Quarantine had been challenging to go through. But majority of my quarantine was e-learning. This is my first ever experiencing e-learning and not gonna lie, it’s quite great, however, since everyone is using the wi-fi, sometimes the connection get’s slow and laggy making it even harder to communicate with my teachers as well as to understand them. I have many pets at home and sometimes, they bark and chirp as loud as they can to get my attention therefore, creating background noises during my zoom session in addition, having to mute my call. It really sucks how nowadays I’m not able to say “i’m tired and I WANT TO GO HOME!” BECAUSE I’M ALREADY HOME :/.

The other day, I felt so stresssed. I had millions of assignments to do eventhough I’ve been so productive and great in managing time. I did assignments right when I got them, I did assignment that were do tomorrow done today. I then wondered what could have happened if I didn’t do all this. My parents then decided to drive me around the empty roads nearby and it felt so refreshing. They couldn’t have decided a better day for this. This kept my mind off things and kept me sane.

Anywas…all the negativity aside, I feel like being quarantined made me more organised and productive because, usually when I have nothing to do I’ll go through my social media accounts, youtube, Netflix, entertaining apps and etc. But, soon enough, it gets boring being on the internet 24/7 and it also damages my eyes. So what I do to solve this is, I start organising my room so that it’s more e-learning friendly.

I really hope it’ll end soon cause, I’m the type of person who LOVESSS going out. But, I’m really thankful for the doctors whom been thriving and working their best on saving this world.

Do or do not. There is no try.

Yoda

I decided to join the first ever SISMO held in SIS Kelapa Gading. The mathletes worked so hard to organise this competition and I’m glad I was able to help support them. The competition was held on a Saturday, 1st of February of 2020.

I woke up early to re-registrate at 8 a.m. in the morning. Before the competition started, they organised an “ice breaker game”. We played this game called 21. So, your given four cards, which is meant to be played in a specific order and sequence using any mathematical operation to then gain the number, 24. I was grouped with two other JC1s and a friend of mine, I guessed I made new friends during SISMO.

Then, the test started. The first test consists of multiple choice questions. I’ve never encountered such tricky questions in my whole entire life, however, I just had to trust my guts and guess the right answers ;). Right after the test we had our first break. My friends were discussing the answers while I was just standing realising I guessed all the answer incorrectly. Well, I guess better luck next time…

After the 30min break, the second round started. Turns out this paper didn’t consist of multiple choice questions so, I wasn’t able to just guess my answers and work my way through it but I was surprised that I was able to solve some of the questions. As time was up I looked around to check on my friends, they had anxiousness written on their faces. Not gonna lie but it was really funny.

Finally, it was lunch. We only had a 15min break beforehand and I didn’t eat much so I was really starving at that point. After lunch, we all gathered around to play Kahoot. Next was the lightning round, in which the top 3 participants in their respective categories were given the privilege to compete in a speed contest of who were able to solve the question first. I was really proud the some of classmates got to participate on the lightning round. As well as the JC1 student I sat beside during the exam. However, I didn’t get to watch most of the lightning round as I was helping my so called “dance crew” on their makeup as well as their outfit. Finally it was time for us to dance our heart out. It was my first ever dancing with the halakatas dance crew and I’m really proud to be part of it. It was a great an unforgetable experience.

Last but not least, it was the awarding ceremony. I am really proud of my classmates. Sadly, I didn’t win anything but I won’t let that stop me from trying my best and to never give up! I hope to take risks, on joining competitions eventhough there was no guarantee of winning but i guess you only live once and I’d rather take the chance then missing it. Turns out, I have this natural curiosity and would love to learn and acquire skills necessary to conduct inquiry and research to show independence in learning. By making blogs like these, I’ve been more reflective and I get to assess and understand my strengths and limitations in order to support my learning and personal development.

“You don’t learn to walk by following rules. You learn by doing and falling over.”

