WPP #9: Unit L Concept 4-8: FCP, Combinations and Permutations

Create your own Playlist on MentorMob!

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

 

  In this student problem you learn how to find the infinite sum of a repeating decimal using your knowledge of the geometric sequences and series.Therefore, you must first know that you can write a geometric sequence by breaking down the decimal portion. You must know that you find the common ratio of a geometric series by dividing a term by the one that precedes. After you have found the common ratio you must know how to write the geometric summation notation of infinite series and finally plug in the values of the infinite formula to get your infinite sum.

It is important to not forget the number before the decimal point (highlighted in yellow above). You must also include this "whole number" with whatever you got as the infinite sum of the sequence you created, so that you can have a complete right answer.

Fibonacci Haiku: The Clique

Alpha.

Beta.

The clique.

Best Friends Forever.

It's hard to get in.

Just know that it's harder to stay in.

http://fc03.deviantart.net/fs51/f/2009/272/0/4/The_Clique_by_peachfan7.png

This shows 5 girls in a popular clique and they are shown to be very fashionable.

SP #5: Unit J Concept 6: Decomposing Partial Fractions together with REPEATED FACTORS

In this student problem you will learn how to decompose a partial fraction with a factor that will be repeated at least once. This specific student problem will have three factors that are repeated. This type of decomposing is very similar to that of concept 5. In both you must separate the factors and put a variable (A,BC, etc,) as the numerator.

However,  you must remember when you separate these factors that are the same you must count up the powers. in the factor that is repeated on the denominator. This means that your first factor that is repeated will go to the power of one and then your second factor repeated to the power of two and so on.

SP #4: Unit J Concept 5: Decomposing Partial Fractions together

In this student problem you will learn how to compose and decompose partial fractions, which contain variable x on either the numerator or denominator or both. You compose them by adding them together as you would a normal fraction. In order to be able to add them together you must have the denominator the same. If you multiply the denominator by another number to make the denominators the same and add the numerators, you must also multiply the numerator by whatever you multiplied the denominator. When you DEcompose the fractions then you must separate the common denominator. You do this by separating each factor into different fractions and putting a variable (A,BC, etc.) as the numerator.

In this student problem you must remember to multiply the numerators by every factor needed in order to have the same common denominator and be able to add the numerators together. Also, when you decompose you must remember to gather the like terms together and not put different terms together in one equation of your system because then your answer will come out wrong.

SV #5: Solving 3-Variable Systems Using Gaussian Elimination plus Gauss-Jordan Elimination

                      In this video you will learn about how to solve 3 variable equations using Gaussian Elimination. You will become familiar with terms throughout the video such as: matrix/matrices, REF, RREF, Elementary Row Operations, Back Substitution, Gaussian-Jordan Elimination, triangle zeroes and stair-step ones. You will learn how to apply each of these in order to be able to solve 3 variable equations. You will learn how to solve step by step using at most 4 steps. Plus you will learn how to check your answer using a calculator.
                       You must pay close attention to the part when we are creating the triangle zeroes and stair-step ones in the matrices. It is tricky to see how you got to the new equation so you must pay close attention to the process of getting to the new equation. It is good to remember the ELEMENTARY ROW OPERATIONS so you can be sure to be on the right track. Make sure to be neat and organized as well.

WPP #6: Unit I Concept 3-5: Interest and compounding

Create your own Playlist on MentorMob!

SV #4: Unit I Concept 2: graphing logarithmic equations

               This video will show you how to graph logarithmic equations using the needed parts. It is similar to solving for exponential equations in that you need to find the same parts like h, k values, key points, asymptote, y and x intercept, domain and range. However, you do not need to find a, b values and the asymptote is vertical so x=h. Furthermore, you solve for the x and y values differently than in exponential equations. Finally, the domain is not all real numbers, instead it has an end point while the range is all real numbers (negative infinity, positive infinity).
            Remember that the logarithmic equation is the inverse of the exponential equation. This will help you remember what are the differences between them and how to find the different parts.

SP #3: Graph the exponential equation, filling out all needed parts

                             This problem shows how to graph exponential equation. It has the key parts we are already familiar with which are the a, b, and k values. The a value in this type of equation shows us at first sight whether the graph will be above or below the asymptote based on whether the value is positive or negative, and k value is the the y=k asymptote. In this equation k=1 so the asymptote is y=1 and since the the a value is positive the graph will be above this asymptote. You can also find other key parts to be able to graph this equation. These parts include: key points (you get from the calculator easily), the x and y intercepts, and the domain and range. Remember that the domain in an exponential equation will always be all real numbers while the range will be either from negative infinity to the asymptote or from the asymptote to positive infinity. In this case it is from 1 to positive infinity.
                            You must pay close attention to whether the graph will have or not have an x-intercept. You know whether the graph will have a x-intercept by knowing that if the equation leads you to getting the log (or natural log/common log in your calculator) of a negative then you cannot solve this equation and therefore there is no x-intercept. A short cut to knowing there is not or there is an x-intercept is by looking at the a and k values of the exponential equation. if they are both positives or both negatives values then the equation will not have an x-intercept like in this example. But if the a and k values differ in that one is negative and the other is positive then there will be an x-intercept.

