Rational Function | Precalculus

This year, after the SAT on Oct 6th, I started my precalculus lesson. One of the sections that we covered in this term is called the Rational Function.  If you didn’t know or forget what it is, it’s a function in the form of r(x) = P(x)/Q(x), where P and Q are both polynomials and have graph that look like the picture at your left.  It was quite difficult for me at first to graph this function but once I noticed the pattern, it was fairly easy and straightforward.

In order to graph this rational function:

  1. Factor the numerator and denominator
  2. Look for intercepts: x-intercept is equal to the zeros of the numerator and y-intercept is equal to C value of numerator divide denominator
  3. Find the vertical asymptotes by determine the zeros of the denominator
  4. Figure out the horizontal asymptote by using the rule below. 
  5. Sketch the graph
r(x)= (x-2)/(x^2-2x-8) 
==> (x-2)/(x-4)(x+2)
x-intercept: 2
y-intercept: 1/4
vertical asymptote: -2, 4
horizontal asymptote: 0
slant asymptote: none

We also learned about slant asymptote, where the degree of the numerator is one greater than the denominator. This also means that there will be no horizontal asymptote. We determined the slant asymptote by divide polynomials with each other and we did not obtain its remainder.  Example below!

r(x)= (x^3+8)/(x^2-x-2) 
==> (x^3+8)/(x-2)(x+1)
x-intercept: -2
y-intercept: -4
vertical asymptote: -1,2
horizontal asymptote: none
slant asymptote: y = x+1

S’more | Stoichiometry

Have you had s’more before? What was it like? Was it good? 

If you (like me) didn’t know what the heck it is,  it is an amazing campfire snack in North America (according to Google) but as a Cambodian, I had never heard of or taste it before. Yet, last week in my Chemistry class, we did a S’more Lab to further our understanding and knowledge about limiting reactants (and get to taste it for the first time). 

We were given Graham crackers (Gc), marshmallow (M), chocolate piece (Cp) to make our own s’more. During the lab, we were required to balance out the equation and figure out limiting and excess reactants as well as calculate the experimental and theoretical yield. I have such a great time with my team doing the lab, by the way. 

  2Gc + M  + 3CP → Gc2MCp3   

This lab, not only it’s a lot of fun, but it had helped me to better understand about experimental and theoretical yield since I wasn’t sure on how to apply it into real life. Overall, I had such an incredible time do the lab and be able to learn about limiting reactants and make our own s’more. Yum! Yum!

No Pressure, No Diamond…

Have you been practicing for the SAT? How do you solve this problem? What is the best way to approach this problem?

Everyone had been talking about the SAT even before the summer break started. In math class this year, we had been arduously allocated all the class time to prep ourselves for the upcoming SAT on October 6th, 2018.

The first three or four weeks of school was not an issue for any of the students until we got to the last two weeks, which nearly the test date, where pressures began to heighten up.

Personally, the most challenging part about SAT to me is the timing. I could say that I basically know almost all of the math contents in the test but the time’s pressure often made me missed some of the questions.

In order to approach this issue, I often set a limit time for myself for each question that I’ve been solving. Furthermore, when I looked at the question and when it seems to have a lot of text or complicated equation, I would quickly skip it and move on to the easier one; this way I am able to complete all the easy one first. Another strategy that I’ve been taking was to always leave at least 4 minutes of the full test to fill up the bubbles. For example, if I did the 38 questions with calculators one and I have 55 minutes, I would limit myself to use only 50 minutes in order to leave 5 minutes in filling the bubbles sheet.

Our math facilitator, Jeff Boucher, always keep telling us that the SAT is not the correct way to measure our capability but it is the stepping stone that we need in order to experience the abundant opportunities that the university offered. This is why it is important to us as the Cambodian change agent. 

“It’s not the size of the dog in the fight, it’s the size of the fight in the dog.” ― Mark Twain

Flame Test Lab

Everything is made of atoms!

We all know that the best way to start a chemistry course is by learning about atoms structure and the element in the periodic table. Well, for my chemistry class this round we did this one cool lab called the Flame Test, in the purpose of understanding how the electron(s) of an element reacts to heat. 

We measured the result of the electron reaction through observing the color of the element when it’s in contact with flame. The reason that we see the colors is that of the energy that emitted by each electron when they excited corresponding to a wavelength of a particular light. 

One of the challenges that my team faced was that some pieces of the element dropped onto the bunsen burner tip so we had to make sure that it clean at all cost when we tested another element. Furthermore, when we tested the potassium chloride, we didn’t see the color change of the flame, so we just assume that the electrons gave out orange, which it isn’t accurate at all. Subsequently, this was a really fascinating and fun lab to do!