Analyzing the Graph of a Polynomial

In pre-calculus, we investigate many topics in the subject, one of which is graphing polynomials.

Above is the graph of the equation (x-2)/(x2-2x-8). Using the graph, we can analyze many characteristics of the polynomial. First, we can identify the y and the x-intercepts, when x and y equal zero, respectively.

We can also recognize the vertical asymptotes, which is the value of x that the graph never touches. In this case, the vertical asymptotes are when x equals to -2 and 4. We can also describe the behavior of the graph as x approaches the vertical asymptote from different directions. For instance, as x approaches -2 from the negative side (left), y approaches negative infinity (-∞), and as x approaches -2 from the positive side (right), y approaches positive infinity (+∞).  The same behavior applies to when x approaches 4 from both directions.

The horizontal asymptote can also be found using this graph. As seen above, the graph never touches the point y equals 0. The behavior of the graph can be observed as y approaches zero from the negative (below) and positive (above) side. In this case, as y approaches zero from below, x approaches -∞ and as y approaches zero from above, x approaches +∞.

Observing Osmosis with Plant and Salted Water

When plant cells absorb or lose water, the water undergoes the process called osmosis. Osmosis is the type of diffusion describing the movement of water from a hypotonic (low solute concentration) environment to a hypertonic (high solute concentration) one.

The term water potential refers to the likelihood of water molecules transporting to another environment. A more dilute solution would have less water potential than that with a high solute concentration.

Water molecules move from high to low water potential. Through this process, the water molecules can transport with them the solutes in forms of molecules or ion.

In AP biology, we conducted an experiment where green beans were soaked in solutions with different salinities and the effect of osmosis on the vegetable was observed.

Three bean samples, for soaking in fresh water and salted water

By soaking the beans in different solutions, there were some physical, textural and taste changes to the beans. In the freshwater, the bean became fresher, with a little lighter skin color and slightly thicker skin. It also became a little more crunchy (however less flexible), less sweet and more watery in term of texture and taste. This might be due to the access of more water in the bean. The bean in 20g/L saltwater became darker with some lighter-colored spots. It was softer and more flexible than the one in freshwater. There was no sweetness in the beans, and it became slightly salty and a little less watery. The bean in the 40g/L saltwater has a similar quality to the one in the 20g/L saltwater solution, except it was more flexible and less watery.

As mentioned, water movement is dependent on the solute of an environment. This means that the water molecule would move to the environment with more solute. In this case, the tissue cell of the green beans contain more solute than the freshwater solution, therefore, causing the water to move into the plant cells. On the other hand, the saltwater has more solute than in the plant tissue so the water from the plant would move to the more solute environment. This instance is similar to how some organisms became dehydrated in seawater because seawater is more solute than their body.

Testing Solubility and Acidity of Over-the-Counter Pharmaceuticals

When we are slightly ill, we often take over-the-counter drugs and often times, they relief our symptoms, but sometimes induce adverse side-effects. So, it’s important to know the characteristics of the medicine we take, and how it may impact us.

In one of our chemistry classes, we investigated the solubility and acidity of over-the-counter medicine—aspirin, Tylenol, Alka-seltzer, and tums—in different solvents.

A drug has to be soluble in order for the body tissues to easily absorb it. Our body should be able to absorb the medication easily for it to be effective. In addition, when drugs are not soluble, it is possible that there’s a residue of that drug in our body, causing adverse effects to our body. I think that is why we usually take medication along with water since more of those drugs are soluble with that solvent.

Discussing Global Security at the 2018 ISPPMUN

Friday 26th October marked the first day of ISPP Model United Nation (MUN) 2018. From 16 different schools and three countries, 400 students gathered to discussed global issues in this event. I was honored to be one of them.

In this year’s MUN, I attended the security council. Even though this committee is known to be the most serious and quite intimidating, I took on the challenge to try something new. In this committee, we discussed the security issues in the Democratic Republic of Congo, Ukraine, and Libya.

Representing the delegate of Kazakhstan, I, along with the delegate of Equatorial Guinea, wrote a resolution on the situation the Democratic Republic of Congo. Typically, there are six or seven delegates working on a resolution. So, it was really challenging for the two of us to write one whole resolution. We ended with a completed resolution with nine operative clauses (solutions).

Working on the resolution

It was really tough debating in the security council. Many experienced delegated looked for resolution with good intention, which we had, as well as clear methods of how those solutions can be established. Since it was my first time in this council, my solutions did not include detailed procedures. This was why the resolution did not pass when all delegates in the committee vote on it.

