“Math is the only place where truth and beauty mean the same thing.” -Danica McKellar

Hello! Welcome back to my blog! Today, much like the rest of the world, school for me has been operating through online means. So that is what this blog is going to be revolved around today; Distance Learning. In this blog, I’ll be explaining how my IGCSE subjects, in general, has integrated into distance learning.

IGCSE Mathematics, English First Language and Biology

The reason why I compiled these three of my IGCSE subjects altogether is due to the fact that the teaching methods have all been quite similar.

For these subjects, we have been learning through Zoom, where our teachers have been making good use of the ‘sharing screen’ option. From this, my class and I have been able to continue our classes as normal as possible. In Mathematics, we have actually started learning basic IB Maths since after Year 10, my school offers the IBDP.

Moreover, we also made use of google classroom and google forms. We were given quizzes on google forms and got enlisted our assignments through google classroom. It was more or less the same for all the other subjects.

In English, we had Zoom calls in which we were all able to discuss through our answers from work assigned to us beforehand, asked questions and listened to discussions with our teacher. A lot of teamwork was necessary in order to ensure that our Zoom calls went on without a hitch as network connections, audio and timings were not always on our side.

IGCSE Chemistry, English Literature and Bahasa Indonesia

Moving on to another 3 of my IGCSE subject choices, these three has had the most assignments based on essays or research.

For Chemistry and English Lit, my teachers hosted Zoom calls to ensure that we all had understand perfectly regarding our tasks assigned and when our assignments were due. Google classroom was also our other source of communication; it was where we submitted our tasks and where our tasks were also assigned.

For Bahasa, so far, we have yet to have a Zoom call. However, our workload was also filled in this subject by submission of essays in various types; descriptive, narrative and persuasive. The work assigned to us for Bahasa through google classroom is enlisted the morning before classes and since all my Bahasa period has ended for this week there are no more submissions as they have already been done and submitted.

IGCSE Economics, Business Studies and Chinese Second Language

And the final three IGCSE subjects I take are these three. These three have a lot in common in terms of how my subject teachers have chosen their teaching methods to be able to accommodate distance learning.

Economics and Business both apply similar teaching methods. For example, we occasionally have a Zoom call either to discuss answers or a topic. However, most of our work has been done through Khan Academy and Kahoot. Our teachers assign us quizzes through both these sites and we answer them. Suffice to say, I actually enjoy quizzes this way because the explanations are simple and easy to grasp from Khan Academy and they provide ample amount of resources to help understand each topic.

As for Chinese, we have been doing past papers and Zoom calls to practice our speaking skills.

The upside of Distance Learning

In conclusion, despite the struggles and complications distance learning has brought into our lives as teaching methods have become harder to do so online, I think that this distance learning revolves heavily around an individual’s own time management and responsibility.

Being at home everyday for the past 3 weeks means that the things I get done each day regardless of a submission date revolves around my productivity. This is actually a good experience for me to learn in preparation for the IBDP and University; where my productivity and time management will determine my level of success in both programs.

Despite the pandemic and IGCSE Summer 2020 exams being cancelled, I do believe that everything happens for the reason. I trust Cambridge’s decision in cancelling the exams because of the great threat posed with the numerous number of students and invigilators gathered in order to conduct the exams. I can’t say I wish to partake in the Fall exams; because I would already be in the IBDP by then.

I know it’s not easy to look on the bright side, but during this pandemic, I want to list the things I am grateful for. I’m grateful for our medics, delivery systems such as Gojek that has helped tremendously with keeping our food and necessities stocked at home in attempts to stay safe and healthy in order to reduce contractions of the virus, I also am grateful for the many relentless sources of aid and help shown by humanity.

I hope we all learn something from this. And that we will come out of this. Stay safe and healthy everyone. Thank you for reading my blogs all this time.

“Mathematics rightly viewed possesses not only truth, but supreme beauty.” -Bertrand Russell

Hi! Welcome back to my blog, it’s been a minute since I last published another post. Today I’ll be talking about my second Mathematics Olympiad I have participated in; SISMO. This Olympiad is partly more special than my first experience which was WMI the preliminary round.

SISMO was a highlight for me because it was the first time I was able to score a medal in something Mathematics related. Maths is not my forte, but I do alright in it I guess you could say–so when my name was on the screen for Bronze Medalists I was thoroughly shocked and pleased! The SISMO team really outdid themselves because the entire atmosphere of the competition was friendly and warm; here’s how it went.

REGISTRATIONS

Registrations started around 7am and after registering myself and receiving a pin with my name and my level (Intermediate), I was ushered into the exam room.

24 Card Game

The first thing we did when the competition started was play an ice-breaker card game called 24. I think the purpose of the game was to lighten up the atmosphere and calm our nerves before doing the tests because it certainly succeeded in doing so.

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The game basically revolved around having 4 random cards displayed in front of you and having to figure out how to get the number 24 from the selection of cards. You are free to subtract, multiply, add and even divide the cards with one another as long as you use all the cards in order to obtain the number 24.

Those who won got to do a lucky draw; whichever red envelope they pick from a box with their eyes closed has a range of 5k-100k. Sadly, majority got 5-10k hahahaha. Since I did not win the 24 game in my table I did not have a chance to do the lucky draw however it was extremely fun to witness the reactions of those who won.

Round 1

SISMO consisted of 2 rounds- 1 and 2. Round 1 was an MCQ test. We had a total of an hour to complete the test. I think that was more than enough time to complete the test because I actually happened to have a lot of extra time.

Round 2

After a short 15 minute break post round 1, round 2 had begin. This time the test was not an MCQ test; you had to work out the answer on your own. Round 2 was definitely more stressful than the first round because we had to come up with an answer rather than just guess and pick a random letter. We were given yet another hour to complete the test.

Despite the challenges, I do not remember round 2 to be so brutal. I think that the most important thing to remember when conducting these tests is to stay calm. Take a deep breathe and rationalize your thoughts.

