SP #6 - Unit K Concept 10: Writing Repeating Decimals as Rational Numbers

When writing a repeating decimal as rational numbers, we need to be able to do this without a calculators. The two significant things you need to know is the geometric series formula and the infinite geometric series formula. Of course, having the correct value of "a" sub "1" and "r" is very crucial because it will be the starting point of everything. Be sure to check your work as you go and I hope you enjoy this problem!

Fibonacci Haiku: Julian

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SP#5: Unit J Concept 6- Repeating Factors in Fraction Decomposition

PART ONE: Remember whatever you mulitply to the denominators to get CD, multiply it to its numerator as well which will be in letter (ABC). When you set it equal to the original equation, remember to put the value of 0 if there isn't any for that term.

PART TWO: Combine like terms! Set it into a system and cancel out the x's and x^2's. Use elimination to solve for a variable (in this case, eliminate A and C in rows 2-3 to find B. After finding B, plug it into row 1 to find A, and then plug in A & B in row 3 to solve for C. Notice that when we plug in the numbers to the corresponding letters, the second equation was not there because the value of B was 0.

PART THREE: Check your answers! From the resulting equation we found from the previous step, do the same thing and find the CD and remmeber to mulitply whatever you did at the bottom to the numerator as well. Combine like terms and you should end up with the origial equation you had in the very beginning and you're done! :- )

SP#4: Unit J Concept 5- Partial Fraction Decomposition with DF

Part 1: COMPOSING. We need to get a common denominator for all three equations by multiplying the bottom of each denominator by the other denominators. After doing this, don't forget to multiply the numberators by it as well! After you get the numerators, combine like terms and put it over the common denominator (which does not need to be FOILED out). That will be your composed equation!

Part 2: To start decomposing, set your equation to A/x+5 + B/x+2 +C/x-7. Do the same thing you did to get common denominators and also for your numerators. (Notice you'll have letters in your equation now!) Set it equal to the numerator we found in the previous part. Combine like terms again and cross off the x^2 and x's to make it a lot easier!

Part 3: Plug in the coefficients into your matrix. After you have that plugged in, find the rref. Your resulting answer should be as shown above. Notice that A=4, B=2, and C=3! It lines up with the equations from the two earlier steps! 

We have successfully decomposed the equation back to its original equation after we composed it! :- ) 

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

Don't be scared when you look at this problem! It's actually really easy even though it's a lot of work! (HENCE MY 8 MINUTE VIDEO, SORRY ABOUT THAT) Be sure to simplify equations when you can so you can make your life so much easier when add/subtracting! Remember, our goal is to get our matrix to be in the Row- Echelon form. This means there will a right triangle of 0's and a staircase of 1's! Follow the Gaussian Elimination and you'll be in good hands. Remember that if you have a consistent dependent, solve until the very end in the matrix even if it means you'll have 2 rows left. Be sure to plug in the value of each letter correctly to ensure an accurate answer at the end.

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

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Viewers need to be aware on what formula you use for the type of problem you are solving. The number correlating to the daily, weekly, monthly, etc. need to be memorized (which should be easy)! In the first problem, be aware that if you don't adjust your window accordingly, the tracing part won't work! (Trust me, I spent 20 minutes trying to figure out why it kept giving me ERROR!) In the second part, remember to find the ln to cancel out the e and continue on after that. Also, when you're looking for the time, remember to convert the rest of the decimal into months. (ex. 9.16 should convert to 9 months and 2 months (round to the next highest number for the months part))

SV#4: Unit I Concept 2: Graphing Logarithmic Functions and Identifying Properties

In this video, students will be learning how to graph logarithmic functions and identify properties. A sentence that will help you during parts of this problem is " the Log's Xylophone was Happy and Rich" which means a "logarithmic graph has a asymptote of x=h, leading to no restrictions on the range".Viewers need to be aware of the "h" value. (Remember that (x-h) so the value will be the opposite sign!) "H" is also our asymptote value so be sure you have the right answer! Another thing you will need to be aware of is accurately solve for the x-intercept and the y-intercept. When you find the x-intercept, you'll need to remember a concept that we learned in Unit H! (Hint: Exponentiate!) Then when you find your y-intercept, remember to set the base equal to each other and this will be another concept that we have already learned in Unit H as well! Also, remember that our graph goes on forever so don't forget to put arrows at the ends of the graph!

SP3: Unit I Concept 1: Exponential functions

*LEFT side of the asymptote

Viewers need to pay special attention to "a" to see whether the graph will be above or below the asymptote. Also, depending on the value of "b" it will say whether the graph is close to the left or right side of the asymptote.  They also have to be sure they don't get the value of H and K mixed up otherwise the asymptote will be wrong. Since this equation has no x-intercept, notice that the graph does not touch the x-axis at all. Also, remember that the graph will never touch the asymptote but it will be very close to it. 

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

** I apologize for all the times I stuttered and/or blanked out in the video :(

There are many things you should watch out for as you find the log in this problem! Be sure that when you are breaking down the numbers that they result with numbers in the clues. If not, you will have a completely different and wrong answer. Also, don't forget to appropriately use addition and subtractions signs whenever there's a multiplication or division sign being used! (Remember addition signs go with multiplication and subtraction signs go with division!)

