e-journal final entry 2: the end (hopefully) of nadya’s headache

Learning is a journey, not a race

This is my first time learning for IGCSE. My old school didn’t use the IGCSE curriculum, they had their own curriculum. When I first entered, I thought IGCSE would be just like any other test but boi was I wrong. Being here and learning for IGCSE for 6 months now, I realize that it’s much very serious. The many subject choices just makes it way harder to choose which subject I would dedicated my utmost time studying for. It’s been a hectic and stressful 6 months filled with last minute homework and projects and procrastination. I thank Mr.Kichan for teaching us and helping us prepare for our mathematics IGCSE.

Source: Jimmy Joe

For this semester’s assignment, we had 3 tasks that we had to do to develop our inquiry skills. First, we had this airplane railroad thingy (sorry, can’t explain, just see later) and then we had 2 magic triangles questions. At first I thought that these questions were just a hassle but they were actually quite fun to do when discussing with a partner!!

AIRPLANES AIRPLANES ✈️

So how does this work? Pretend that the overlay picture is an airplane railroad. We’re supposed to find the equation line so the airplane can land perfect so no lives are lost. Equations that are off from the road will crash and the passengers will die. In this question, the topics included are gradient / slope, linear equation, x and y intercepts and graphing equations.

So first what I did here is the y-intercept. I then put the y-intercept coordinate which is (0,-2) into the equation y=mx+b. I then checked the graph for another point and used the formula y2-y1 divided by x2-x1 to find the slope and then plugged in the slope into the equation.

Screenshot from desmos.com

This is another example. I first check the y-intercept (the point that sticks to the y axis) which is (0,11). Then afterwards i find another point which is (1,7). I used the formula to find the slope which is y2-y1 divided by x2-x1. This gets me 11-7/0-1 which is -4. Then i just plugged everything into the y=mx+b formula. The -4 is the m (gradient / slope) and the 11 is the y-intercept. This gives us y=-4x+11.

Screenshot from desmos.com

MAGICAL TRIANGLES

Our task was to solve the question in the image below: to explore and find out the perimeter and area of the magical Koch’s snowflake triangles. Topics in use is 2D shape perimeter and area formulas (but way more complicated than those 2nd grade 2D shapes formulas kay).

Wathall, J., Harcet, J., Harrison, R., Heinrichs, L. and Torres-Skoumal, M. (2019). Education Bookshelf Mathematics Analysis and Approaches Higher Level. [online] Retrieved 20 November 2019, from Bookshelf.oxfordsecondary.co.uk
The triangles are equilateral
1st iteration has 4 sides and 2nd iteration has 16. Each iteration, times 4 sides.

Perimeter of the triangles

Finally counting the perimeter. Everything is explained in the picture already.
Pictures are screenshots of my digital handwriting using the app autodesk sketchbook (yes i use my arts drawing app)

Areas of the weird triangles

I counted the original length of the area of the triangle and added it with the newer areas as the iteration increases.
I hope you appreciate the green ink. I’m expecting some major green theme in your wedding. Btw green symbolizes wealth, good luck, health and growth so yeah uwu

ANOTHER WEIRD TRIANGLE 🤦🏻‍♀️ IM SO TIRED 😭😭😭

Our task was to solve all the 6 questions in the picture below of the Sierpinski’s weird and confusing triangles by exploring. Topics in use are the law of indices, 2D shape triangle area formula, ratio, etc.

This picture is what we have to do.

Wathall, J., Harcet, J., Harrison, R., Heinrichs, L. and Torres-Skoumal, M. (2019). Education Bookshelf Mathematics Analysis and Approaches Higher Level. [online] Retrieved 20 November 2019, from Bookshelf.oxfordsecondary.co.uk

Construct the next iteration and fill the table (above)

More green ink yayyyy

What are the patterns?

Pattern for the number of green squares
Pattern (length of one side of the triangle)
Pattern for area of the triangle

What do they have that are in common with each other?

Picture is self-explanatory

Form a conjecture to obtain the numbers if you were to expand the table further to stage 4, 5 and 6 *sigh*

First of all this is what conjecture means (picture taken from google.com, pop-up search result: oxford dictionary)
Plug in the n to the formulas like above
Tadaa!! Easy peasy but time draining, jk

How would you compare the set of numbers collected?