Kahoot And Lightning Round

After Round 2 had ended, it was time for lunch then followed by a Kahoot round! Here, all the candidates and even teachers played an online kahoot to further test our mathematics capability on a wider scale. I had fun doing this because my friends and I were able to debate which answers were the right one and why they were not.

Later on, once the Kahoot had ended, the Lightning tiebreaker round had begin. Those who were in the Top 3 with nearly similar scores competed for 1st place. As part of the audience, it was fun for me to watch geniuses calculate mentally in 5 seconds before hitting the buzzer and saying the answer. It then became remorseful when I saw their frustration upon being unable to answer it as it was such a shame, sometimes their answers were wrong by a difference only.

As the lightning round came to a close, SISKG’s Halakatas dancers graced the stage with a lovely performance that captivated the audience. They simply never disappoint.

Awarding Ceremony

Ah finally, the most awaited for moment; the awarding ceremony. Here I was incredibly astonished because I actually won bronze.

It’s true what they say, you never know until you try so do not be afraid to try! Would I do it again next time? Why not!

IB Learner Profile

Open-minded

SISMO taught me to be more open-minded because you simply do not know the result of your efforts until you finally try. By being open-minded, I was able to adapt better to my situation at hand regardless of being a newbie at math olympiads.

Thinkers

This particular learner profile was heavily used by me during SISMO because I analyzed the questions and methods of answering them. I had to keep both an open-mind yet in touch with my logic. Especially in round 2, you must be able to thoroughly think through the question and what it is asking and how to answer it.

Knowledgeable

From SISMO, I indeed became more knowledgeable regarding my capabilities and mathematics. It was surely an event I am forever grateful to have partaken in. Nothing and nobody else is a better teacher than experience.

Reflective

This learner profile was heavily used by me during SISMO due to the fact that I reflected on my answers, why I answered the way I did and how I did so. By being reflective, I pondered more in depth regarding the question and method of answering it.

Risk–takers

I think that this particular learner profile is heavily significant because I took a lot of risks with my answers. I trusted my gut and answered what I best believed was the right one. After all, if you do not take risks how will you ever know the outcome?

Well that’s all today. Thanks for keeping up with me in my blog and see ya on the next one!

Unforgettable moment in IGCSE Math

My unforgettable moment in IGCSE Math so far would have to be upon the discovery that my batch was the glorious batch who was lucky to be the batch that got the new syllabus. No doubt, this moment was a show stopper because my entire grade did not expect this to occur. Regardless, what is math without its challenges?

#IGCSEMATHS2020 #FIRSTBATCH

“Math may not teach us to add love or subtract hate, but it gives us hope that every problem has a solution.” -Anon

In my Final Entry 2 blog post, I’ll be discussing some of the most abstract and mind-bonkering mathematical techniques, questions and methods that hopefully make you feel hope upon reading it because you gained new knowledge! I’m also going to wrap around my IGCSE experience so far, for the past 1.5 years.

This blog post is actually my ‘semester assignment’. Each year, for every subject I take I am required to submit a final project at the end of each semester which accumulates my knowledge of understanding regarding the subjects’ lessons. For maths, I’m required to submit a blog regarding 3 different investigations; A, B and C. So without further ado, welcome to my almost final entry.

INVESTIGATION A – HIT THE RUNWAY

For the first investigation, we were instructed to land our ‘planes’ safely back on ground with a linear equation.

Here, my task was to safely ‘land’ my plane back to the ground. The red line showcased my plane landing safely on the ground. The equation on the left side of the picture is the equation of the red line.

Next, we were assigned to be able to ‘move’ our plane. Everyone in my class were each paired with a JC1 (Grade 11) Maths AAHL student who was to help us add more life to our plane. My partner, taught me how to circle my plane first before finally landing because sometimes we aren’t sure if the conditions on the ground are safe or already suitable enough to land on.

Tadaaaaaaaa

INVESTIGATION B – KOCH’S SNOWFLAKE

Moving on to the next investigation, this investigation is about developing and enhancing one’s inquiry skills with Koch’s snowflake.

First, it is stated that the length of each side of the original triangle is at 81cm.

In order to get the perimeter of stage 0, 81 x 3 = 243cm, because each side has a length of 81 and perimeter is the accumulation of all the sides of a shape. Now we want to find the area of stage 0. A formula we can use to get the area of a triangle is 1/2 ab sin c. So 1/2 x 81 x 81 x sin 60 = 2840.99 which is equivalent to 2891. So the area of stage 0 is 2891cm^2.

Next we have stage 1. In Stage 1, 3 smaller equilateral triangles are added on each side of the original triangle from stage 0.

Now, in order to get the area of stage 1 and by using the same formula to get the area of the shape at stage 0;

Stage 3.

Stage 4

Okay so I realized I wrote Stage 2 as Stage 3 and Stage 3 as Stage 4 my bad hehe. Moving on to,,

INVESTIGATION C – SIERPINSKI’S TRIANGLE

1. This is what my iteration looked like.

2. Tadaaaa

3. The patterns emerging from my table is that they are all multiples of the first answer in stage 1. 4 and 8 are multiples of 2, 16 and 64 are multiples of 4.

To talk in patterns,

• number of green triangles in each side = 3n^2
• length of one side of green triangle = (1/2)^n
• area of each green triangle = (1/4)^n

4. These patterns have in common similar denominators which can all be divided by the denominator from the previous pattern’s.

5. Based on my results, if I were to continue stage 4 , 5 and 6, I would integrate the use of the formula above to easily answer them. For example, the number of green triangles in stage 4 would be 3 to the power of 4 which is equivalent to 81, stage 5 a total of 243 triangles from 3 to the power of 5 and stage 6 would have 729 triangles. Once a pattern is understood and the formula is obtained, all one simply does is integrate ‘n’ with the actual number.

6. How would I compare the sets of number obtained?

I would compare the sets of numbers obtained by referring to the patterns present among each stage and why the relation is there.

