2 or 3 or 4, etc (could be any number) and factor tree again until they are. Luckily, that is not the case in this problem because all the factors are prime numbers. After you have your logs, expand using the product and quotient laws. Make sure if you have more than one of the same clue you add the number of same clues as a number coefficient in front of your log (since it is the same it is like a number exponent --- power law), this will mean you have that many of the values in the clues. Combine like terms at the end so your final answer after substitution is correct. Other than that, you're all set.

Good luck and thank you!

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

            Hello my name is Ivan and this video will demonstrate how to graph a rational function. To graph this function, we will need to find it's assymptotes and some of the points that lie in its path, some of which are the y-intercepts and x-intercepts. We will also be using our graphing calculator to list some limit notation and figure out which general path our curves will follow. Make sure to find all you can first before graphing.

           The viewer must pay special attention to the factorization of the bottom and top. The top will require some Unit F skills and if you go wrong, your graph may not end up looking correct. When finding vertical assymptotes, if something cancels out, do not forget to take it out from the simplified equation and find it's y-value by plugging it's x-value to the simplified equation. Make sure you cancel out the denominator when finding x-intercepts. Also, use the simplified equation when finding the y-intercepts. We must do this because we have a hole, and plugging x as 0 into the original equation could yield an incorrect value for the y-intercept. Make sure you use your trace function with the calculator so you obtain correct points. Remember, the graph has to hug the assymptotes and it cannot go through the hole we found.

                                             Thank You

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

         


            Hello my name is Ivan and today we will be solving a polynomial with real and complex roots. This problem is a fourth degree polynomial which we must find the roots for. To begin, we will use Descartes Rule of Signs to find the number of all the possible positive or negative roots. Following that, you find all the possible real zeroes using the p's and q's. Now that we have an idea of where to start, we can use synthetic division to find a zero hero using the Factor Theorem. Our graphing calculator can give us a shortcut to do this, if needed. Once a zero hero is found, that is the first zero and you can continue using synthetic division with the answer row to try the rest of the possible roots until you condense down into a quadratic. From there, you can use the quadratic formula or try to factor it yourself with your favorite method, if possible.

            The viewer must pay special attention to the answer they obtain. In the end, there should be four zeroes, since the degree of our polynomial is four. Also, the viewer can find an answer more quick by using a graphing calculator to find a zero hero. To do this, go to "2ND", "CALC", "ZERO", "LFTBOUND", "RTBOUND", and your calculator will yield results. Make sure every step in synthetic division is correct, or else you can miss a valuable zero hero. Pay special attention to fractions because they can be confusing to work with while doing synthetic division.

                                                                                   THANK YOU!

SP#2: Unit E Concept 7 - Graphing a polynomial and identifying all key parts

          This picture presents a polynomial and executes the solutions needed to find its properties, including: x-int, y-int, zeroes (with multiplicities), end behavior. You must find the x-intercepts (with multiplicities), y-intercept, and identify end behavior. With those values, you must graph your polynomial and make sure it corresponds with your findings. The steps to the problem are shown on the top and the answers are in the bottom portion of the picture. The arrows correspond to the parts you may look at if you are stuck on your own.

           Note that the extrema and intervals of increase and decrease do not need to be found, they are there if you need help in determining how far to go when creating the "humps" of the graph. Make sure to factor all the way through so your zeroes match the degree of the polynomial. Also, make the factors equal to zero so you get the right value. List the multiplicity of each zero even if it only shows up once.

WPP#4: Unit E Concept 3 - Maximizing Area

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WPP#3: Unit E Concept 2 - Path of Water Polo Ball

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

In this concept we will be identifying x-intercepts, y-intercepts, vertex (max/min), axis of quadratics and graphing them. The quadratic is in standard form.This picture illustrates the process involved in finding the parts to a quadratic function. The parent function, vertex, y-intercept, axis of symmetry, and x-intercepts must be found using the standard form.

 Realize that the quadratic is facing downward because the "a" value is negative. Also, when completing the square, make sure the right value for "b" is kept and no improper change is made, specially when taking out the "a" coefficient. Use a calculator to find the x-intercepts. Good Luck!

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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