I double checked the internet for answers to the weird triangles and discussed with my friends uwu so yeah.

Reflective: I reflect back on my working and double check. I reflect on my mistakes and try to not repeat it again next time and learn from the mistake so I can do a better performance next time and progress.

Inquirers: I let my curiosity wander and inquiry and research and explore on how to solve the questions. At first, I learn independently and then discuss with others. I learn with enthusiasm and sustain my love of learning throughout life.

Knowledgeable: I develop and use conceptual understanding that I have learned in the past, explore new knowledge formulas and techniques.

Thinkers: I use critical and creative thinking skills to analyse and take solve complex problems. I make well thought out calculations to avoid silly mistakes.

Communicators: I express my thoughts confidently and creatively during discussions with others. I collaborate effectively, listening carefully to the perspectives of other student opinions.

The first amazing test was very memorable 😂😂 mostly because i died on that day. After a long month of vacation and holiday and jetlag, we immediately go to school and faced the monstrous atrocity called The Amazing Test. It was my first time doing IGCSE so I didn’t know that we couldn’t use a correction tape. It said “no correction fluid” on the instruction page so I thought correction tape was allowed TwT. Ahhhh skskskskskskksksk anyways, lost so much points because of that sigh. I’m so sed.

Anindita, N. (2019). Digital Painting by Niken Anindita | ARTWOONZ. Retrieved 20 Nov. 2019, from https://artwoonz.com/digital-painting-niken-anindita/

All the banners are made my me using the app Phonto. The dragon background picture is drawn by Niken Anindita from artwoonz. Maybe I should’ve made the banners green too hmmm,, ehhh too late ig

From here is when the headache finally ends. YAYY WE MADE IT!(=´∀`)人(´∀`=)

#firstbatch #igcsemath2020 #unforgetablemoments

The story of Arachne 🕷 🕸

Who is she? 🕷🕸

Arachne was a Lydian maiden, the daughter of Idmon of Colophon, who was famous for his purple dyed cloths. She was credited to have invented linen cloth and nets while her son Closter introduced the use of spindle in the manufacture of wool. She was said to have been a native of Hypæpæ, near Colophon in Asia Minor.

Art by Irrenhorros on Devianart

The Weaving Contest 🕷🕸

Arachne was a very good weaver, but she was too prideful. Arachne bragged about being a better weaver than the Athena Herself, the Goddess of Crafts which caused the goddess Athena to get angry and challenge Arachne to a weaving contest.

The Weaving Contest
Art by Unknown

Athena wove a beautiful cloth of the gods and goddesses together on Mount Olympus while Arachne wove a cloth making fun of the gods and goddesses, showing them getting drunk and falling down and making a mess of things.

When Athena saw the embroidery Arachne had made, she became angrier. Athena cursed Arachne and turned her into the first ever Spider.

Another version of the myth tells about an agreement between Athena and Arachne for who lost the weaving contest would never be allowed to weave ever again. In this version, Arachne lost and Athena took pity on her and turned her into a spider so she could still weave with her webs.

Rick Riordan’s version of Arachne

The Story of Medusa 🐍

So Mr Kichan told me to publish something that I like in WordPress and welp, i’m a big mythology geek. So today, i’ll be telling my version of the Greek myth Medusa.

Art by Irrenhorrors on Devianart

”In the middle is the Gorgon Medusa, an enormous monster about whom snaky locks twist their hissing mouths; her eyes stare malevolently, and under the base of her chin the tail-ends of serpents have tied knots.”

– Virgilius Maro

Who is She? 🐍

Medusa means “guardian” or “protectress”. She is a monster, a Gorgon, generally described as a human female with living venomous snakes in place of hair. Those who gazed upon her face would turn to stone.

Medusa.
Art by unknown.

How she was cursed 🐍

Medusa was known as the most beautiful mortal who lived in Athens. She was born with a beautiful face. Ovid especially praised the glory of her hair, “the most beautiful of her charms.”