IB LEARNER PROFILE

Reflective – This blog post got me reflecting on my past math blogs and how far I made it. Regardless of the still long way I have to go, once in a while it is healthy to look back on the progress you’ve made.

Open-minded – I’ll be honest, when I first saw the booklet outlining our semester assignment, I was horrified. But as I got to it and started doing it, I realize how keeping an open mind is truly important. Simply because if I hadn’t I would have stressed myself even more by limiting the extents of a question and its solutions.

Inquirers – I feel like this ib learner profile in general sounds typical, however I promise this one has the most significant impact and is a sole reason why I was able to accomplish this ejournal. I cannot stress how important it is to ASK QUESTIONS if you do not understand. I asked for guidance to my MAAHL partner and got the job done. Without asking, I’d be in tears and unfinished by now.

With that said, cheers to 6 more months left in this IGCSE journey of mine. Best of luck to y’all out there! Remember, ask for help if you need it; your teachers are there for a reason! Ciao!!

BIBLIOGRAPHY

“Transformation is a process, and as life happens there are tons of ups and downs. It’s a journey of discovery – there are moments on mountaintops and moments in deep valleys of despair.” – Rick Warren // where the transformation from a mountaintop to valley coexists with a matrix 😉

Hi hi! Welcome back to another Maths blog post after the Bali one. It’s been a heavy and rushed couple weeks; chasing deadlines and exams are fast approaching vRoOooomM.

Anyways, in today’s blog I’ll be discussing Transformation and Matrices.

There are many ways to transform a shape. Whether it be by reflection, rotation, translation or enlargement, the shape is transformed from its original one to a new one. First, let’s get into reflection.

Reflection is basically the exact same shape just reflected off the original one. Like when you stand in front of your friend and when your friend lifts her left hand, you lift your right in order to ‘reflect’ your friend’s left hand from your perspective.

In Maths however, this is how you apply reflection.

Tadaaaa. That’s how easy reflection is.

Moving on, we have Rotation.

Rotation is the rotating of a shape by an angle in the direction of either clockwise or anticlockwise, following a centre of rotation. I promise it’s easier than it sounds.

See! Rotation is quite simple now isn’t it? The bird in the animation first starts rotating 90degrees clockwise, then goes on in a full 360 rotation around the bed! The rotation occurs at a centre of (0,0) because as the bird rotates, it’s body position doesn’t move, it only rotates.

Whoever said notes are important seriously knew what they’re talking about.

Next we have Translation. Translation’s basically moving. The shape is moved in the form of column vectors (x,y). X represents how many units the original shape has moved whether it be towards the left or right. If it’s to the left, the X would be represented with a negative sign (-). But if it’s to the right, it’ll be positive. The same concept exists for Y however, the only difference is that negative (-) means going down and positive (+) means going up.

Lots of words there so here’s a picture to simplify what I just explained.

I LOVE my notes guys honestly. My notes are my holy grail everything written in all my Ejournals comes from my notes.

Last but not least, Enlargement. This in my opinion is quite tricky because just like everything else in transformation, the accuracy of points from the shape plotted are very very important.

Enlargement is kinda pretty much resizing the shape whether making it bigger or smaller. The enlargement takes place by a scale factor, with accordance to a centre point of (x,y).

It gets even funner! Because enlargement occurs even through inversion. Basically same concept except that the scale factor has a negative sign (-) in front of it.

Matrices

Matrices are a set of numbers arranged rectangularly. We can add, subtract and multiply matrices with one another. Matrices simply cannot be divided. But not to worry, division takes place in the form of Inverse Matrices.

Before we straightaway get into Inverse Matrices, let’s dive into the common rule for matrices.

In some of my notes presented earlier throughout this blog, some matrices were present. That’s because matrices and transformations coexist. You can determine the matrix of the shape from it’s translation.

When matrices are added or subtracted with one another, normal addition and subtraction takes place.

However, when it comes to multiplying matrices, a row x column concept occurs. Basically we multiply the 1st row of the first matrix by the 1st column of the second matrix.

Inverse matrix is a little different with multiplying matrices.

First, let’s establish how to calculate the inverse of a matrix.

Next, how to multiply matrix by inverse, where I = identity of the matrix.

Real-Life Applications

Real-life application of matrices are used everywhere in our daily lives. Graphic softwares such as Adobe Photoshop integrates the uses of matrices into their system allowing them to be able alter images, hence the name ‘photoshop’.

A cool thing about how matrices are used is that they are part of the software automation system for robots. A basic, key element for robot movements are actually matrices!!

Transformations occur more often in our lives than you may think. When we look at the mirror, or when cars take a turn from one lane to another, or even when the wheels on one’s car rolls round and round each time the car moves. Transformation is everywhere around us even if you don’t realize it.

IB Learner Profile

The IB Learner Profiles I learned throughout these two topics were Thinkers and Reflective.

Thinkers because these two topics required a lot of thinking and even when you think you understand the question, you still gotta think and be able to construct your working and answer carefully.

Reflective due to the fact that each time regardless whether or not I got the answer to the question, I looked back and paid attention to my working and how I was able to answer it or if I wasn’t, went back to the question and thought real hard about it.

Nevertheless, whether it be Maths or another subject, you should always think and if you have the extra time, reflect about your answers. Goodluck!

“We didn’t realize we were making memories, we just knew we were having fun” -Anon

Welcome back to my blog! This blog going to be about my grade’s learning journey to Tabanan, Bali. Here, our goal was to be able to give back to the community and enrich our knowledge of the real world; away from a classroom.

Day 1

We arrived in Bali at 10.30 am local time, grabbed ahold of our luggage and immediately headed for our Resort, UmaDhatu. We reached 2 hours later. Upon arrival, we were greeted with the staff and then welcomed into our villas. Me and 3 of my friends got to call Villa A7 our home for the next 4 days. But before this, we experienced an attack with all things insect and mosquitoes in our former villas and even after BayGon-ing the life out of our villa, the insects still wouldn’t quit so we requested a change and thankfully we got it!