All delegates, and chairs (facilitators) in the security council

Despite the fact that this particular MUN taught me a lot, I discover that discussing security is not my thing. I flashed my memory back to last year’s conference when I was in the environmental council, and how I enjoyed it more. However, this doesn’t make the world’s security issue less important to me.

Why FDR’s First Inaugural Address Still Remains Powerful Today

In literacy essential, we examined the topic of American history as our first unit. Using the platform CommonLit and other resources, we dissected the speech “Give Me Liberty, Give Me Death,” understood the causes of American Civil War, analyzed the Great Depression and etc, while also expanded our vocabulary usage and studied grammatical concepts. At the end of the term, we were able to choose our final assessment project. I chose to write a rhetorical analysis essay on President Franklin Delano Roosevelt first inaugural address “Only Thing We Have to Fear Is Fear Itself.” Below is the essay I’ve written about how and why FDR used the rhetorical appeals in his speech.  

Rhetorical Analysis on FDR’s First Inaugural Address

“Only Thing We Have to Fear Is Fear Itself”

Starting in 1929, one of the most tragic economic crisis, the Great Depression, occurred. This catastrophe caused many citizens to be unemployed and bank loans were halted. However, when President Franklin Delano Roosevelt (FDR) was elected in 1932, he promised to bring America out of the depression by providing jobs to citizens and strengthening America’s policy. In his inaugural address — delivered on March 4th, 1933 — President FDR explained the economic issues that America was facing and presented his solutions to the audience. Throughout his rousing speech, FDR offered logical solutions about the problems arisen in the United States from 1929 to 1939. He projected his speech in a unifying language that built his credibility to “fix” America and reassure Americans to believe through government involvement and collaboration, America could recover.

Throughout his speech, President FDR used the logos appeal to describe the problem America faced and the reason behind his proposed solutions to reform the US Constitution. FDR explained the dire condition of the economy concerning America to reinforce the importance of his speech. He elaborated on the problem by stating, “values have shrunken to fantastic levels; taxes have risen; our ability to pay has fallen; government of all kinds is faced by serious curtailment of income…” He also proved his solutions would work by asserting, “we are stricken by no plague of locusts,” and “our Constitution is so simple and practical that it is possible always to meet extraordinary needs by changes in emphasis and arrangement without loss of essential form.” These logical reasons persuaded the audience that his resolutions were necessary and had the ability to pull America out of the Great Depression.  

In addition to the appeal to logic, President Roosevelt used ethos by communicating in phrases that built his reliability with his audience and guaranteed he had the ability to heal his country. He assured the audience that he will solve the economic issue of his country by claiming, “I shall spare no effort to restore world trade by international economic readjustment, but the emergency at home cannot wait on that accomplishment.” Later in his speech, he went on to say, “for the trust reposed in me, I will return the courage and the devotion that benefit the time. I can do no less,” which further ensure his audience. With these promises, President Franklin Roosevelt had made his citizens believed that he would support them.

Similarly, FDR established a relationship with his citizens by using pronouns such as “we” and “our,” and called his citizens to collaborate with the government in order to build up the trust for him. He emotionally conveyed, “we face the arduous days that lie before us in the warm courage of the national unity.” With this he called the citizens to action by pleading, “if I read the temper of our people correctly, we now realize as we have never realized before our interdependence on each other; that we can not merely take but we must give as well.” By entreating this, he emphasized the importance of collaboration to both the citizens and the government, therefore, convinced Americans to rely on him while also cooperate.

On the whole, President Franklin Delano Roosevelt effectively delivered his first inaugural speech with rhetorical appeals such as logos, ethos, and pathos. His influential speech is still engraved in American citizens today. Besides, he did not just present his solutions in his speech but also execute them to action. Many of the policies that were established during his time in office still serve Americans today, and this is part of the reason why he remains one of the most respected American presidents.


Why does Flame Change its Color When Contacting With Different Chemical?

When an element has contact with flame, heat excites the electrons in the atom. This allows the electron to go from their ground states to a higher energy level.  In this state, the electrons are unstable, so they needed to emit energy to return to their ground state. In this case, we could see a color that corresponds to the wavelength of light emitted by the energy in the form of electromagnetic radiation. 

Above is an explanation of why we see different colors when elements or chemical compounds are put with flame. To see this concept with our bare eyes, we did the flame test lab as part of our chemistry class. 

Six different compounds of salt were used in this experiment. Each of them was placed on the flame from a burner. Those different salt compounds emitted different colors, such as yellow, orange, mint green, red and magenta. Then, the wavelengths of the color were identified. 

When copper is put with flame, we can see a mint-green color. The wavelength corresponding to that color is about 5000 angstroms.

