SP#7: Unit Q Concept 2: Finding All Trig Functions When Given One Trig fFunction and Quadrant

This SP7 was made in collaboration with Mason Nguyen.  Please visit the other awesome posts on their blog by going here

Using Identities

Using SOHCAHTOA

 The viewer must pay special attention to identifying which quadrant the triangle is in. This is crucial because it determines which trig functions will be positive and which ones will be negative. Additionally, it is important to pay attention to the denominator, there cannot be a radical in the denominator, it must be rationalized. Lastly, the viewer should be able to recognize that the trig functions were solved in two ways, through the use of identities and  SohCahToa, these two methods resulted in the same correct answers! :)

SP 6: Unit K Concept 10: Writing a Repeating Decimal as a Rational Number Using Geometric Series

The viewer needs to pay attention to finding the ratio by dividing the second term by the first. Additionally, when dividing the numerator by a fraction, multiply the top and bottom by its reciprocal. It is crucial to remember the whole number 6 at the beginning of the problem. Add it to the solution by multiplying top and bottom by 99 to get the same denominator and then add the two.

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

 

The viewer must pay special attention to setting up the equations. It is important to remember that set the coefficients of the numerator equal to the term letters of the right side. Additionally, for this particular problem , we were unable to use our calculator because it gave us decimals. Instead, I used to process of elimination to find the value of A. Then, I plugged it into one of the original equations to find B and C. Lastly, I plugged in all three terms to find D. It is crucial that the viewer carefully solve for these values because small mathematical mistakes will lead to the wrong solutions.

SP #4 - Unit J Concept 5: Partial Fraction Decomposition with distinct factors

 

 For part 1, special attention should be payed to multiplying out the numerator. There is a lot of room for small mistakes, so it is important to make sure your math is correct. Also, be careful when distributing negative numbers, you must distribute the negative to everything in the parentheses, then combine like terms!

  

 For part 2, the viewer should be careful when writing the equations. It is important to copy correctly and not forget any negative signs. It is also crucial the viewer remembers to cancel out the x's.

For part 3, plug in the coefficients into the calculator. It is crucial you plug in the right numbers or else you will get the wrong answer. It is important to recheck what you plugged in.

For part 4, follow the necessary steps to find the ordered triple. The viewer should be able to follow the steps as stated in the image. It is important not to forget the closing parentheses! The fourth column provides the ordered triple, notice that these are the numerators of the original equation found in part 1!

SP #3 Unit I Concept 1:Graphing Exponential Functions

The viewer needs to pay close attention to solving or the x-intercept. We cannot take the log of a negative number, so if this occurs, it is undefined, meaning no x-intercept. Additionally, it is important to notice that the range depends on the asymptote. If you look at the graph, you can see that the graph never goes below 1 and goes up to infinity, giving us the range of (1, infinity). Also when choosing key points, the 3rd key point should be h.

SP # 2:Unit E Concept 7: Graphing Polynomial With Multiplicities

           The problem is about graphing a polynomial. This included finding the x-intercepts, y-intercept, zeroes with multiplicities, and end behavior. A polynomial is given in which we have to factor. This will help us determine how to graph the equation demonstrating how they behave at the extremas and in the middle.

           While graphing polynomials, special attention should be payed to a zeroes multiplicity so we know how to act around the x-axis. Additionally, it is important to remember that multiplicities of 1 go through the graph while two bounce, and three curve. We also need to pay close attention to the end behavior so we know what direction our graph should start and end at.

SP# 1: Unit E Concept 1: Identifying x & y-intercepts, Vertex, Axis of Quadratics, and Graphing

       This problem is about changing an equation from standard from into parent function form so that it is easier to graph. In this problem, you are trying to find the vertex, x-intercepts, y-intercept, and the axis of symmetry. Multiple steps are necessary to finding the solution. These steps will ultimately make graphing the equation easier and more accurate.
       In order to understand, special attention should be given to finding the vertex. We must remember that h is the opposite of its sign in the parent function. Additionally, it is necessary to recall that the x-intercepts may have 1, 2 or none (imaginary) x-intercepts. Also, to better understand, we must also recognize that the parent function allows us to provide an accurate representation of the function.