Afterwards, we got lunch in Braja Village and continued our activities there, which consisted of sign making.

This activity was to make signs for the villagers living in Braja. They wish for their village to be a tourist area in order to prevent their kids from wanting to constantly leave the village when they reach their teen years. As of now, the only ones living in the village are the elderly and young children. All teens have left the village.

When the clock striked 6 pm, we headed back to our villas after another delightful meal. As I’m currently writing another entry in this blog of mine, I’m in my villa in one of the rooms with my friends talking, relaxing, sharing snacks and unwinding after an eventful and tiring day.

Oh, and there’s my friend doing a face mask because according to her “Skincare is always a must.”

Day 2

A day in the life of a Sesandan Villager

Second day in Bali and our morning started out incredibly eventful; breakfast at 730 and off to Braja Village again afterwards. There, the girls and the boys were separated for different tasks. The boys were assigned to put up the signs we made yesterday and the girls to plant a sacred plant 🌱 of the entire district in Sesandan.

We all then met up in a traditional shop called Warung. We cooled ourselves with some vanilla ice cream mochi and then went back to Braja for lunch. However, this journey back was super long and tiring. We circled the entire village and towards the end, a few of my friends and I gave up walking and hopped into one of the cars instead which when asked, the tour leader admitted that the cars were provided for us to use but they enjoyed teasing us so much that they did not tell us till after that the cars were up for our use.

After lunch, we split ourselves into groups of 7 or 6 and got cooking!! We cooked Ayam Betutu; a traditional delicious delicacy of Bali’s.

Our food actually turned out surprisingly okay. The boys in our group did most of the work because surprise, surprise majority of the girls didn’t know how to chop the ingredients and the guys proved themselves worthy of the job because they had experience helping their parents cook at home.

The highlight of today was after we enjoyed our dinner which we all cooked ourselves (even when our chicken lacked salt but it was alright as we added more salt) and went swimming in our resort. We all had such a blast and were able to relax after another tiring but productive day.

Day 3  

Day 3 and it started out a little rough – my villa mates and I got left behind everybody else. They all had left for Braja and we were still in our villa; each preoccupied with preparing our bags for the day.

When we finally realized, we called and a car was sent to pick us up. Thankfully, it was a short ride away. We then ventured further into Sesandan. Our destination this time was their glorious waterfall. After a 30minute trek, we finally arrived.

I don’t remember how long we were there for because we had so much fun laughing and venturing into the waters. But I do remember the STRUGGLES of arriving in this waterfall. The roads were so steep and rocky. Smart me decided to wear slides instead of my shoes because waterfalls, shoes and socks did not add up in any equation.

After a coconut refreshment, we bid our goodbyes to Braja and it’s wonderful people who cared for us like their own that afternoon after another delicious lunch and headed towards Bali Selfie Spot and Swing, Sesandan.

The swing is honestly super instragammable AND fun!! We spent about 2-3 hours here simply due to the fact that everyone wanted a turn on the swing and we were also served refreshments.

When we finally arrived back in our villas, we did some exciting recycling!! Go green💚💚. With the help of my teammates I created a piggy bank out of recycled plastic bottles. Hehehe for someone like me who has no artistic talent at all, I was proud of what I did.

Okay so that’s day 3, now off to bed as we have another long day tomorrow and I suffered a horrible sore throat today. Regardless, it still did not keep me from talking or attempting to talk all day. Good night!

Day 4

Here’s to reaching the last full day in our trip here in Bali. Today has to be one of the most tiring days; endless activities and the excitement of the last day pushing through.

For starters, we left our villas at 830am on the dot and headed for a local school where we would be teaching grades 1-6. My group got to teach grade 2 and they were honestly such a cute batch due to their adorable shyness and major interest in learning.

We taught them how to introduce themselves and how to say “Aku suka main…” in English. The term “Aku suka main..” means “I like to play…” in English.  When they made progress, my team and I decided to teach them the 5 W’s. When we got to ‘Who’, they pronounced it ‘Ho’. Suffice to say, we were horrified and corrected them immediately. I was quite disappointed because my throat still was sore and teaching the kids was a complication with my hoarse voice:(

Next, we stopped by a traditional house where we learned how to make traditional balinese offerings.

Afterwards, we ventured off into a rice field where we learned how to plant rice and even got a chance to sit on the back of the cows whilst they plowed the field. Because I was scared of possibly falling into the ground, I skipped plowing but did the planting.

◦ Here’s an example of planting and plowing.

Afterwards, we tasted fresh coconuts plucked from the tree right in front of us. Then, it was finally time for lunch ❤️. Lunch was a traditional balinese one which tasted wonderful.

Sometime later after our hearty meal, we arrived in Desa Timpag; an owl breeding project. We spent about half an hour there before being whisked away to an orphanage; SOS Children’s Village Bali.

There, some students from my grade performed songs and dances. Towards the end, we presented our gifts for them: school supplies and our recycled art work. My piggybank got chosen by a sweet little girl!

I also made friends with a literal Angel. Like seriously. Her name’s Angel.

We then said our goodbyes and departed for our villas. To recognize the end of our trip and our last night here, we celebrated with a barbecue.

Day 4 was one of the highlights of the trip for me.

Day 5

Going home today:(. Bali was without a doubt, a blast. I enjoyed my time there so much leaving was sad.

To start off, we visited a Kofi Luwak Plantation. Bali is also well-known for their coffee. This coffee is adapted from the animal, Luwak. The coffee beans come from the Luwak’s poo. But don’t worry, the beans have a tough seed coat where the bacteria from the poo do not touch the beans and is still hygienic enough to be consumed.

Picture creds to my friend Hanny.

After the coffee tasting, we had lunch in Kurnia Village. To signify the end of our trip, we visited Krishna; a Bali souvenir shop. Krishna is famous in Bali for their trinkets of Balinese gifts and cuisine to bring back for friends, family and of course yourself.

