WPP#10: Unit L Concept 9-14: Basic probability(one event), probability of independent "AND" events(multiple events with and without replacement), probability of "OR" events(mutually and non-mutually exclusive), and probability of events that require Combinations to determine sample space

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WPP#9: Unit L Concept 4-8: Calculating possibilities with FCP, combinations(one event and multiple events), permutations, and distinguishable permutations

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

The viewer needs to be careful to not forget to add in the 6 at the end of the fraction(13/99). Also, the viewer needs to make sure that they wrote their first term as a fraction by just putting the term over 100,since the decimal is rounded to the hundreds. Lastly, the viewer needs to make sure they know the difference between summation notation and the summation formula.

Fibonacci Beauty Ratio (Extra Credit)

Chelsea A. Foot to Navel: 99 cm   Navel to top of Head: 62 cm   Ratio: 99/62=1.60 cm
Navel to chin: 40 cm                      chin to top of head: 21 cm       Ratio:40/21=1.90 cm
Knee to navel: 53 cm                      Foot to knee: 49 cm                Ratio: 53/49=1.08 cm

Average: 1.53 cm

Diana P. Foot to Navel: 100 cm   Navel to top of Head: 65 cm   Ratio: 100/65=1.54cm
Navel to chin: 44 cm                      chin to top of head: 20 cm       Ratio:40/20=2.2 cm
Knee to navel: 53 cm                      Foot to knee: 49 cm                Ratio: 53/49=1.08 cm

Average: 1.61 cm

Helena C. Foot to Navel: 101 cm   Navel to top of Head: 63 cm   Ratio: 101/63.=1.60 cm
Navel to chin: 46 cm                      chin to top of head: 19 cm       Ratio:46/19=2.42 cm
Knee to navel: 57 cm                      Foot to knee: 49 cm                Ratio: 57/49=1.16 cm

Average: 1.73 cm

Tracey P. Foot to Navel: 102 cm   Navel to top of Head: 63 cm   Ratio: 102/63=1.6 cm
Navel to chin: 43 cm                      chin to top of head: 21 cm       Ratio:43/21=2.05 cm
Knee to navel: 52 cm                      Foot to knee: 48 cm                Ratio: 52/48=1.08 cm

Average: 1.58 cm

Melissa A. Foot to Navel: 103 cm   Navel to top of Head: 63 cm   Ratio: 103/63=1.63 cm
Navel to chin: 45 cm                      chin to top of head: 19 cm       Ratio:45/19=2.37 cm
Knee to navel: 54 cm                      Foot to knee: 50 cm                Ratio: 54/50=1.08 cm

Average: 1.69 cm

According to Fibonacci's Golden Ratio, Diana P. is the most beautiful person out of this list because she was the closest to the number  1.6180339887. I believe the Beauty Ratio is very interesting because everything in our body is proportional. It makes me realize that the human body is very unique and valuable and that everything was made for a specific reason. It also makes me realize that we find something disproportional to be ugly. For example, if someone has a big nose they want to get cosmetic surgery to reshape their nose to make it proportional to their face. Therefore, I think the Beauty Ratio is only one factor of what makes someone beautiful.

Fibonacci Haiku: No Pardoning the Turkey

Thanksgiving 

Turkey

No school

Eating too much

Leftovers for a whole month

Mashed potatoes are essential for a delicious dinner

http://www.bing.com/images/search?q=turkey+clipart&qs=HS&form=QBIR&pq=turke&sc=8-5&sp=1&sk=#view=detail&id=5585B25828A7AF204C4E066D44A05EF1302A4FDA&selectedIndex=23

SP#5: Unit J Concept 6: Partial fraction decomposition with repeated factors

The viewer needs to pay close attention into inputting the coefficients of the system correctly. Also, the viewer needs to be very careful to not make the mistake of just distributing the square to the x and -2. It is not x^2+4, instead it is (x-2)times(x-2). Finally, the viewer need to not leave out a negative when combining like terms.

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

The viewer needs to pay special attention to first multiplying the expressions first and then distributing the number up at top in part 1 of the problem in order to correctly solve this problem. Next, the viewer needs to be careful when combing like terms because negatives can be easily lost since there are many numbers. Lastly, in part 2 of the problem the viewer needs to remember to get rid of the x's and x^2's when writing the system.

SV#5: Unit J Concept 3-4: Solving three varibles systems with Gauss-Jordan elimination/matrices/row-echelon form/ back-substitution and solving non square systems

The viewer needs to pay special attention of dividing the original equations as much as possible. Also, the viewer need to pay special attention to correctly distributing the number to each applied row to get the new row. Lastly, the viewer needs to double check what they are plugging in for ref and rref because for ref you put the original equations and rref you put in the last matrix's number.

WPP#6: Unit I Concept 3-5: Compound interest, continously compounding interest, and investment application(Pert)

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SV#4: Unit I Concept 2: Graphing logarithmic functions and identifying x and y intercepts, asymptotes, domain, and range

The viewer needs to pay close attention when finding the h of the equation to take the opposite of the number that is inside the parentheses. Also, the viewer needs to be careful to remember to make no changes to the k. Finally, the viewer must keep in mind that x=o when solving for the y-intercept and y=o when solving for the x-intercept. 