She worked as a maiden in Athena’s temple when one day, the great sea god, Poseidon visited the temple. Poseidon seems to have been seduced by Medusa’s charms. For once, he couldn’t resist the temptation and impregnated Medusa in the temple of Athena.

Enraged, the virgin goddess Athena transformed Medusa’s enchanting hair into a coil of serpents for the desecration of her temple, turning the once beautiful mortal into a hideous monster.

Athena cursing Medusa.

The legend of Perseus 🐍

As Perseus was the son of Zeus, he was aided by the gods to hunt down Medusa. Perseus received the Cap of Invisibility from Hades, a pair of winged shoes from Hermes, a reflective bronze shield from Athena and a sword from Hephaestus. With these divine gifts, Perseus sought out Medusa and decapitated her with the bronze shield while she was asleep.

Persus hunting Medusa.
Art by unknown.

When the blood dripped from Medusa’s head onto the plains of Libya, each drop of blood transformed into venomous serpents. Perseus then returned his magical loans and gave Medusa’s head as a votive gift to Athena, who set it on Zeus’ shield (which she carried), as the Gorgoneion.

Athena and her shield
Art by unknown

Medusa’s Children 🐍

For Medusa was pregnant at the time of her death, when Perseus severed her head, her two unborn children, Chrysaor and Pegasus, suddenly sprang from her neck.

The Gorgons were awoken by the noise and did their best to avenge the death of her sister, but they could neither see nor catch Perseus, for he was wearing Hades’ Cap of Invisibility and Hermes’ winged shoes. So, they went back to their secluded abode to mourn Medusa.

Pindar, a great Ancient Greek poet, says that upon hearing their gloomy lament, Athena was so touched that she modeled after it the mournful music of the double pipe, the aulos.

Pegasus. Art by Fortunino Matania.

Thanks for reading!! 🐍

Picture from the show Gods School

e-journal 5: saa, kakegurui mashou? 🃏🎰💸

Ignorance gives one a large range of probabilities.

– George Eliot
Source: Kakegurui
As a thrill junkie, I absolutely adore taking risks. That feeling of dread, your heart beating so fast that you can hear it drumming in your ear. Well, if you’re like me and Jabami Yumeko, you’d surely love this topic. Today, i’m here to discuss sets and probability. Enjoy!
Okay. So, before going to the fun part– probability, we’re going to discuss sets first. We need to understand sets first before going to probability to get a better view on the topic. *Title means “nowwww, let’s gamble, shall we? from the anime Kakegurui ♥️

In practical life, we are compelled to follow what is most probable; in speculative thought we are compelled to follow truth.

– Baruch Spinoza
Source: Kakegurui

𝑺𝒐 𝒘𝒉𝒂𝒕 𝒂𝒓𝒆 𝒔𝒆𝒕𝒔?

A set is a group / collection of data. Each data in a set is called a member / element of the set. Ex: the set of all weebs in the world, the set of all apples on a tree, and the set of all numbers between 0 and 100.

When the elements of a set are listed, it is customary to enclose the list in curly brackets. For example, set N, all natural numbers between and including 5 to 10. Written as: K = {5,6,7,8,9,10}. Some of the common symbols used in sets:

source: https://www.kullabs.com/classes/subjects/units/lessons/notes/note-detail/2312

This is what it looks like when drawn in a Venn Diagram:

source: https://www.researchgate.net/figure/A-Venn-diagram-of-unions-and-intersections-for-two-sets-A-and-B-and-their-complements_fig1_3324531

A few terminology:

Source: http://subsurfwiki.org/wiki/Words_of_estimative_probability

For every action, there’s an infinity of outcomes. Countless trillions are possible, many milliards are likely, millions might be considered probable, several occur as possibilities to us as observers- and one comes true.

– China Miéville


Now, finally!! To the fun part- 𝑷𝒓𝒐𝒃𝒂𝒃𝒊𝒍𝒊𝒕𝒚!

Source: Kakegurui

Probability is: the chance for something to happen. Formula:

Source: wiki how
Example: in a classroom of 24 students, 10 students watches Attack on Titan. The probability in this case is 5/12. This is because the total possible outcome is 24, since there are 24 space samples and 10 favorable outcomes. Simplify 10/24 = 5/12

The concept of randomness and coincidence will be obsolete when people can finally define a formulation of patterned interaction between all things within the universe.

