Registration

I woke up a little late which leads to me being one of the few people left to register. I find it funny how the students of our own school are the ones that came the latest to the registration. other students from places that are so far came way earlier from the given time as they were scared for the traffic. All we had to do in the registration was to say our name and they will find our name tag for us.

24 cards

24 cards is a card game where one team is given 4 cards and based on those cards we have to make mathematical equation that will lead to the final result of 24, we can either subtract, divide, add, multiply the numbers using the given numbers there in the card. this was a fun game tho I would love to have more chances of playing. our team only played twice as there were a lot of students and I think they ran out of cards to give us.

Round 1

round 1 was the multiple choice questions. i hav e n ever seen a question paper as extreme as SISMO’s before, even WMI’s question paper is not this hard. I was so shocked and scared when i saw the paper, however i still tried my best to answer all questions and for those questions that i’m sure i can answer, i spend more time on it.

Round 2

i answered this paper not knowing there is a round 2 to this competition. i actually thought that was only going to be one set of paper which is only the multiple choice one. the round 2 question paper was especially hard, i’m pretty sure i canonly nswer less than 10% off the whole question paper 2. this picture is to show how stress students got when they were doing the paper 2.

well okay maybe not everyone’s stressed

Kahoot!

if i’m to be fully honest, i didn’t really pay attention to the game as i was mostly chatting with my friends. we joined the game and still press on random answers. i’m pretty sure we were on the few last place of the game but it’s okay. 🙂

Awardings

we were called back to the multi purpose hall for the awardings and I was surprised when I was called for Bronze. I was definitely not expecting it as I couldn’t do a lot of questions from both the question papers. the awardings didn’t take long and we even took pictures with our teachers.

IB Learner Profiles

Risk Taker – not exactly used to joining competitions this challenging but with the courage and will I joined, and honestly am happy to have joined it

Communicator – collaborated with strangers to discuss how the 24 card game was played

Thinker – applied thinking skills critically and creatively and recognized and answered complex problems

“Mathematics is the door and key to sciences.”

Roger Bacon

investigation A

For the first investigation, we were asked to create an airplane runway, thus the name “Hit The Runway”. And we had to equate the line of the runway, for it to be exact, as from a realistic and logical standpoint, we have to make the exact and precise line. Because obviously, without a precise landing, the plane wouldn’t land safely.

And as you can see , the equation of the original straight runway line is y=3.15.

Then, there are also circles on the grid. These circles represent and are used to implify when planes have to revolve around the runway before landing, as they have to find the precise angle to land, as it has to be parallel as well.
The equations of the circle are as follows:

Investigation B

A) PERIMETER

first iteration : since each side of the triangle is 81 cm , 81*3=243 cm

second iteration : two triangles are overlapped we can find the perimeter by dividing {((81/3)*4)*3} = 324 cm

third iteration : to find the smallest length we can divide 81/3/3=9 cm 9*8*6 = 432 cm

fourth iteration : 81/3/3/3=3 cm so, 3*4*47 = 564 cm

B) AREA

C) OBSERVATION

D) MODEL

investigation C

no. 1

no. 2

no. 3

no. 4

no. 5

no. 6

for the number of green triangles, it increases as the stage number increases

for the length of one side of one green triangle (units), it decreases as the stage number increases

for the area of each green triangle (units^2), it decreases as the stage number increases

that’s the end to my final eJournal of 2019, I really do hope you all find my blogs useful and maybe could help you understand maths a little.

#igcsemath2020

#firstbatch

day 1

Today started off roughly. I had to wake up at 3 AM to get ready to meet in our school. We departed from our school at around 5 AM and even at the bus I couldn’t get any sleep. We arrived at Bandara Soekarno Hatta at around 6 AM.

The boarding time for our flight was 7:10 but the gate didn’t open until 7:25. The duration of our flight was around 1 hour 30 minutes which honestly didn’t feel that long. We arrived at 10:30 bali time which is 1 hour ahead of jakarta’s time. As soon as we reached there, we waited for our luggage to come out and after we got them we immediately walked to our bus.

