WPP# 9 Unit L Concepts 4-8 - FCP, Combinations, Permutations, and Distinguishable Permutations

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SP#6 : Unit K Concept 10 - Writing repeating decimals as rational numbers

Problem: 12.365365

When doing this type of problem, you should ignore the whole number before the decimal. You should remember to add it on the final rational number in the end. Because you get a fraction as your rational number, to add the whole number from before, you have to use a common denominator and multiply the factor into the top and bottom. Be careful when you are doing this so you don't get the answer wrong.

Fibonacci Haiku: Black Friday

Screams

Tugs

Aggressive Pushing

Battling Soccer Moms 

They are Black Friday Shoppers

Look out because they will bite and scratch.

http://a.abcnews.com/images/US/gty_black_friday_shoppers_jt_111127_wg.jpg

SP5: Unit J Concept 6 - Partial Fraction Decomposition with repeated factors

The student must remember that when there is a repeated factor, they must count up the powers, so if there was (x-1)^3, then the denominator will be split into A/(x-1) + B/(x-1)^2 + C/(x-1)^3. They must also pay attention to how they are FOILing and distributing their numbers so that they don't make any mistakes. Make sure that you care adding/subtracting your like terms correctly. 

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

In this concept, the student must be careful when factoring and FOILing to find their common denominator. They must make sure that they are grouping them together and combining the like terms correctly so that their matrix set up doesn't get mixed up. This would slow down their process to find the partial fractions of the problem. 

SV #5 Unit J Concept 3-4 - Matrices

The student should make sure that they are paying attention to their multiplying and adding/subtracting. If they make a mistake in this then it could make it harder for the student to get the zeroes and stairstep 1's, making the process take longer. The student should pay close attention to when they are inputting in their numbers in the calculator, they should double check that they inputted the things correctly. 

*forgot to mention in video, when plugging in the original 3 equations into the calculator, what you do is you press 2nd and then matrix. You go to edit and you plug in all the equations as you see it. Then press 2nd quit and go back to 2nd matrix. Go to MATH and scroll until you find rref(. You select that and go back to 2nd matrix. You then select A because it is the matrix that you have filled in earlier. Then add the  parenthesis to close the problem. Click enter and the matrix should pop up. You should see the three 0's and it equals 1. The three 0's in row 3 confirm that our system is INCONSISTENT. 

WPP#6 Unit I Concepts 3-5 - Compounding and Continuously Compounding Interest

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

The students needs to remember that in this concept, the range is going to be (negative infinity, positive infinity) and NOT the domain (that is concept 1). Also they need to remember that when they are plotting the asymptote, it has to be vertical, not horizontal (that is concept 1). The student also needs to remember that the graph will be going on forever, so the picture in their calculator is not the entire graph (remember to draw arrows at the end of graph). 

Problem: Log 5 (x + 4) - 2

SP #3 Unit I Concept 1: Graphing Exponential Functions

In this concept you will be learning how to graph exponential functions as well as identify the x-intercepts, y-intercepts, asymptotes, domain and range. The parent graph is y = a times b^(x-h) + k. You will be using the parent graph to find the asymptote, the x-intercepts, y-intercepts, domain and range.

Be careful plugging 0 into y to find the x-intercept as well as plugging in 0 for x when finding the y intercept. Make sure that you are using your algebra solving skills correctly when finding the intercepts. Remember that you CANNOT take the log or natural log of a negative number (if is undefined and that means that you will not have a x intercept). Remember to put arrows on the ends of your graph because it goes on forever.

Problem: f(x) = -2 times 3^(x+1) - 1

SV #3 Unit H Concept 7 - Finding Logs Given Approximations

Problem: 945/96

The student must pay attention when they are finding the factors of 945/96. They must remember that they are only allowed to use factors from the numbers that are given to them in the clues. They may be tempted to break down the numbers further, but they must remember to only use numbers given to them. Also be careful when putting the addition/subtraction signs, pay attention to which are multiplied (the numerator) and which are divided (denominator).

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

So in this concept, you will be determining the asymptote of a function. You will determine if it is a horizontal asymptote, a slant asymptote, a vertical asymptote and if it has a hole or not. You will then find its domain, x-intercepts, y-intercepts and then plot and graph its points. You will be learning how to do this problem:
(x^3 + 3x^2 +2x) / (x^2 -3x -4)

The viewer needs to pay attention to the degrees of the function because it determines what kind of asymptote the function is. They also to need to pay attention when using long division when finding the slant.

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

In this concept you will be finding the zeroes of a polynomial that is not factorable. Not only that, but you will also find the imaginary zeroes, even though this concept is similar to concept 6, remember that you will be finding imaginary numbers in this concept. You will be using the skills from previous concepts like p's and q's, Descartes's Rule of Signs and synthetic division and a skill from earlier units like either completing the square or using the quadratic formula.




Be careful when doing synthetic division because you might make a mistake if you rush and that can keep you from finding your zero hero resulting in taking a longer time to solve a problem (which is terrible when taking a test). Also be careful when using the quadratic formula, make sure your signs are correct and you have the correct terms in place. Make sure than when you are using the Rule of Signs, you are changing the ones that have a negative exponent and keeping the ones with a positive exponent the same! 

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

Concept 7 is all about graphing polynomials, using the skills from previous concepts you will factor the equation, find the end behavior, find the x-intercepts (as well as the multiplicities), and find the y-intercepts. You may need to find the Extremas and intervals of increase and decrease, but only when instructions tell you to do so. Down below is the problem and the solution.

Problem: x^4 + x^3 - 6x^2 - 4x + 8

Things that you should pay attention to are when you are finding the x-intercepts, please remember that the numbers you see will be opposite, meaning it will be either negative or positive depending on what it is in factored form, as an example: (x-3) will be +3. Also pay attention to if an x-intercept will be a Through, Bounce, or Curve based on its multiplicities.

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

 The problem involves changing an equation from standard form to parent function form: 

f(x) a(x-h)^2 + k. Then from that equation the student must find the x-intercepts, y-intercepts, vertex, axis of symmetry and graph the equation. Using this, the sketch of the equation will look more accurate and detailed. 

When doing this type of problem, it is very important to pay attention when completing the square (to turn the standard equation to parent function form) because when factoring out a number from one side, it must be factored out on the other as well (Step 3). Another important thing to focus on is when you are finding the vertex, the "h" is always opposite from what it is in the equation. Also, it is a good idea to memorize the parent function equation so when facing this type of problem, the student doesn't spend time trying to remember the formula.

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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