– Toba Beta
Source: Kakegurui

𝑻𝒓𝒆𝒆 𝑫𝒊𝒂𝒈𝒓𝒂𝒎 🌳

In probability, tree diagrams may be used to represent a probability space. Tree diagrams may represent a series of independent events or conditional probabilities (will be explained later). Each node on the diagram represents an event and is associated with the probability of that event happening.

I believe that we do not know anything for certain, but everything probably.

– Christiaan Huygens
Source: Kakegurui

Independent Event

Independent events are probability whose chances don’t change, whose chances stays the same. For example:
Source: https://www.onlinemathlearning.com/tree-diagram.html
Like in the example above, the chance of getting Head 3 times is 1/8 because 1/2 x 1/2 x 1/2. The probabilities for every coin being tossed is always 1/2.

All statistics have outliers.

– Nenia Campbell
Source: Kakegurui

Conditional Probability

Probability of an event (A), given that another (B) has already occurred. Below is a formula to find the conditional probability of something:
Source: https://medium.com/@mithunmanohar/machine-learning-101-what-the-is-a-conditional-probability-f0f9a9ec6cda
Below is an example of a conditional probability question and how to solve it:
Source: https://m.youtube.com/watch?v=hR0fQ31-3lg

The theory of probability is the only mathematical tool available to help map the unknown and the uncontrollable. It is fortunate that this tool, while tricky, is extraordinarily powerful and convenient.

– Benoit Mandelbrot
Source: Kakegurui

Real Life Application of Probability

1. Insurance Companies 🏥 💉

Probability helps in analyzing the best plan of insurance which suits you and your family the most. For example, you are an active smoker, and chances of getting lungs disease are higher in you. So, instead of choosing an insurance scheme for your vehicle or house, you may go for your health insurance first, because the chance of your getting sick are higher.

Source: Shigatsu Wa Kimi No Uso

2. Lottery Tickets 🎫 🎟

In a typical Lottery game, each player chooses six distinct numbers from a particular range. If all the six numbers on a ticket match with that of the winning lottery ticket, the ticket holder is a Jackpot winner- regardless of the order of the numbers. The probability of this happening is 1 out of 10 lakh.

Source: https://gifer.com/en/7Emi


3. Gambling 🎰💸

Pretty much self explanatory. For example, when playing cards. There is a probability of getting a desired card when we randomly pick one out of 52. For example, the probability of picking up an ace in a 52 deck of cards is 4/52; since there are 4 aces in the deck. The odds of picking up any other card is therefore 52/52 – 4/52 = 48/52.

Source: Kakegurui

Take the probability of loss times the amount of possible loss from the probability of gain times the amount of possible gain. That is what we’re trying to do. It’s imperfect, but that’s what it’s all about.

– Warren Buffett


Thank You For Reading!!

Have A Great Day!!


e-journal 4: 📊📈 𝑵𝒆𝒆𝒅 𝑴𝒐𝒓𝒆 𝑫𝒂𝒕𝒂?

– ̗̀ Welcome to my blog! Today I’m gonna explain about Data Statistics. Enjoy! 👩🏻‍🏫 ̖́-

Image Source: starsandaspirations tumblr

📊

Sta•tis•tics

[stuh-tis-tiks], n,

1. The only science where two recognized experts, using exactly the same set of data, may come to completely opposite conclusions.

https://funnyjunk.com/funny_pictures/4613599/Statistics+about+statistics/

𝑷𝒖𝒓𝒑𝒐𝒔𝒆 𝒐𝒇 𝑩𝒐𝒙 𝒂𝒏𝒅 𝑾𝒉𝒊𝒔𝒌𝒆𝒓𝒔 𝑮𝒓𝒂𝒑𝒉 📦 🐈

It is often used in explanatory data analysis. This type of graph is used to show the shape of the distribution, its central value, and its variability. In a box and whisper plot, the ends of the box are the upper and lower quartiles, so the box spans the interquartile range.