Richard Branson

I’ve been studying in SIS KG for the past 10 years and 3/20 of this has been the experience of the IGCSE programme. The experience has been great. We are given tests, assignments and preparations to help us get ready for the IGCSE exams. For this term’s semester assignment we are given 3 investigations. Investigation A, B and C.

Part A: “Abigail”s airline”

In investigation A we were told to graph a line that would overlap the dotted lines on the runway. The topic involved was Linear Programming. We all know that an equation of a line is “y = mx+c” How I got the answer was first, I typed down “y = ”

• 

• 

Based on these pictures you could see the difference it would make if m is a positive number or a negative number. Then since i know that m is a negative number, I just trial and errored to find which negative number it’ll be. In this case it’s -4. To position the line in the correct place, I change “c” or so called the “y-intercept”. If c is anegative number, it’ll shift to the left and if c is a positive number the graph would shift to the right.

Part B: “Devloping Inquiry Skills”

In Investigation B, we are given the length of each side of the triangle is 81 cm. We were told to calculate the perimeter; area of the snowflake at each iteration. The topic involved is sequences.

Finding the perimeter at each oteration

The perimeter of the snowflake after n iterations is:

Pn = 3 * s * (4/3)^n

where s = side length of original triangle (81cm), n = no. of sides

---

So on the first iteration, the perimeter of the triangle is

3(81)*(4/3)^(0) = 243cm

Second iteration: 3(81)*(4/3)^(1)= 324cm

Third iteration: 3(81)*(4/3)^(2)= 432cm

Forth iteration: 3(81)*(4/3)^(3)= 576cm

Finding the area of the snowflake at each iteration

The are to find Koch’s snowflake at any given iteration is given by:

(2s^2√3)/5

where s = side length of original triangle (81cm)

So, the area is (2(81^2)(3^1/2))/5 = 4545.6 cm^2

Part C: “Sierpinski’s triangle”

1.

2.

3.

The pattern I obeserved in relation to the number of green triangles:

3^n

The pattern I observed in relation to the length of one side of one green triangle:

(1/2)^n

The pattern I observed in relation to the area of the green triangle:

(1/4)^n

Where n is the number of stages.

4.

I observed that all these patterns are arithmetic sequences, which uses “n” as the index.

5.

6.

As the number of stages increases, the length of one side of one green triangle decreases by a factor of 1/2, and the area of each green triangle decreases by a factor of 1/4.

Reflection

I have consequentluy learnt the IB learner profiles of being a thinker, because thinking helps define and organise esperiences, plan, leadrn, reflect and create; it is important that we make the best use of the gift of knowledge so that we achieve greay feats and heights in every way of our life; being open-minded helps us to learn and grow, strengthening your belief in yourself.

Unforgettable Moments

They say the small things in life are the most precious. They are the ones that make you smile and think how great life is. Your life is filled with moments you wish you could re-live over and over again. When i was in grade nine, I entered a mathematics competition with my classmates. After grinding at the competition for several hours, i finally managed to finsih the paper. I got pretty good scores for the past papers, so i figured I had it in the bag. Few months later when the results came, I got a bad score and didn’t make it to the next round. Welp I guess I still suck at guessing :3 but on the bright side, few of my friends made it to the next round and I’m proud of them. 😀

#IGCSEMath2020 #FirstBatch

“It’s not about perfect. It’s about effort. And when you implement that effort into your life. Every single day, that’s where transformation happens. That’s how change occurs. Keep going. Remember why you started.”

Anonymous

Matrix

In mathematics, a matrix (plural: matrices) is a rectangular array (cf. irregular matrix) of numbers, symbols, or expressions, arranged in rows and columns. There are many different things you can do with them.

Adding

To add two matrices, add the numbers in the matching positions. If the matrices are different sizes or doesn’t have the same order of matrix, the addition is undefined or also known as impossible.

and it works the same way for subtraction:

Subtracting

Just remember that the formula of the order of matrix is:

Row x Columns

How does the order of matrix effect multiplying matrices you ask?