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

                                    This video shows you how to find a log with given clues, so it is like a treasure hunt. You use the given clues to add them or subtract them to one another using the product and quotient laws as well as the exponential law. You must also be sure to know the log property that shows that a log base (b) and the number (b) will equal one and use this clue besides the other clues given to solve the treasure hunt. This could be similar to finding the factors of your "treasure"(the log you want to find) but instead of coming up with random factors you use the ones given in the clues.
                                     Remember that when you use a clue more than once you use the exponent law to put the exponent number in front of the clue you used more than once when writing out your solution. Also, remember how to use the property log shown above properly. To illustrate, when you have log base (7) 7 you know that equals 1. However when you are solving the log you need to find you use the number 7 one of the possible factors, you do not use the number one.

SV #2: Unit G Concept 1-7: Graphing polynomials and their asymptotes

                        In this video I am explaining how to graph the polynomials with their asymptotes. The asymptotes are like boundaries that the graphs cannot touch except maybe sometimes for the horizontal and slant asymptotes but never for the vertical asymptotes. I show how to find the equation and points for each of these asymptotes. Furthermore, I show how to find holes in the graph. Plus, the domain, y and x intercepts and graphing more points using the calculator.

                       One thing you must special attention to is that when you have a hole you find the x intercepts and y intercept by using the simplified equation, not the original equation.

SV #1: Unit F Concept 10: Given Polynomial of 4th or 5th Degree Find ALL Zeroes, including real and complex.

                                 In this video you will learn Unit F Concept 10, which is similar to Unit F Concept 6. The difference is that you will end up with irrational zeroes at the end instead of just rational numbers. You will follow the same steps as in the Unit F Concept 6 until the end when you end up with irrational zeroes. You will learn how you found irrational zeroes in the first place, and you will learn how to put them into factor form, in factorization.
                                 One thing you need to pay close attention to is that when you write out the factors you must have a number of "x's" in the factorization equal to the degree of the equation. This means that if the equation is up to the fourth degree then you must have four "x's" in your factorization. You cannot leave the irrational zeroes without the x and count them as factors. They are not factors unless you use the proper way to turn them into factors with the variable x.

SP #2: Unit E Concept 7

                  In this Student Problem we are first reviewing how to create a polynomial expression starting with the zeroes and their multiplicity. This is labeled 1 with a circle around it in the picture above. Then, the following step are numbered as well up until six. All the steps shown are taken to learn how to use information known to graph a polynomial. This information includes: how to find factors based on zeroes, how to multiply factors, how to interpret end behavior, how to solve for your y-intercept, and finally how to use the multiplicity number to know whether the line of a graph goes through, bounces, or curves.
                  In order to complete this student problem correctly you must remember that the zeroes are opposite of the factors so it will always be (x minus "zero"). Another key thing you must remember is how to know whether a line goes through, bounces, or curves using the multiplicity number. Mrs. Kirch's catchy tune of "1,2,3, TBC" is a good way to remember. If the multiplicity is 1, then the line goes Through, if it is 2 then the line Bounces, and if it is 3 the line Curves.

WPP #4: Unit E Concept 3

Create your own Playlist on MentorMob!

SP#1 Unit E Concept 1

                 In this student problem we are learning to change a standard form equation to a parent function form so we can easily find key points to make a graph. The key points include the vertex, which is either the maximum or minimum of a graph, the axis of symmetry, which is also known as the line of symmetry or simply the axis, and the x-intercepts. The y-intercept can also be found by the parent function but it is easier to use the standard form equation to find the y-intercept.

                   Something you need to remember is that since this is a quadratic equation, your graph must look like a parabola. The vertex can be either maximum, showing the parabola going down, or it can be minimum, showing the parabola going up. The axis can be used to write other points in the graph using the rule of symmetry. Finally, another thing you need to remember is that the x-intercepts can have radicals or they can even be imaginary numbers, which means the x-axis is not touched.

WPP #3: Unit E Concept 2

Create your own Playlist on MentorMob!

WPP#1: Unit A Concept 6

Create your own Playlist on MentorMob!

WPP#2: Unit A Concept 7

Create your own Playlist on MentorMob!