Saying goodbye is always hard. Thankfully, the thought of coming back soothes the goodbye. We arrived in the airport after saying bye to Krishna and our last taste of Bali.

What did we learn?

This trip to Bali made me more aware of the different lifestyles I live and the people of Tabanan. For one, it increased my awareness of the world outside mine and led me to a state of open-mindedness where I was able to adapt and accept the differences present and be respectful of it.

Since I was sick with a horrible sore throat during the trip which led to me losing my voice for 2 days, the importance of my health in all ways mental, physical and emotional became more evidently valuable to me. This understanding of how I need to balance my well-being together along with having fun taught me to be responsible of myself because no one else takes care of me but me.

Next, being able to communicate with the locals and expand my knowledge on their way of life and respecting it broadened my communication and knowledge. I also learned how to think quickly on how to fix a problem and face it during the trip. We had moments of unsureness where even the guide couldn’t help much because it was an activity where we had to learn on our own how to do. So this trip heightened my thinking.

I loved the visit to the orphanage. Even if I didn’t take part in any performance, I was able to interact with the kids and loved every moment of it. Those kids taught me to care better towards those around me.

Moreover, this trip taught me my strengths and weaknesses. It taught me how to know better and not put myself in unwanted situations. I became reflective of my actions and responses to the situation thrown in front of me to solve.

Real-life application of Maths in Bali

During the second day, most of us if not us all went swimming in our resort. There, we rode the slides and even jumped off the cliff!! The slide was incredibly bumpy; a ridiculous curve of  50degrees. I nearly flew off the slide and landed ungracefully with a slight bang. Me and my friends nearly drowned when we whooshed into the water because the force of gravity was so strong 😂.

Even the cliff, was so scary when standing on top. It was a literal 90degrees!!! However, it was still worth the experience.

Next, when we were separated into groups by gender: boys and girls because the activities scheduled were different. This is a real-life application of sets and venn diagrams. The universal set consisted of us all 33 students. However, we were all separated into two groups; girls and boys. The only element both groups had in common was Carl. Him, being a boy was obviously in the boys’ group. However due to his injury, he joined the girls’ activities.

The most obvious real-life application of Maths in our Bali trip was counting of money, of course, Almost everyday we went to Indomaret which was our only source of supplies.  We also had to estimate exactly how much 1Litre bottles of water we would use up in a night to cook PopMie (instant noodles of an Indonesian brand) because my villa became the ultimate hub for boiling water and making your Popmie.

Maths is truly all around us. You can’t deny it so might as well embrace it.

To Bali and the memories it’ll forever hold. Thanks for reading my super long blog. See you on the next one.

👋🏻

Probability, Sets and Venn Diagrams — what a nice set! When put altogether, these three form quite the formidable combo, don’t they? After all, “A reasonable probability is the only certainty.” -E.W. Howe. And that only certainty is the set of life, love and balance intersecting with each other.

I don’t know about you, but when these chapters were first introduced, I wasn’t too keen on them. However, as I analyzed the questions, workings and practiced, it became clear to me that logic, for the most part, played a crucial role in these chapters.

Sets And Venn Diagrams

To start off, sets refer to the set or group of items or subjects. In order to master this chapter, one must remember the key terms.

Universal set refers to the Venn Diagram as a whole. But when translated into the language of sets, this is called ‘Set Builder Notation’. It is the elements inside the venn diagram(s). An example of a set builder notation is showed above. To grasp an easier understanding, Union is whether or not they have the same elements or not, everything is included even the elements outside. Intersection, on the other hand, is only for common elements. Don’t stress, just breathe in breathe out and you’ll get it.

Real-Life Application Of Sets And Venn Diagrams

I easily compare Sets and Venn Diagrams to would be when considering what next item I want to buy. To simplify, I’ll be using brand names so if you’re part of any brands mentioned please don’t copyright me I adore and am a repeat customer of your brand :).

Let’s talk shoes. For example, you have the latest pair of Nike Vapormax, Jordans and Cortez. You also have the 2018 edition of Presto, AirForce1 and both 2018 and 19 editions of AirMax. You want to buy a pair of Nike Huaraches next. So an example of the venn diagram showcasing the example above would be like this.

Probability

Probability is a branch of maths which analyses random experiment. The only reason I understood this chapter was because of the use of a tree diagram whenever applicable and the formulas written below:

• For Complimentary events (events excluding said element)
  • P(A’) = 1 – P(A)

• For Combined events
  • P(A U B) = P(A) + P(B) – P(A N B)

• For Conditional probability
  • P(A l B) = P(A N B)/P(B) ; where l refers to given that

• For Independent event; where if one event occurs it does no affect other event as there is no intersection between the events and is considered as ‘mutually exclusive’ as there are no intersections
  • P(C N D) = P(C) x P(D)

Remember, in probability, if there is no keyword only, then it will mean everything.

Real-Life Application Of Probability

Probability honestly is everywhere around us. What is the probability I will wake up tomorrow? The probability I will get my life together before this month ends? The possibilities are endless…..But on a more serious and educational note, here’s an example of how probability is used in real life:

Weather forecasts. Weather forecasts uses probability to predict how the weather will be tomorrow. Will it rain? Shine? Probability helps us determine which event is more likely to happen. “The probability of rain tomorrow is 75%.” Upon learning this, immediately one plans out how their day will be. The use of probability is immensely underrated in real life. When planning weddings or out-door events, the probability of whether or not it’ll be rain or shine that day plays a huge factor towards planning and catering event needs. Thus, with the use of probability, we are able to plan for the future with peace and less anxiety of rain suddenly pouring on the day itself.

More importantly, the use of probability in weather forecasts help us plan our #OOTD. It even helps us pick which shoes would be less heartbreaking to sacrifice to walk with in the rain.

Keep practicing and with continuous effort, you’ll be alright. See you on the next blog!