As shown above, the one encircled should be equal to each other, if not, the question is said to be impossible to answer.

There are two easy tricks on how to multiply matrices:

1. Mr. Kichan’s way

2. The zipper method:

Dividing

We don’t actually divide matrices but instead, we find the inverse of a matrix so that we could multiply them like so:

What is the inverse of a matrix?

The Inverse of a Matrix is the same idea but we write it  A^-1

Therefore, 8 would be 1/8. In addition,  ¹/₈ can also be written  8^-1.

Before we carry on calculating the inverse, we should first know what is identity matrix.

Identity Matrix could be 2×2 in size, 3×3,4×4 and so on.

Now let’s calculate, here’s the formula:

1. You should remember to first, swap the positions of a and d, put negatives in front of b and c
2. Then, make the determinant (ab-bc) a reciprocal so that we could divide everything by the determinant.

An example would be:

Additional notes:

How to multiply a matrix by a constant.

Combining Operations

Example:

Transformation:

Rotation

Rotation. A transformation in which a plane figure turns around a fixed center point. In other words, one point on the plane, the center of rotation, is fixed and everything else on the plane rotates about that point by a given angle.

Reflection

In geometry, a reflection is a type of rigid transformation in which the preimage is flipped across a line of reflection to create the image. Each point of the image is the same distance from the line as the preimage is, just on the opposite side of the line.

The central line is called the mirror line.

Translation

Translation is a term used in geometry to describe a function that moves an object a certain distance. The object is not altered in any other way. It is not rotated, reflected or re-sized.

Resizing or Enlargement

Enlargement, sometimes called scaling or dilation, is a kind of transformation that changes the size of an object. The image created is similar to the object.

Additional notes:

What is similar?

Similar figures are figures that have the same shape, but may have different sizes. 

What is congruent?

Exactly equal in size and shape. For any set of congruent geometric figures, corresponding sides, angles, faces, etc. are congruent.

Only applicable for centre of origin.

Real life applications of transformation and matrices:

1. flipping images in a computer (transformation)
2. mass production of shoes and spectacle frames. (transformation)
3. Matrices are used in representing the real world data’s like the population of people, infant mortality rate and etc.

This ends here, thanks for reading :3

On our last day of bali, it was really hard for us to wake up. As I leaned back and rested my head against the headboard, my eyes began to feel heavy. It was drizzling that morning I didn’t want to leave my bed. My friends had to wake me up several times till I was very aware of what i’m doing. To prevent falling asleep, I took a shower and we immediately went to the eating area and ate our breakfast. Then we repacked our luggage and was on the way to visit the coffee luwak plantation.

We saw different coffees and they showed us the process of how coffee beans are being made as well as the actual asian palm civet. We were given testers on different coffees and teas for us to buy. I decided to buy 4 different ones for my parents and my sister I bought herbal tea, rosella tea, vanilla tea and cocoa tea.

Next, we went to krisna to buy oleh-oleh (souvenir) for our loved ones and then we went back to the airport. We were blessed that it rained that day because if it did days before we would be soaking wet and we wouldn’t be able to do most of the activities.

In conclusion, to be honest, at first i wasn’t really enjoying the trip to Bali. The activities we did was kind of boring and the fact that we were going to Bali instead of Japan killed me. But then, I realized that no matter where you go, as long as u have your friends they’ll make any activity exciting and fun. This trip would always have a special place in my heart. The fact that this learning journey would be the last learning journey I would go with my friends after all these years we’ve been together till we part ways is really emotional. Thanks to those whom fulfilled my heart with happiness. I never felt so grateful. It’s been amazing. Probability of going back, 100%.（＾ω＾)♡

On the forth day, we went to a local elementary school to experience being a teacher simply by introducing ourselves as well as teaching them how to speak english. We taught them how to introduce themselves in english, what’s their hobby and what would they want to be when you grow up.

After visiting the local school, got involve in experiencing the daily life activities to enrich our experience with local people. We made these cool dragonfly catcher using daun kelapa and it turned out like this.

