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.

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. 

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.