We headed straight to our villa from the airport which took us almost 1-2 hours. I fell asleep and I woke up feeling so fresh. When we got our assigned villas, it didn’t look too bad from the outside, but when we walked inside, there were so much ants everywhere. There was even a spider on our bed which definitely freaked me out so much.

After going in our villa, we then ride the car to get to our lunch place. The food wasn’t that bad, like it was at least bearable. After eating our lunch, we were assigned for sign painting, which was honestly so hard and messy as we didn’t have rulers with us.

We had dinner shortly after we finished the sign and the food wasn’t bad at all. We went back to our villa after having dinner and my “villamate” and we cleaned our villa so that we can sleep well.

day 2

Today I woke up at 6:30 AM and shortly after Yoana’s alarm started ringing like crazy, it was so annoying. We got ready and ate our breakfast which is not so far away from us. I didn’t really felt like eating as I’m not used to eating just shortly after I woke up.

Afterwards we hopped on to the car and went to Braja Village which is the same village we went to yesterday. We started planting trees and watering those trees and then we head back to the village. We had our lunch break and not long after we started our cooking class.

We made ayam betutu, chopped the ingredients, and mixed it well with the chicken. After awhile, we dropped in the chicken and the spices and let the water to evaporate until it’s dry. We ate our own cooking for dinner but they still provided us with more food.

We went back to our villa after dinner and we swam.

day 3

This day was the last day of us visiting Braja village. It was our last lunch there. We had our dinner back in the villa. Today was extremely exhausting, we walked quite the distance.

However, I couldn’t say that I regretted it, I actually love the scenery of the green plantation. At first in the waterfall, I wasn’t brave enough to go down, but when i had the courage, I just walked in slowly. I jumped when I saw a somehow water spider? Honestly I don’t even know what that insect was. I got so scared i quickly ran out to the ground again.

I saw a few people having real fun in the middle of the waterfall, so I decided to come in from another place to avoid the insects. It was sooooo relaxing, apart from the fact that I got splashed a few times and that I almost slipped a zillion times as the rocks are pretty slippery.

After all those tiring activities, we went back to our villa to eat dinner and make a product from recycled waste.

day 4

Today is going to be our last day here in Bali and I’m not sure whether I’m relieved or happy or sad. I might not like the villa but I do enjoy having fun with my friends.

The day went on pretty quickly. I especially loved our barbeque night, and the little karaoke, more like a mini dj party.

When we went to the elementary school, I felt so blessed, and I understood that money isn’t the only thing that keeps a person happy. We didn’t spend much time there but every minute of it was precious to me. After our short visit to the school, we went to the village and learned how to make some offerings. It’s kind of like an origami to me.

Next we planted grains, which I didn’t as I didn’t want to get down to the mud. We had our lunch and afterwards we went to the owl breeding and orphanage. My friends sang and danced in the orpahnage which are all so spectacular while I just sat there watching them.

When the activities are over, we went back to our villa and celebrated as it is our last night there. This trip has been a wonderful and exciting journey and I definitely would love to go on another trip with all my friends.

“math is a language, speak it.”

so in this journal i will be focusing on two topics which are not exactly connected,but somehow will be easier to understand with the help of each other.

SETS

a set is a collection of distinct objects, considered as an object in its own right.

here are a few examples, along with the answers, to help understand and apply sets better :

PROBABILITIES

probability is a branch of mathematics that analyses random experiments

that’s the end of this journal, i hope this gave you all a brief idea of what sets and probabilities are and i really hope that it could help you with your own works!

just a simple how-to blog that will definitely save your time during exams

in this journal, I will be showing how to possibly find the mean of any data given by using your scientific calculator

the scientific calculator that I’m reffering to in this journal is CASIO fx-991ES PLUS which is very commonly used

to INPUT TABLE :

