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Showing posts with label SV. Show all posts
Showing posts with label SV. Show all posts

Monday, November 11, 2013

SV #5: Unit J Concept 3 - Gaussian Elimination


        The first and foremost important thing to remember to do, is distinguish which rows and numbers you need to work on, and which rows you may use in order to eliminate the numbers. It's really the entire backbone of this concept. Another important thing to remember to do is to calculate correctly, for if you mess up even once, you will proceed to arrive at a wrong answer. Lastly, you should check your answers with a calculator, if an answer sheet is not readily available. That is all.

Sunday, October 27, 2013

SV #4: Unit I Concept 2 - Graphing Logarithmic Equations


        Some important things that need to be noted whilst completing problems of this particular field of study, are: remembering how these types of problems share the same structure, remembering how you find the asymptotes for logarithmic equations, and remembering the domain/range of logarithmic equations. First of all, the parent type function for these problems  is log base b of (x minus h) plus k. Second of all, the asymptotes for logarithmic equations will always be x = h, and you can remember this specific rule with the phrase "The Log's Xylophone was Happy and Rich", where you derive x = h from "Xylophone was Happy". Lastly, the domain of logarithmic equations will always be restricted (unless there's no h value), and their ranges will never be restricted. This can also be remembered by the previously noted phrase, and is extracted from "Rich", in which the r proclaims that the range is to never be restricted. The end.

Wednesday, October 16, 2013

SV #3: Unit H Concept 7 - Expanding Logarithms


        Some important things you must pay attention to are how you synthesize logarithms from factors of big numbers, and remembering to substitute in the variables. Also, you must remember to utilize the properties of logs in order to formulate more logarithms that you may be required to utilize in order to get to the desired endpoint. Another somewhat important thing to remember to do is to turn the denominator log into subtraction. Lastly, if none of the given clues can fit in, you may be able to multiply the endpoint in order to factor the number. Either that, or you're wrong. Anyways, the end.

Tuesday, October 8, 2013

SV #2: Unit G Concepts 1-7 - Finding All Parts and Graphing A Rational Function


        This problem elaborates upon rational functions, and (kind-of) how to graph them. In just this one problem, we utilize many different concepts, such as factoring and all that, yet the foremost important things, however, are to remember what to do to find asymptotes/points. And all of that, we have committed to memory, through DIVAH. Anyways, to find the intercepts and all, we just have to remember to set the other value to 0. Graphing is pretty easy, as all you really do is make the values that head on to infinity, slowly approach the asymptotes (basically, you just make something nearly parallel to the asymptotes).
        Some special things that you need to remember are what to do to find stuff, how to graph, and how to put all of this into your calculator to make it easier and or check. Anyways, you always have either a horizontal asymptote (ratio for same degree on top and bottom, y = 0 for degree being bigger on bottom), a slant asymptote (when the top degree is bigger by 1, y equals the numerator divided by the denominator, leaving out the remainder), or none (when the top degree is bigger by more than 1). To graph, all you do is just kind-of make lines parallel to the asymptotes, and that will reach infinity on some value. To put all of this into your calculator, you might have to just do it. That is all.

Sunday, September 29, 2013

SV #1: Unit F Concept 10 - Finding All Real and Imaginary Zeroes of A Polynomial


        This problem concerns deriving zeroes from given polynomials of either the 4th or 5th degree. Basically, you work out the problem until you arrive at an end result of 4 zeroes (for 4th degree polynomials), or 5 zeroes (for 5th degree polynomials). In doing so, however, there are several crucial steps that must be taken in order to ensure the success of your efforts. Anyways, this could be useful in graphing, too.
       Some important things that one must pay attention about in order to master this concept include remembering to use the rational roots theorem, and the Descartes Rule of Signs, and remembering to put zeroes in to fill voids when an x is missing in the polynomial. The most important thing, however, is to remember that you may more easily complete this process by utilizing a graphing calculator in order to identify zero heroes. But, as scholars, is it not more honorable to walk the path filled with thorns in order to ensure our complete mastery of this concept? Either way, yeah; it is easier to use the graphing calculator.