“Facts are stubborn things, but statistics are pliable.” – Mark Twain

Static energy occurs when two materials rub against each other, jolting electrons in their wake and transferring these electrons. In comparison, statistics are similar to static energy because statistic involves the correlation present between variables.

Statistic and Data work hand-in-hand. By using the data, statistic shows a piece of the data from a numerical data. However, unlike facts, statistics may be wrong if the data given is wrong too.

BOX OF WHISKERS

Box of whiskers is a measure of the minimum, maximum, lower quartile, upper quartile and median points from a given data. Statistics revolves all around these. We all know how to find mean, median and mode. The interquartile range, box of whiskers and percentile, however, sounds relatively new even though we’ve studied it before but never realized we did.

A box of whisker is drawn like a model. First, a number line is drawn starting from the lowest number to the highest number from the data you are given.

Then, above the number line draw a line from the minimum point, stop where the Lower Quartile is, and from there draw a box or rectangle; stopping at the Upper Quartile. Continue the line until you reach the maximum point. Draw a line in the box noting where the median is. Don’t forget to label all the important points; minimum, maximum, lower quartile, median and upper quartile.

The example above shows how a box of whiskers should be drawn and presented.

Note, Formula to obtain: (where n = number of terms)

• 1st quartile/lower quartile is the 1/4(n+1)th position of the number
• 3rd quartile/upper quartile is the 3/4(n +1)th position of the number
• median is the 1/2(n+1)th position of the number

REAL-LIFE APPLICATIONS

A real-life application of statistics and data would be social media. A minute may not seem as much now does it? But statistics show that in the time span of 60 seconds, a gazillion transactions and actions take place in social media.

Statistics come in the form of data piled altogether to show a large quantity of numerical data. The time we spend gaming, texting, updating our status or even aimlessly scrolling through social media apps all compile into a statistical data report in which how many people are doing the exact same thing at the same time all over the world in a time span of 60 seconds.

Another real-life application of statistics are cars. There are always many cars on the street. If you actually count the number of cars you see; the type of cars and their respective brands, you’d realize how simple statistics are and that it’s simply everywhere.

Statistics aren’t hard to look for; you just have to pay attention.

In the picture above, spotted are 3 buses (one in the back), 4 Toyota Alphard’s and 2 taxis. The number of cars in the street and how many of the same cars are along side one another is another example of a real-life application of statistics.

In conclusion, don’t fret about statistics, take a deep breath and calm yourself down. Know your formulas and remember how to apply it. See you on the next blog! 🙂

Hi! So I’m back with the blog during one of the most stressful times of the semester; every day is a day nearer to our final exams. I’m stressed, sleep-deprived and mentally exhausted. But it’s still no excuse to slack off. Henceforth, welcome to my current, on-going journey to achieve either an A or A* (a girl can dream, can’t she) for a two year course known as IGCSE.

Without further ado, let’s dive into my “Do’s and Don’ts” and notes which saved my life multiple times studying for a test for each of these chapters.

Chapter 1: Numbers

From sequences to proportions and approximations, there is not a single point this chapter leaves out regarding numbers. Here are my keynotes and what I learned in this chapter.

• Terminating = 0.2 (ends immediately)
• Recurring/repeating = 0.3333333333333 which can be written as 0.3 with a dot above the 3
• 0/R = 0, where R does not equal to 0
• 0/0 is undefined (does not exist)
• 1 decimal place in terms of tens = 0.1
• The values of simple and compound interest are the same after a year, year after year compounds adds on interest after interest.
• Incremental = increasing, Diminishing = decreasing
• In standard form, the whole number must always be greater than 1, and less than 10. Eg. 1.11 x 10^4
• Distance = speed x time
• Sequences

Arithmetic Sequence

• Un = U1 + ( n – 1 ) d

Where n = number of terms

d = common difference

U1 = First term

Un = N term (term we are looking for; the unknown term)

Quadratic Sequence

• The expression is, Un = an^2 + bn + c

Where c is constant,

2a = common difference ( 2nd level of differences )

3a + b = U2 – U1

a + b + c = U1

Cubic Sequence

• The expression is Un = an^3 + bn^2 + cn + d

Where 6a = common difference ( 3rd level of differences )

12a + 2b = 1st second difference in the second level of differences

7a + 3b + c = U2 – U1

a + b + c + d = U1

Sum of an Arithmetic Sequence

• Sn = n/2 [ 2(U1) + (n – 1)d ]

Numbers plays a huge role in our lives. The quantity of fruits we want to buy, the price of an item, the number of days in a week and the number of houses lined up in a single row. These are represented by numbers.

Chapter 2: Algebra

The amount of fundamental understanding required to ace this chapter sorta scared me because there truly is no escape from algebra.

• In the general quadratic formula of y = ax^2 + bx + c, if a is bigger than zero, meaning that it’s value is positive, the parabola opens outwards.
• Quadratic Formula of y = ax^2 + bx + c where X = -b -+(square root) b^2 – 4(a)(c) / 2(a)

• y = mx + c
• An expression has no equal sign. Eg. x^2 + 8x + 12

• An equation has equal sign. Eg. x^2 + 8x + 12 =0

• Every time both sides are divided or multiplied by a negative number, flip the symbol. > becomes < when divided/multiplied by a negative number

• When it comes to graphing linear inequalities, if the gradient/slope goes up, then the graph is positive. If it goes down, it’s negative.
• 2/x = 2x^-1
• Any number raised to the power of 0(zero) is 1(one). However, this does not work when the base is 0(zero).

Along the way, I learned that Algebra wasn’t to be feared much because I remembered how you have to apply your logic when it comes to Algebra. Algebra may not be so relatable when applied to real-life experiences, but it’s there all right. Think of it this way, when someone slides into your DMs, you determine whether or not the slope is positive or negative. Basically, you’re the ‘a’ in y = ax^2 + bx + c.