Next, we walked along with local farmers in a farmer hat and equipment towards the rice fields. Further more, got involve with them in traditionally rice cultivating process up to planting rice. We were given knowledge about the tropical fruits and spices plantation, a local demonstrated how he climbs the coconut tree to get the coconuts, then they served us a young coconut as refreshment.

After exhausted with all the farmer activities for over four hours, we ate a traditional set menu lunch which wad served in a Balinese house compound together.

After lunch, we went to the biggest rice field in Bali and saw owls. They take care of the owls strictly. If we were caught killing them or stealing them, they would immediately be arrested for 5 years. Owls are being kept because it prevent the rats from eating the rice.

We then drove to an orphanage where we performed several talent shows and taught them how to dance “Let’s kill this love” by Blackpink. It was a fun experience.

We ended the day with barbecue by the pool. As well as jamming all night to throwback songs, buying midnight snacks from Indomaret and also trying to staying up all night. It was an unforgetable night.💚

On the third day, we went trekking to see the waterfall. We had to walk down 93 stairs. Once we arrived, everyone changed into their swimming suit and started swimming while, some of us were admiring the view.

After trekking, we went to a photo location where you could ride a swing that was few meters high. There were a couple other photo locations but the swing caught my eye. As I was scared to ride the swing because I am afraid of heights, I saw everyone swinging above me therefore showing an angle of elevation

Finally we head back to the resort. We then ate dinner then, recycled a bunch of plastic bottles and our group turned out like this.

On the second day, we were told that we would have our breakfast at 7:30. We ate bakmi goreng, nasi goreng and kerupuk. After lunch the boys were separated from the girls. The boys were told to display the signs we made and the girls were told to plant these traditional plants they plant whenever there’s a ceremony.

After planting, we walked around the neighborhood and learned more things about their culture. Every house in Bali have these wooden doors and they are designed to be thin and short the reason is because when the door is thin, people would have to go in the house one by one and when the door is short those whom are tall would bend down. Therefore, they look like their bowing. This way they seem to be respectful.

We then went back to have lunch. ps. it was really tiring. We ate shrimp, chicken with sambal terasi. For desert we ate pisang goreng. After lunch we were divided into groups and we were assigned to cook ayam betutu (the probability of me getting it to taste good is zero, but turns out it really wasn’t that bad) and this is how ours turn out:

We had our dinner and we went straight back to the hotel. Since we had an early dinner, we went swimming. It was really fun they had slides we could slide on and also a cliff you could jump off from.

Finally, after a long and tiring day. We went back to our villa.

We went to Bali for our learning journey. We boarded the plane for about 2 hours and we landed safely. We then immediately went straight to the villa for 1 hour and 30 mins. The teachers gave us few minutes to unpack our things and we were off to eat our lunch. We ate chicken, otak-otak, tahu and rice. After lunch, our task was to make signs for the village. We were divided to groups of 4 and each of the groups were told on what we were suppose to write and for our group we were told to do this:

They gave us two rectangular cuboids that were previously stuck together which made the base of the sign and this is how ours turn out.

Afterwards, we ate our dinner. We ate sate, tempe and rice and pisang goreng for desert. It was delicious! Then we finally head back to the villa to take a rest.

Statistics is the grammar of science

Karl Pearson

Sets

What is a set?

In mathematics, a set is a collection of distinct objects, known as elements or members of the set.

Notations in sets:

How to read sets?

 ∈ = { x | 2 ≤ x < 15, x ∈ Z }

“universal set is a set of x such that x is larger or equal to 2 and lesser than 15, where x is an integer”

• The Universal Set is the set that has everything.
• The Empty Set has no elements: { }

Example 1

For example, Kaylyn wants to buy stationaries. These stationaries include a pencil, an eraser, a pen, a notebook and a ruler. So the set of stationaries for Kaylyn would be listed as follows.