Nonetheless, this experiment was not conducted perfectly. One possible source of error can be from the way the color was observed. Color is something that is subjective. This would lead to inaccuracy in the wavelengths of chemicals identified. To avoid this error, a colorimeter can be used to accurately measure the wavelength.  


Writing a Play Depicting an Issue in the Society

We’ve learned so many ethical concepts here at Liger, and we want to have a platform where we can share those ideas with others, especially Cambodians. So this year, we started a mobile theater project, and I was glad to be part of the writing group this round. Our mission is to share with rural Cambodians ideas relating to healthy relationships amongst each other, as well as raising awareness about plastic pollution, marine conservation, and education, through short plays. This term I was part of the team that wrote a play reflecting a problem in the society, particularly body image.

It’s a challenge to create a play regarding sensitive issues, like body image. We want to clearly convey that it is a problem in a way that is not offensive and controversial. In order to do that, we need to be careful about every part of our play by making sure the play is not oversimplified (loosely communicate the problem), does not contain stereotypical characters or inappropriate joke relating to the topics. It is extremely crucial that we keep those things in mind as change agents. We want to raise awareness about a problem, while we avoid turning it into a controversial topic.

AP Biology Lab | How Much Water is in a Model Organism

This year I’m taking Advanced Placement biology class to continue my passion for science. Besides listening to presentations by our facilitator, students also go the opportunity to apply our knowledge through labs.

The first lab we did was relating to water in organisms. Water is in every organism; it makes up approximately 60 to 90 percents of every organism. Water is important for various functions including respiration, metabolism, and homeostasis. The objective was to extract water out of model organisms (fruits and vegetable) and figure out how much water is in that organism. We weren’t given an instruction on how we should … our lab, so we needed to invent our own procedures. My partner and I got carrot as our model organism. Below is the procedure we’ve created for our lab:

“The carrot was washed, dried and weighed three times: the average weight was calculated. To ease the process of blending, the carrot was chopped into small pieces. Then, the carrot was blended until it was ground. The paste was placed into a strainer and was squeezed to extract liquid. Finally, extracted juice was weighed three times and the average weight was calculated.”

Fruits and vegetable scraps and juice


The result told us that water made up approximately 45 percents of carrots mass. However, according to the US National Library of Medicine, the amount of water in a carrot is 86 to 89%. Our result was inaccurate because our method was manual so there might be some errors along the way. For instance, there may be parts of carrots that were wasted unnecessarily. Despite the inaccuracy, we can use our data to compare with other organisms that my classmates worked on. For example, we can tell that watermelon contains the most water, while logan contains the least amount of water.

Graph showing percent of water in different organisms, according to our experiment



Unit Circle | Math

As SAT test date is approaching, I practiced both the math and verbal section frequently. A topic in SAT that I learned was the unit circle. This topic is a foundation to the idea of calculus. I’ll be taking pre-calculus class for the rest of the school year so this will be helpful.

A unit circle is a circle with the radius of 1. This circle helps us understand and calculate the angles and lengths of special triangles — 30-60-90 and 45-45-90 triangles. In other words, the unit circle is made up of special triangles.

Below is a drawing I made that explain unit circle.

Unit Circle with 30-60-90 triangle
Unit Circle with 45-45-90 triangle



Why I Want to be a Part of Liger Edge?

This year, Liger initiated its own online school newspaper — Liger Edge. The goal is to keep track of and share with the world the abundant activities we do at Liger. The articles come in dual language and will help communicate opinions and experiences we have to create discussion.

I was chosen to be the English editor in chief. Being in this role, I hope to learn more about my classmates writing style and help improve their writing skills as necessary. Additionally, the reason I want to be part of the school newspaper is that I want to spread my love of reading and writing. I believe that people would love reading if they can find something that would interest them. In a similar way, I also want to give a voice to and project the beauty of Cambodia through my articles.

My first article was about the International Vulture Awareness Day, which happened on the 1st of September. Below is an excerpt from my article:

Saturday, September 1st marked this year’s International Vulture Awareness Day. The intention of the day was to communicate information about vulture conservation to a greater audience and spotlight the important works done by vulture conservationists worldwide. Opportunely, two organizations in Cambodia participated in the celebration of this event by sharing their work as conservationists in Cambodia.

Angkor Centre for Conservation of Biodiversity took the opportunity of this day to inform Cambodians through the popular social media platform Facebook about the “destructive consequences of using poison for hunting in attempt to encourage local hunters to abandon this practice.” The post came along with a 3-minute video discussing the decline of vultures due to hunters’ practices and what this means for us, humans.

Photo from BirdLife International Cambodia Programme