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

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SP #6: Unit K Concept 10 - Writing a Repeated Decimal as a Rational Number Using Geometric Sequence

 

The viewer needs to pay special attention to finding the ratio by dividing the second term by the first. When we reach dividing the two fractions, we need to multiply the reciprocal of the second number in order to cancel. It is crucial to remember the whole number 5 from 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 fractions.

Fibonacci Haiku: Happiness or Success

Happiness

Success

Which one?

Success equals happiness

Or does happiness equal success?

Have a smile on your face every day

 

http://images.soulpancake.s3.amazonaws.com/e3487dc9d49a4c8fab157c2dfe58cee5.jpg

 



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

 

The viewer must pay special attention to setting up the equations, and that they distribute carefully and properly. It is important to remember to set the coefficients of the numerator equal to the term letters of the right side (if there is no number for the term, make sure to add in "0" in the front). Because of our answers being fractions, we cannot use the "rref" function on our calculator.

SP #4: Unit J Concept 5 - Partial Fraction Decomposition with Distinct Factors

 
For part 1, make sure to pay special attention to multiplying out the numerator. Make sure to carefully distribute, this including negatives, otherwise one mistake could change your whole answer.

 

For part 2, the viewer should be careful when writing the equations. It is important to copy correctly and not forget any negative signs.

For part 2 (wasn't enough room), 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. The fourth column provides the ordered triple, making them the numerators of the original equation found in part 1.

SV #5: Unit J Concepts 3-4 - Solving Three-Variable Systems

 The viewer must pay attention to interchanging (arranging) the system before using the boxes to find the "zero triangle" and the "stair-step one line", which would make the process of solving the matrix easier. They also need to pay close attention to multiplying a row by a constant and adding/subtracting it to another row correctly, otherwise it could mess up the whole matrix. The view must know when solving, row 3 goes with row 2, and row 2 goes with row 1.

WPP #6: Unit I Concept 3-5 - Compound Interest, Continuously Compounding Interest, and Investment Application

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SV #4: Unit I Concept 3-5 - Graphing Logarithmic Equations

In this video, the viewer needs to pay attention to how the logarithmic equation is not able to plugged into the graphing calculator because of its different numbered base (other than 10). In order for us to do so, we need to use the change of base formula- natural logs- which then gives us our graph. In finding the x-intercept, we must remember how to exponentiate and get rid of the logarithm. When finding the y-intercept it is important to know how to plug in the logarithm if the base is again not 10, which leads to using the change of base formula again. When finding the intercepts, if a number value of natural log is negative, the point is undefined. Because logarithmic equations are inverse to exponential equations, we know that the domain and range are flipped. The domain is restricted by the asymptote while the range has no restrictions.

SP #3: Unit I Concept 1 - Graphing Exponential Functions

The viewer needs to pay attention to "a", which determines whether the graph will be above the asymptote (positive "a") or below the asymptote (negative "a"). We also need to pay attention to solving for the x-intercept. If we get a negative number on one side, we cannot take the natural log of it, making it undefined. This is lead to NO x-intercept for this graph. Another concept to recognize for these problems are the range, which depend on the "a", whether it is above or below the asymptote, and the asymptote itself.

SV #3: Unit H Concept 7 - Finding Logs Given Approximation

This problem is about finding logs given approximations, which incorporated previous concepts learned, such as product, quotient, and power laws. It covers how to take our "clues" and multiply or divide them to equate them to our solution. We substitute the logs for the given values.

One thing to pay special attention to is recognizing that because there is a denominator, the log values will be subtracted. The viewer also needs attention themselves to expanding the clues using the properties of logs. If the log has an exponent, they need to use the power property, which then gives a coefficient to the log value. This means bringing the exponent to the front of the log. It is also important to recognize that you need to substitute in the values given after you have completely expanded your log.

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

The problem is about graphing a rational function. This video addresses vertical, horizontal, and slant asymptotes, and finds the holes and the x and y-intercepts of the function. Using past concepts (domain, long division, interval notation) will help us in graphing this function.

We need to pay special attention how to find the x and y-intercepts because it is crucial to remember to use the simplified equation, not the original rational function. Another concept we need to pay attention to finding the holes, plugging in the found x-value into the simplified equation to find the y-value of the hole. When plotting the hole, represent it as an open circle, which symbolizes that the graph does not go through this point. Lastly, through using the limit notation of the vertical asymptote, it gives you an idea of what the graph will look like.

SV #1: Unit F Concept 10 - Finding zeroes (real and complex) of a 5th or 4th degree Polynomial

This problem is about finding real, irrational, and imaginary and irrational zeroes by using p divided by q to find possible zeroes and the Descartes Rule of Signs to find the number of positive and negative zeros.

It is important to remember to not include certain fractions in our p/q's because we may have already written the reduced form of it already. It is also good to remember that in Descartes Rule of Signs, that we must account for irrational or imaginary zeroes by pairing the real zeroes. A helpful step is also to take out the greatest common multiple from the quadratic (after finding 2 zeroes) because it makes smaller, nicer numbers for when we plug them into our quadratic formula. Concerning writing factors, remember to multiply x by the number of the denominator of the irrational zero so we have the entirety of it over one number. It is also good to remember to distribute any GCF we took out previously, to a factor that contains a fraction to make the factors look "pretty" and "clean".

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

This problem is about graphing a polynomial, which included a y-intercept and x-intercepts (or zeroes) with multiplicities, and end behavior. When a polynomial is given, we first have to factor. With the help of multiplicities- the number of times a zero shows on a graph, it will help us determine how to graph the equation demonstrating how they behave at the extremas and in the middle.

While graphing polynomials, you should pay special attention to the zeroes and their multiplicity. Multiplicities determine how the middle of the graph looks like: multiplicities of one go through the graph, 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.

WPP #4: Unit E Concept 3 - Maximizing Area

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WPP #3: Unit E Concept 3 - Path of "Football"

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SP #1: Unit E Concept 1 - Identifying X-intercepts, Y-intercepts, Vertex (max/min), Axis of Quadratics and Graphing

This problem is about changing an equation in standard form f(x)=ax^2+bx+c into parent function form f(x)=a(x-h)^2+k so that it is easier to graph. With the parent function, it is easier to find and identify the vertex, y-intercept, axis, and x-intercepts. Though it takes several steps to find these parts of the graph, it will result in a more accurate and detailed sketch of the graph.

Some special things to pay attention to would include the (h, k), included in the parent function, which acts as the vertex of the graph. In certain examples, the x-intercepts do not come out with real numbers. With the imaginary numbers, we are not able to graph the points on the graph.

WPP #2: Unit A Concept 7 - Profit, Revenue, and Cost

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WPP #1: Unit A Concept 6 - Linear Models

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