Chapter 3: Mensuration

Mensuration. Mensuration revolves around shapes and it’s area, length, volume and perimeter. To highlight, listed below is my ‘holy grail’ for Mensuration.

• 180 degrees = pi rad
• 360 degrees = 2pi rad
• Area of minor sector of a circle [ theta/360degrees x pi(r^2) ]
• Perimeter of minor arc length [ theta/360degrees x 2pi(r) ]
• Formula to get the Volume and Surface area of so, so many shapes.
• Heron’s formula

I actually like this topic despite how sometimes frustrating it can be because the circles remind me of Pizza !! And that’s it. That’s my real-life application of Mensuration.

Chapter 4: Geometry

This chapter in my opinion, required logical thinking the most than compared to the other chapters. From the Pythagoras theorem to circle theorems and how symmetrical/similar shapes are, it can be a lot to comprehend and analyze.

• Fundamental results ( angles on a straight line, vertically opposite angles and angles at a point )
• The Pythagoras theorem
• Circle theorem
• To never estimate values before the final answer.
• N = number of sides of a polygon
• The value of each interior angle of a polygon = (n-2) x 180/2
• Each exterior angle of a polygon = 360/n
• All types of symmetry ( planes, lines, rotational )
• Identifying unknown angles by using circle theorems
• Similarity

Whilst learning this chapter, I’d sometimes get frustrated because I simply did not understand where I went wrong. The real-life application of Chapter 4 which hits closest to home than any others, would be that: sometimes when I feel like I’m stuck in a circle I can’t seem to escape, it really depends which angle of the circle I’m stuck in which makes it seem unbearable. Because sometimes I’m at the wrong angle of life. It takes being in the angle at the center to realize this.

Chapter 5: Trigonometry

Trigonometry’s actually one of my favorite topics, that is, until three-dimensional problems came along. I don’t necessarily hate it, more like get frustrated due to the simple fact that it can be unclear to me what the question is truly about. Despite it all, the pointers I have down below helped me through all the gruesome struggles Trigonometry has to offer.

• SOHCAHTOA (Commonly used for Right-angled triangles)
• Bearings ( always refer to North, Clockwise, 3digits)
• Sine rule (1 matching pair/ 1 angle and it’s matching side)
• Cosine rule (find the length of the unknown by using angle and lengths given)
• Angle Of Elevation/Depression (calculate from eye level of observer)
• Three-dimensional problems ( regularly draw the triangle which contains the unknown you are instructed to find. )
• Scale drawings ( habitually state the scale used )

Three-dimensional problems have continued to help me imagine things more vividly and accurately. For instance, the perfect slice of cake. In order to cut the perfect slice of cake, one must be able to visualize and picture in their heads how to cautiously slice the cake into perfect pieces.

Chapter 6: Graphs

This chapter has always been one of my weakest points in maths. I guess somethings just weren’t meant to be; like me and graphs. Despite this, I still put effort and try my best at it. Listed down below are my hints and tricks to survive this gruesome chapter; I wish you the best of luck and hope you do better than me when it comes to graphs because really, me and graphs are an absolute mismatch.

• Drawing graphs accurately (extend tangent line, keep lines neat and do not ‘shade’ lines)
• Gradient is always rise/run or Y2-Y1/X2-X1
• The form y = mx + c where m is the gradient and c is constant
• Plotting curves neatly according to it’s equation
• Interpreting graphs (it’s minimum/maximum point, amplitude)
• Graphical solution of equations (translate the graph drawn into a solution)
• Distance = speed x time
• Speed-time graphs (Acceleration – speeding up, deceleration – slowing down)
• In a speed-time graph, the acceleration/deceleration is the gradient. To find the distance, one must calculate the area of the shape formed by speed and time.
• Distance-time graph, the total distance taken is always calculated from the trip back and forth.
• For both Speed and Distance-time graphs, same straight line means the same gradient.
• Depending whether it is a speed/distance time graph, it is always represented on the y-axis whilst the time is represented on the x-axis.
• First Derivative Test aka Calculus aka omg- keywords
• relative extrema = turning points
• gradient function = dy/dx
• critical points = point(s) in a curve which has a gradient of zero
• For example, in the equation of 2x^3 – 12x^2 + 32,
• dy/dx = 6x^2 – 24x
• Multiply the power of the variables by the first term and then deduct 1 from the powers. If the number has no variables, automatically it is a zero.
• Then, factorize 6x^2 – 24x becoming 6x ( x – 4 )
• X1 = 0 and X2 = 4
• Now, input the X values to the very first equation of 2x^3 – 12x^2 + 32 in order to get the curve of the graph

I don’t really have a real-life application when it comes to this chapter. However, I think what represents the minimum and maximum points of a graph resembles our highest highs and lowest lows in life. If life was a straight line, what’s so enticing about it? So think of the ‘X’ as situations and problems representing the maximum and minimum point(s) of highs and lows we face in life.

Mathematics Competitions and UN Training

These competitions and state tests honestly were such a ‘ I’m so done ‘ phase in my life due to the fact that the use of calculators were prohibited. To any extent, I am grateful that I got to experience the Mathematics competitions because it gave me a better hindsight to Mathematics.

• Sets and Vectors

This particular topic was one I enjoyed and made some sense of. You see, sets are collections of things — like a set of clothes priced at a range of $15-$20. That’s a set. Items placed inside these brackets { } are sets.

There are no proper way to organize numbers inside a set. If A is { 1,6,4,5,8, 7,9 } and B is { 4,1,8,5,9,7,6 } , these two are equal sets because the numbers inside the sets are the same. Order does not matter.

A Subset however, is when pieces are taken from the set to form a subset. For example, a subset of A is { 1,5,8 }. This is because the pieces in the subset are the same pieces in Set A, only that not all the pieces of A are complete.

A Proper Subset is when all the elements of A except one is present in it. { 9,8,1,6,4,5 } is a proper subset of A because only one piece is not present.

Null Set { } is subsets of every set, because every set has the brackets { } in it.