“𝑺𝒕𝒂𝒕𝒊𝒔𝒕𝒊𝒄𝒔 𝒂𝒓𝒆 𝒏𝒐 𝒔𝒖𝒃𝒔𝒕𝒊𝒕𝒖𝒕𝒆 𝒇𝒐𝒓 𝒋𝒖𝒅𝒈𝒆𝒎𝒆𝒏𝒕” -𝑯𝒆𝒏𝒓𝒚 𝑪𝒍𝒂𝒚

Image Source: starsandaspirations tumblr

𝑯𝒐𝒘 𝒕𝒐 𝒖𝒔𝒆 𝒕𝒉𝒆 𝑺𝒄𝒊𝒆𝒏𝒕𝒊𝒇𝒊𝒄 𝑪𝒂𝒍𝒄𝒖𝒍𝒂𝒕𝒐𝒓 📱

To find the a and b (for the equation of regression line, y=a+bx) and the r (correlation),
To find the n (amount of data), standard deviation of x and y, mean x and mean y,
Image Source: starsandaspirations tumblr and https://memegenerator.net/instance/68545174/confused-jack-sparrow-your-face-when-you-try-to-understand-statistics

📉 𝑬𝒒𝒖𝒂𝒕𝒊𝒐𝒏 𝒐𝒇 𝑹𝒆𝒈𝒓𝒆𝒔𝒔𝒊𝒐𝒏 𝑳𝒊𝒏𝒆

y = A + Bx

A is y-intercept while B is the gradient / slope. This equation is similar to the equation y = mx + b. X is the explanatory variable and Y is the dependent variable.

“𝑴𝒂𝒕𝒖𝒓𝒊𝒕𝒚 𝒊𝒔 𝒕𝒉𝒆 𝒄𝒂𝒑𝒂𝒄𝒊𝒕𝒚 𝒕𝒐 𝒆𝒏𝒅𝒖𝒓𝒆 𝒖𝒏𝒄𝒆𝒓𝒕𝒂𝒊𝒏𝒕𝒚”

𝑱𝒐𝒉𝒏 𝑭𝒊𝒏𝒍𝒆𝒚

Image Source: starsandaspirations tumblr

𝑹𝒆𝒂𝒍 𝑳𝒊𝒇𝒆 𝑨𝒑𝒑𝒍𝒊𝒄𝒂𝒕𝒊𝒐𝒏 🌃💸

“𝑰𝒇 𝒚𝒐𝒖 𝒏𝒆𝒆𝒅 𝒔𝒕𝒂𝒕𝒊𝒔𝒕𝒊𝒄𝒔 𝒕𝒐 𝒑𝒓𝒐𝒗𝒆 𝒊𝒕, 𝒊𝒕 𝒑𝒓𝒐𝒃𝒂𝒃𝒍𝒚 𝒊𝒔𝒏’𝒕 𝒕𝒓𝒖𝒆” 𝑩𝒂𝒓𝒃𝒂𝒓𝒂 𝑫𝒐𝒚𝒍𝒆

Example 1: 🌨 Weather Forecasting ⛅️

We all watch the weather forecast. Have you ever thought on how they get that information? Some computer models build on statistical concepts. These computers compare prior weather forecasts with the current weather and predict the future weather.
https://memegenerator.net/instance/56888925/confused-baby-1-so-youre-telling-me-i-need-statistics

Example 2: 💉 Medicine 💊

Statistics play a big role in the medical field. Before any drugs are prescribed, scientists must show a statistically valid rate of effectiveness.
https://imgflip.com/i/1134k0 https://www.google.co.id/url?sa=i&source=web&cd=&ved=2ahUKEwinx4XDkvHjAhXMfX0KHQ8nBE8QjB16BAgBEAM&url=https%3A%2F%2Fmemebase.cheezburger.com%2Fgraphjam%2Ftag%2Foranges&psig=AOvVaw3E1B9vaUrhVl85H8Vyja0P&ust=1565280515284809

𝑻𝒉𝒂𝒏𝒌𝒔 𝒇𝒐𝒓 𝒓𝒆𝒂𝒅𝒊𝒏𝒈! 𝑯𝒂𝒗𝒆 𝒂 𝒏𝒊𝒄𝒆 𝒅𝒂𝒚! 𝑼𝒘𝑼

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