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

This problem is about how to graph rational functions. This whole unit was an immediate jump into it so now it's all shown step by step in my lovely video for you! We start off from identifying the equation to finding vertical asymptotes, to holes (if there are any!), to domain, x-intercepts, y-intercepts, finding key points, and graphing the points! It sounds like a lot but when you work out all the steps, it shouldn't take you more than 10 minutes to do!

The very very very first thing you need to know is how to identify between a horizontal asymptote and a slant asymptote. (If you remembered the songs, this will be a piece of cake! Yum, I love cake!) The only new things you need to know is vertical asymptote and holes which can be a struggle but once you get the hang of it, it'll be a breeze! That's really all you need to know how to do because everything else is review such as finding domain, x-intercepts, y-intercepts, and plotting points on a graph! Also, don't forget to factor accurately! Since this is a slant asymptote, be sure when you perform long division that it is right!

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

*Sorry I stuttered a lot!
This problem is about finding zeroes of a 5th or 4th degree polynomial. Throughout the unit we have learned the steps into finding the zeros which will all be incorporated in this video. By using the rational roots theorem, Descartes Rule of Signs, synthetic division, and quadratic formula, we can find the zeros of the polynomial.

You will need to pay special attention to each step because they are all crucial into finding your zeroes. In the rational roots theorem, remember that it's p over q and not the other way around. For the Descartes Rule of Signs, be sure to change the signs only on numbers with a odd numbered degree. Don't forget that we count down by 2's so we can account imaginary numbers! For synthetic division, even if you don't get zero hero in your first try, don't be disappointed, just use other numbers and eventually you'll get zero heroes and get your equation to a polynomial where you will either factor or use the quadratic equation.

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

This problem is about being able to sketch a graph with the given polynomial. By factoring the equation and setting the factors equal to 0 to solve for zeroes, we can find our points in order to graph it. Besides finding out our x-intercepts and  y-intercepts, we also need to know our end behaviors (how the graph acts at the extremes). We can identify the end behavior by examining our leading coefficient (whether it's positive or negative) and the degree (whether it's even or negative). There are four types of end behaviors (even positive, even negative, odd positive, and odd negative). Not only do you need to know the end behaviors but also the zero's multiplicity so you know how it acts around the x-axis, this is where TBC-123 comes in handy. To accurately sketch the graph, we can also find our extremas, the minimum and maximum, and the intervals of increase and decrease.

To make sure you're doing all this accurately, you should pay special attention to your factors and end behaviors. If you can't factor your equation correctly, then your zeros will come out different and not precise. Also, the end behaviors must be the correct so make sure you have the song and dance moves memorized so you know how the graph will look like! Lastly, you should make sure you have the TBC-123 down. If there's a M of 1, that means the graph will go THROUGH the point. If the M is 2, then the graph will BOUNCE off the point. Then if your M is 3, your graph will curve through the point. Remember that each point is a door and it's the only way you can get through the x-axis. If there isn't a point (door) there, that means it's just a wall and you can't walk through a wall!

WPP#4: Unit E Concept 3 - 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

This problem is about identifying the four main parts of a quadratic on a graph. These main parts are the x-intercepts, y-intercepts, vertex (max/min), axis of quadratics (and graphing). This example will show you how to change the quadratic to a parent function equation and will also show you how to graph the quadratic in the end. Also, we will be completing the square so hopefully you haven't forgotten how to do that!

In order to understand how to identify the parts and be able to graph this, you must pay special attention to how you complete the square and getting the correct information on the right (the parent function equation, vertex, etc.) in order to accurately graph the quadratic.

The first step you need to do is to add 10 to the other side, cancelling the 10 on the left. You will then have 2x^2+8x=10. Take out a two for your coefficient and complete the square. You will be left with 2(x+2)^2=18. For the parent function equation, just subtract 18 from both sides and you will have your equation: 2(x+2)^2-18. At this point you can find your vertex, which is (-2, -18). Plug 0 into 'x' to solve for the y-intercept. The axis of symmetry will be x=h so x=-2. Afterwards add 18 back on both sides from the parent graph equation and continue to solve for the x-intercepts. Since your answers for the x-intercepts are whole number and does not have a radical or anything, that will be your exact & approximate answer. Also, since there isn't any imaginary number, you will be able to graph this and it will touch the x-axis.

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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About Me

Hi, my name is Alexis. To be honest, I spent my entire summer watching movies/TV shows on Netflix. That's something I like to do half the time. (The other half is sleeping!) Out of all my friends, I'm the only one who has a place for cats in my heart. But other than movies, sleeping, and cats, I love to go camping during the summer. That's the only thing I look forward to as the school year ends! I also like to eat and try new food. This quote best describes my relationship with food: "Life's too short, eat dessert first!"

As a student, I try my best to pass all my classes with A/B's. Math is probably one of my favorite class. Although there are times I do struggle in learning concepts, I think it's pretty easy once you get the concepts. Math is just memorizing formulas and plugging it in. That's what I like best about it. There's no need to over analyze anything or do anything besides solving an equation. The best way I learn are through lectures and examples. I'm a visual learner so everything said to me, I need to write it all down so I can lay out the problem. When learning new concepts, I usually get it instantly but when I don't, I try to go back and focus on that concept until I understand it and can solve it without any help.