A = {pencil, eraser, pen, notebook, ruler}

Where A is the name of the set, and the brackets indicate that the objects written between them belong to the set.

Example 2

What is the set of all odd whole numbers between 0 and 10?

Solution:  ∈ = {1,3,5,7,9}

Note: that the use of the word between means that the range of numbers given is not inclusive. As a result, the numbers 0 and 10 are not listed as elements in this set.

The following conventions are used with sets:

• Capital letters are used to denote sets.
• Lowercase letters are used to denote elements of sets.
• Curly brackets { } denote a list of elements in a set.

Venn diagram

Note: A proper subset is a subset but a subset is not a proper subset.

Union

Facebook U Twitter = {Al, Courtney, Freda, Bob, Dave, Ernie, Gary}

Not everyone is in that set. Only those that use facebook and twitter or both. In other words we combine the elements of the two sets.

Intersection

“Intersection” is when you must be in BOTH sets.

In our case that means they use both Facebook and Twitter. Which is Bob. The symbol for Intersection is C.

Facebook ∩ Twitter = {Bob}

Complement

Complement is referred as “everything that is not”.

Facebook^c

Which means “everyone that is not using facebook”, like this:

Facebook^c = { Dave, Ernie, Gary }

Probability

Probability is a branch of math that analyses random experiments.

Basically:

Probability line:

Complementary events→ are two outcomes of an event that are the only two possible outcomes.

P(A^c) = 1 – P(A)

This is like flipping a coin and getting heads or tails. Rolling a die and getting a 1 or 2 are not complementary since there are other outcomes that may happen (3, 4, 5 or 6).

Combined or compound events→ in probability, when two or more experiments are conducted together.

P(AUB) = P(A) + P(B) – P(A∩B)

QUESTION 1

In a class of 29 students, 20 students studied French, 15 students studied Malay and B studied both. A student was chosen at random from the class, find the probability that the student:

a) Studies French

20/29

b) Studies neither language

2/29

c) Studies at least one language

(20+15)-8/29 = 27/29

d) Studies both language

8/29

e) Studies Malay given that they study French.

8/8+12 = 8/20 = 2/5

f) Studies French given that they study Malay.

8/(7+9) = 8/15

g) study both language given that they study at least one of the languages.

8/27

Question 2:

The numbers 3,4, 5, 6, 7, 8, 9, 10 are each written on an identical piece of card and place in a bag. A random experiment is; a card is selected at random from the bag. Let A be the event ‘a prime number is chosen’ and B be the event ‘an even number is chosen’.

a) Draw a Venn diagram that describes the random experiment.

b) Determine whether he events A and B are mutually exclusive.

Events A & B are mutually exclusive because P(A∩B) = 0. Which means, if A occurs B doesn’t occur.

C = ‘an odd number is chosen’

D = ‘a square number is chosen’

c) Draw a Venn diagram that describes the random experiments.

d) Determine whether the events C and D are independent events.

They are independent if, P(C∩D) = P(C) x P(D)

Therefore,

1/8 = 4/8 x 2/8

1/8 = 1/8

Tree diagram

Question 3

A jar contains 7 counters, of which 4 are white and the rest are black. Three counters are drawn, one at a time and without replacements, from the jar. Find the probability that the two counters of each colour are left in the jar.

P(WWB) = 4/7(3/6)(3/5) = 6/35

P(BWW) = 3/7(4/6)(3/5) = 6/35

P(WWB) = 4/7(3/6)(3/5) = 6/35

6/35 + 6/35 + 6/35 = 18/35

Note: Relative Frequency→ can be expressed into percentage or decimal.

Real life examples

Sets

1. In the kitchen, the plates are kept separate from bowls and cups.
2. School bags have divisions where the sets of notebooks and textbooks are kept separately.
3. In shopping malls, clothing shops are on another floor whereas the food court is at another part of the mall.

Probability

1. Weather forecasting
2. Lottery tickets
3. Sports strategies

Thanks for reading my eJournal! 🙂