Venn Diagram. A venn diagram shows all the possible relations between many, numerous sets.

The symbols inside the venn diagram (n) represents and. Venn diagrams showcase the relations between different variables and even sets.

Mathematics Competition Training

• cos 45 = 1/square root of 2 multiplied by square root of 2/square root of 2
• sin^2x = (sinx)^2
• Compound angle identity

COS ( A +/- B ) = COS A COS B +/- SIN A SIN B

SIN ( A +/- B ) = SIN A COS B +/- COS A SIN B

• Double Angle Identities

COS^2 A + SIN^2 A = 1

• Circumcenter

The center of a triangle’s circumcenter.

• Centroid

A line from a corner to the midpoint on the opposite side. Where all three lines intersect-this is called a centroid.

• Incenter

A line drawn from the corner, splitting the angle in half.

• Orthocenter

A line drawn at right angles to a side which extends to the opposite corner. When all the lines intersect, it is then called the orthocenter.

Even though I absolutely disliked the no calculator use policy, I learnt a lot about my own capabilities and attributes. Frankly, these competitions and tests were a toss-up of my luck. But at the end of the day, the critical thinking skills it taught me was worth it. It taught me to never assume any features of the problem unless stated in the question.

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And after 6 days of continuous writing (and even some buffering), I’ve finally reached the end of my 3rd blog! Thank you for keeping up with my many, many notes and lessons learned on this tremendously blessed but stressed on-going journey of mine.

Wishing you guys the very best of luck for your exams and if you have passed yours already, congrats! See you on my next blog!

“You can’t criticize geometry; it’s never wrong.” – Paul Rand

Welcome back to my blog! As you have read from the title of this blog post, I’ll be talking about how referable geometry and trigonometry is in real life and not just in textbooks. To start off, geometry is the study of mathematics which focuses on a plethora of shapes and it’s sizes. To help you picture what geometry is in your head and o get a relative understanding of the topic, imagine a pizza. I hope you’re not getting hungry, but pizzas actually come in multiple shapes and sizes, don’t they? Sure the pizza you’re aware of comes in a circle, but if you take a piece from it, it comes in the shape of a triangle.

Since we know have a basic understanding of geometry, let’s #moveon to Trigonometry. Trigonometry as we may or may not know, is a sine of times. – Anonymous.

Trigonometry is the study of mathematics which its center of attention is dealing on the unbreakable relationship between the sides and angles of triangles. Hey at least neither the side(s) or the angle(s) have to move on from each other like how we moved on from Geometry to Trigonometry.

Now that both the meanings of geometry and trigonometry has been introduced, let’s discuss how both geometry and trigonometry is used and applied to everything around us because like what Paul Dirac said, “God used beautiful mathematics in creating the world.”

First things first, Geometry.

A car enters the roundabout and encircles the entire route once before exiting.

By circling the entire roundabout, the car has made a circle shape.

This is a simple and basic use of geometry in our daily lives. This also includes Trigonometry because the car has to make a specific degree when exiting the roundabout.

Not convinced or impressed yet? Keep reading.

Next up, we have the beauty of art pieces.

You see, this art piece is composed of many rectangles and cuboids in different colors and sizes. How is geometry not applied in our daily lives? We can even apply trigonometry on the triangles made by shapes colliding and overshadowing one another in the said art piece.

Geometry is used in designing and our imagination. When you imagine a house, it’s roof is long in length like that of a rectangle’s, when you imagine the wheels of the newly launched super car it’s circular like a sphere.

Don’t overthink it; Geometry’s not supposed to be that complicated. (But if it gets complicated then calm down, and think outside the box you’re mind is currently stuck in.)

Moving on to Trigonometry,

This is an example of Trigonometry; one we all are guilty of doing everyday. For example, if you’re below on the city grounds facing up ahead towards the big, tall building, the angle you’d see the building is called the angle of elevation and represents how tall the building is from your eyes.

Trigonometry also is relevant when it comes to operating our TV. Electrical engineers use the mathematics of trigonometry to help enable us to flip through TV channels. Trigonometry is used for the flow of energy and to help with the change of direction whenever we switch channels.

The same goes for architecture. When designing or sketching a draft, architects must have the specific idea of what they are going to build. For example, the must know the specific slant of the roof and the angle between the walls and the roof.

Maths is everywhere around us whether we like it or not. I wasn’t always a huge fan of Maths, now I think it’s alright because I realized how relevant and common maths is in our ever day lives. We apply maths when we count money to buy something, maths is used to direct the surging flow of electricity as I’m typing this up.

With that said, it doesn’t take much to try and remember mathematics because if you look left or right, up or down, you’re head is already turning at a specific angle!

I’ll be frank. I’m not the best in maths or the worst either. I do okay. Sometimes I don’t understand a question and can’t seem to solve it regardless of what I do. In those moments, I question the existence of maths. Then I remember how math brings together beautiful things like dessert!!

Would you look at that perfect ice cream swirl and how the cone is standing 90 degrees straight?

With leaving things on a sweet note, you’ve reached the end of my second blogpost! I hope you’ve absorbed some of my (mostly food-related) real life applications of geometry and trigonometry and always remember; maths doesn’t get easier by hoping it will, it gets easier by doing it. -Paul Hamos.

• “Take chances, make mistakes. That’s how you grow.” – Mary Tyler Moore.

We all make silly mistakes–it doesn’t matter how old we are, mistakes are inevitable. What matters is whether or not the mistake was done on purpose and how we took responsibility for our mistake.

“The lesson will keep repeating itself until we’ve learned from it.”-Oprah Winfrey

So in honor of my very first blog post, here is a whole plethora of silly mistakes I’ve committed in the past and as sad as I am to admit, will most likely happen again in the future because sometimes I work against myself.

To infuriate myself and my readers furthermore,

Until here it is officially established that the number 2 and I don’t go along with one another despite me liking the number 2 and having nothing against it.