SP#7: Unit Q Concept 2: Finding All Trig Function Values Using Identities

Please see my SP#7, made in collaboration with Vivian Pham, by visiting her blog here.  Also be sure to check out the other awesome posts on her blog.

SP#6: Unit K Concept 10 - Writing Repeating Decimals as Rational Numbers

The viewer must pay attention to the numbers and which numbers go with what part in the formula. Also, don't forget to add the whole number to the fraction in the end. The viewer also must not get confused with geometric and arithmetic, since for geometric to find the ratio you divide the numbers. Remember to multiply by a reciprocal to cancel the fraction out

SP #5: Unit J Concept 6 - Partial Fraction Decomposition with repeated factors

The reader must be careful when doing this problem because there are four equation. Also, make sure you do your math correctly or one incorrect variable can mess up your whole system. Also, make sure that you multiply the numerators and combine like terms correctly. Check your work!

SP #4 - Partial Fraction Decomposition with distinct factors

This part is called composing. We combine the fractions into a larger fraction. We then combine like terms. 

This part is called decomposition. We are given a large fraction and are trying to find the small fractions that multiplied to make it. 

Simply type the left part into the calculator and using rref you will get the answer on the right, which is your A, B, and C. 

This is what you started with when you plug A, B, and C, back together. CONGRATS. 

SP #3 Unit I Concept 1:Graphing Exponential Functions

The viewer needs to pay attention to solving the x-intercept. If you get a negative log, you have to make sure to know that you cannot take the log of something. Therefore, the x intercept is undefined and there is no x-intercept. Also you must acknowledge that the range changes all the time because it depends on the asymptote. If it the graph is below the asymptote, the  graph will go up until the asymptote. If it is above, it will start at the asymptote to infinity.

SP # 2: Unit E Concept 7: Graphing polynomials, including x-intercept, y-intercept, zeroes, (with multiplicities), end behavior.

This problem is about graphing polynomials by defining how they behave at extremas, how they behave in the middle, where their highest and lowest points are, where their intercepts are, and defining their intervals. In addition, we are dealing with multiplicity of zeroes and how it defines our graph (remember 1 is through, 2 is bounce, 3 is curve?) We will be finding the x-intercept, y-intercept, determining the end behavior, finding extrema, and noting if the graph has intervals of increase or decrease with a set equation. To make a graph efficient, we must find all these aspects.

The viewer needs to pay special attention to the end behavior and how to find it. The degree and the coefficient determines the end behavior. There is even (degree) positive (coefficient), even positive, odd negative, odd positive. The viewer needs to know which direction the end behaviors go by this. Another thing that the view has to be careful on is when they factor the equation, because it is easy to make simple mistakes. Also, the viewer has to make sure they plot their graph right and where it goes through, bounce, or curve, and apply it to the graph.

SP# 1: Unit E Concept 1: Identifying x-intercepts, y-intercepts, vertex (max,min), axis of quadratics, and graphing them

This problem is about demonstrating the process of establishing a parent function equation with a standard form to begin with. The vertex, x-intercepts, y-intercepts, and axis is to be found. To make a graph the most efficient and accurate, these steps are necessary. 

The viewer needs to recognize to (x-h) in the parent function equation. The parent function equation is y=a(x-h)^2+k. To graph the x-point of the vertex, you need to know that h is opposite of what it appears to be. For example (5-2)^2. That (-2) would be 2 when you graph it. Another thing you must acknowledge is that the x-intercepts may include imaginary numbers, and when that happens you cannot graph it since it is imaginary for the x-intercepts.