Tuesday, December 10, 2013

SP#6: Unit K Concept 10: Writing a Repeating Decimal as a RationalNumber Using a Geometric Series


     In order to solve this problem correctly, the viewer should note the infinitely repeating part of the decimal consisting of three digits. In addition, they should memorize the infinite geometric series equation. Furthermore, the viewer should pay special attention to the addition of the non-repeating part of the decimal at the end of the problem. One thing that one should always keep in mind when solving this type of problem is to reduce the fraction whenever possible.

Saturday, November 30, 2013

Fibonacci Haiku: Personal Statements

https://vle.whs.bucks.sch.uk/file.php/4000/Images/personal_statement.jpg

College
Applications
Personal Statements
Answer two prompts
What do I write about?
I need to make a good first impression
Knowing yourself is one thing, writing about yourself for a stranger is another.

Friday, November 22, 2013

SP#5: Unit J Concept 6: Partial Fraction Decomposition with RepeatedFactors


















     In order to understand how to solve this problem from Concept 6, the viewer must pay special attention to the steps taken when decomposing the fraction. Note that the powers increase for each repeated factor. Another thing that the viewer should focus on is the combining of the rows of the system. This action allows us to use the processes of elimination and substitution in order to obtain the answers for the variables. One last thing that should be recognized is the checking of the answers using the Reduced-Row Echelon Form (RREF) feature on a graphing calculator.

Thursday, November 21, 2013

SP#4: Unit J Concept 5: Partial Fraction Decomposition withDistinctFactors













    

     In order to understand how to solve this problem, the viewer should pay special attention to the algebraic means of obtaining a common denominator for multiple fractions. Furthermore, they should note the steps taken to distribute and combine like terms. When decomposing a fraction, one should be aware of how the terms are separated using letters. Finally, the viewer should keep in mind the method of utilizing the Reduced-Row Echelon Form (RREF) feature to check the answer on a graphing calculator.

Tuesday, November 19, 2013

SV#5: Unit J Concepts 3-4: Solving Three-Variable Systems with Gaussian Elimination & Solving Non-Square Systems



     In order to understand how to solve this problem, the viewer must pay special attention to the four steps of  Gaussian elimination. They are important to know, because they avoid the possibility of redundant or unnecessary work. Another thing that the viewer should take note of are the steps of checking answers using the Reduced-Row Echelon Form (RREF) feature on a graphing calculator.

Sunday, October 27, 2013

SV#4: Unit I Concept 2: Graphing Logarithmic Functions & Indentifying Key Parts





     In order to understand how to solve the problem, the viewer must pay special attention to the sentence: "The LOG's Xylophone was Happy and Rich." This means that the graph of a logarithmic function has an asymptote of x=h, and that there are no restrictions on its range. Another thing that the viewer should take note of is the use of the Change of Base Formula throughout the problem. This is crucial because it enables one to correctly input logarithmic functions into a graphing calculator.

SP#3: Unit I Concept 1: Graphing Exponential Functions & IndentifyingKey Parts


      In order to understand how to solve this problem, the viewer needs to pay special attention to the four parts of the exponential graph equation and how they affect the graph. Another thing to take note of is the fact that exponential graphs have an asymptote of y=k, which means that there are no restrictions on the domain (-inf. , + inf.). The viewer should also pay attention to how the range of the graph is written: from the lowest point to the highest point. Another thing to be aware of is the use of the 2nd TABLE function when obtaining the y-values of the key points.



Thursday, October 17, 2013

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

                                     
     In order to understand how to solve this problem, the viewer needs to pay special attention to the "clues" that are given. They are important because they guide you when expanding your expression. They viewer should also focus on the properties of logs, because they help us determine our two "hidden clues". One more thing that the viewer should pay attention to is that when factoring the parts of the initial log, you can stop once you have found your clues.

Monday, October 7, 2013

SV#2: Unit G Concepts 1-7: Graphing Rational Functions








                                                                                                                    
      This problem is about how to graph rational functions and all of their parts. In this problem, we encounter a rational function with a slant asymptote instead of a horizontal asymptote. After finding the asymptote and its equation using long division, we then solve for the vertical asymptote, its equation, and limit notation. In this problem we obtain one hole. Once we have found the domain, x-intercepts and y-intercept, we the graph the asymptotes and all the other components of the rational function on a coordinate plane.            

     In order to understand the problem, the viewer should pay special attention to the process of factoring trinomials and other polynomials. In addition, they should focus on how to write the limit notation of the vertical asymptote and the domain of the graph. The viewer would also greatly benefit from paying attention to the use of the factored rational function throughout the problem.

Sunday, September 29, 2013

SV#1: Unit F Concept 10: How to Find All Real & Complex Zeroes FromPolynomials of 4th or 5th Degree





     This problem is about how to find all zeroes (both real and complex) when given a polynomial of the 4th or 5th degree. In this problem, one must find the p's and the q's of the polynomial and and then utilize Descartes Rule of Signs. Afterwards, synthetic division is applied to determine any or all real zeroes, and to reduce the polynomial to a quadratic. In order to find the complex zeroes, one can either factor or plug in the values of the quadratic into the Quadratic Formula.

     In order to understand how to solve such a problem, the viewer needs to pay attention to the steps taken to find all of the possible real zeroes. This is important because it enables them to narrow down from literally an infinite amount of possibilities. Another thing the viewer needs to pay attention to is how to rewrite the complex zeroes after using the Quadratic Formula.

Friday, September 20, 2013

SP#2: Unit E Concept 7: Graphing Polynomials with Multiplicities and End Behavior



     This problem is about factoring a polynomial and determining its end behavior. In addition, the problem asks us to find the y-intercept and the multiplicity of the x-intercept(s). Using all the information gathered from the original equation, we graph the polynomial on a coordinate plane.

     In order to understand how to successfully complete the problem, one must pay attention to the first term and degree of the equation. These parts of the polynomial are crucial because they enable someone to determine the end behavior of a graph. Another thing someone should be wary of is the multiplicities of the x-intercepts. They determine how the graph acts around the x-axis: 1=through; 2=bounce; 3=curve.

Tuesday, September 10, 2013

WPP#3: Unit E Concept 2: Finding the Maximum and Minimum Values of Quadratic Applications Using a Graphing Calculator



SP#1: Unit E Concept 1: Identifying and Accurately Graphing the Parts of a Quadratic





     This problem is about identifying the different parts of a quadratic in standard form and graphing them accurately. The parts of the graph of a quadratic include: vertex, x-intercepts, a y-intercept, and an axis of symmetry. In order to graph a quadratic easily, one must first change if from standard form to parent function form.

     In order to understand how to accurately graph a quadratic, the viewer needs to pay special attention to the steps of completing the square. It is through that process that the quadratic is rewritten in parent function form. Using the values of h and k in the parent function equation, the viewer can obtain the vertex and the axis of symmetry. Another thing the viewer should pay attention to is how to how to get the y-intercept. This can be done by plugging in O for x in the original function. The last thing that the viewer should be aware of is that you can find the x-intercepts by solving the simplified version of the function that is reached after completing the square.