SP#3: Unit I Concept 1: Graphing exponential functions and identifying x and y intercepts, asymptotes, domain, and range

The viewer need to pay special attention to the "a" of the equation because since it is negative it is going to be below the asymptote in order to understand this problem. Also, the viewer needs to pay attention to the asymptote because it is negative three, which will make the graph not have any x-intercepts. Finally, the last thing the viewer needs to pay attention to in order to understand this problem is the range because since the graph is below the graph the notation is going to everything below the asymptote to the asymptote.

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

Student Video Three is about finding logs given clues(approximations). In order to, get the numbers the problem have you will need to take the numbers in the approximations and either multiply them or divide them together to equal the solution. After, you factorized the solution, you will need to expand your approximations, which means one log for each approximation in the problem. Finally, you substitute the letters given to the approximations.

The viewer needs to remember the hidden approximations of log base of base# =1 and log base 1=0. In addition, the viewer needs to remember that you can only multiply or divide the approximations to get the solution. Finally, the viewer needs to remember that if the problem is a factor, then it is using the quotient rule, which means there will be subtraction. The denominators are represented by the subtraction sign.

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

This Student Video is about finding all the pieces of a rational function and graphing all the parts. In order to, graph our rational functions we first need to sketch our asymptotes (horizontal or slant[never both] and vertical[if we have one]). Then, we need to plot any holes with open circles. Next, we need to plot the x and y intercepts whether if it is many or one. Finally, we use the vertical asymptote to divide the graph into sections and find at least three points in each section to help graph. To find the horizontal asymptote if any, you compare the degrees of the numerator and denominator and if bigger on bottom:y=0, same degree:asymptote is the ratio of the coefficients, and bigger degree on top: no horizontal asymptote. Slant asymptotes only exists if the numerator's degree is one bigger than the denominator and you use long division to divide the rational function and everything except the remainder is the equation of the slant asymptote. To find vertical asymptotes you factor both the top and bottom f the rational function  and cross off any common factors. Then, you set the denominator equal to zero and solve.

The viewer needs to pay attention to the cancellation of common factors will give you holes and holes are plotted with open circles. Also, they need to remember that domain is both vertical asymptote and holes. Finally, the viewer needs to pay attention for the number of x-intercepts. X-intercepts can have more than one or none, but y-intercepts is only one or none.

SV#1: Unit F Concept10: Finding all real and imaginary zeroes of a polynomial

Student Video#1 is about finding all the real and imaginary zeroes of a quartic or quintic polynomial. This includes the process of listing out all possible real/rational zeroes(p's and q's), finding out how many possible positive and negative real zeroes there will be by using the Descartes' Rule of Signs, finding zero heroes using a number from your p/q list or graphing calculator. Once you find a zero hero, you now use your answer row with a degree lower as a new header and keep on dividing it until your polynomial is a quadratic. Once you get a quadratic formula you take a GCF if possible and factor or solve using the quadratic formula.

The viewer needs to pay special attention to all the positive and negative changes when synthetic dividing because adding when supposed to subtract or vice verse really will make you get wrong polynomials and make it harder to find zeroes. Also, the viewer needs to pay special attention to distributing the negatives correctly when using the quadratic formula because then the numbers will not come out and the equation will not make any sense. All these precautions should be taken to get the correct answer and save time because when you get something wrong it takes time to look over your work trying to find mistakes.

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

 

       This problem is about graphing a fourth degree polynomial in standard form. Once, we factor out the equation we set the factors equal to zero and then we get our x-intercepts also  known as zeroes. We needed to include the multiplicity of each zero.

       Multiplicity is just how many times that order pair comes up in the graph and how you are going to approach that order pair(straight through, bounce off, or curve). Then, this problem called for the y-intercept, which is found by plugging x=0 to every x in the original equation. Lastly, to find the end behavior you look if the leading coefficient is positive or negative and look if the biggest degree is even or odd.

WPP#4: Unit E Concept 3: Quadratic Applications (Max Area)

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WPP#3: Unit E Concept 2: Quadratic Applications (Path of Football)

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

This problem is about taking a quadratic equation in standard form and changing it to get it into parent function form. We change it by moving the last number to the other side and then factoring out anything if possible. Then, we add the magic number to both sides. We get the magic number by dividing b(the middle number) by two and then taking the answer and squaring it. Then, we take the perfect squares of the quadratic equation with the magic number. In other words, by completing the square.

  Graphing a quadratic equation is way easier if it is in parent function for because we can get the vertex and everything else quickly. The vertex is the h and k in the parent function form(f(x)=a(x-h)^2+k. By using the parent function form we can make sketches more accurate and detailed. The viewer needs to pay special attention to foiling out a two and remembering to put that two to the other side and then multiplying first with the magic number and then adding/subtracting the number that was already there.

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

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WPP#1: Unit A Concept 6: Linear Models

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