• mode, 3: STAT

• 2: A +BX

• then enter data given on your table

to find MEAN/AVERAGE of either x or y

• use the previous data you’ve typed in
• press AC (trust me)
• shift 1, 4: Var

• and to find the mean of either x or y, you can press 2 for x and 5 for y

REAL LIFE APPLICATIONS

1. mean can be useful when you might want to find the average of your disposable income per month in the future, this will help you plan your spendings based on your income
2. mean can help you guess or atleast have a bit of thought of how much something would cost, how much you could save or how much you lose
3. mean allows you to roughly calculate and estimate your previous ir next unknown result

welcome back! so here i am, cramming up all the knowledge learnt throughout ninth grade in this let’s say “well organised” blog. right on this third blog of mine, you will be able to see the do’s and don’t(s) that i’ve learnt throughout the year, which can be included as life hacks i guess. it has helped me in many different ways i could ever think of. this ejournal will be based on the textbook i am currently using, which is oxford’s complete mathematics for cambridge igcse. have fun!

“we do not learn from doing, we learn from reflecting what we’ve done previously”

Topic 1 : Sequences

few basic sequences and their general formula:

• arithmetic sequence [Un = U1 + (n – 1)d]
• quadratic sequence [Un = an^2 + bn + c]
• cubic sequence [Un = an^3 + bn^2 + cn + d]

these three sequences are the most basic and commonly used.

ARITHMETIC SEQUENCE

Un = U1 + (n – 1)d

this is the general formula of arithmetic sequence to find the nth term of a sequence

U1 = first term

n = number of terms

d = first level common difference

*additional information*

to find the SUM of arithmetic sequence, use the formula : Sn = n/2 (2 U1 + (n – 1)d

QUADRATIC SEQUENCE

Un = an^2 + bn + c

2a = second level common difference (always constant)

3a + b = 2nd term – 1st term

a + b + c = 1st term

*always remember the formulas and how to obtain the unknown values, abcd, etc.*

CUBIC SEQUENCE

Un = an^3 + bn^2 + cn + d

6a = third level common difference (always constant)

12a + 2b = 1st second level difference

7a + 3b + c = 2nd term – 1st term

a + b + c + d = first term

*IMPORTANT*

zero/R, where R is not equals to zero will always be zero

zero over any real numbers is equals to zero as long as the real number is not zero

Topic 2 : Estimation and Approximation

in this topic, we are going to focus on significant firgures, and the upper bound and lower bound of a number.

SIGNIFICANT FIGURES (s.f.)

1. all non-zero are significant figures

examples : 12 345 678 (8 s.f)

789 ( 3 s.f)

2. zero digit between non zero digit are significant

examples : 105 ( 3 s.f)

90000000009 ( 11 s.f )

3. in decimals, zero digit after non zero digit are significant

examples : 1.30 ( 3 s.f )

3839.530 ( 8 s.f. )

4. in decimals, zero digit before non zero digit are non significant

examples : 0.003 ( 1 s.f.)

0.0305 ( 3 s.f.)

5. in a whole number, zero digit after non zero digit could be significant

examples : 4998

( round of into two significant figure) = 5000 (2 s.f.)

(round of into three significant figure) = 5000 (3 s.f.)

5199

(round of into one significant figures) = 5000 (1 s.f.)

UPPER BOUND vs LOWER BOUND

upper bound is the highest number possible in order to have a specific value

lower bound is the lowest number possible in order to have that same specific value

so in other words, when upper bounds and lower bounds are being rounded off, they must end at the same exact number or value.

REAL LIFE APPLICATIONS

to round off money, profits, to make counting numbers easier. to see the possibilites of the high and low values which will still lead up to the same amount.

Topic 3 : Simple and Compound Interest

simple and compound interest is mainly used to find the rate of interest, number of years, future value, present value, or the compounded amount of time

SIMPLE INTEREST

I = Prn/100

where:

I = interest

P = principal amount

r = rate of interest

n = number of years

F.V = P + I

F.V = future value

COMPOUND INTEREST

incremental change : F.V = PV ( 1 + r/100t )^nt

decreasing/diminishing change : F.V = P.V ( 1 – r/100t )^nt

where:

F.V = future value

P.V = present value

r = rate of interest

t = compounded (anually, semi annual, monthly, weekly, daily)

n = number of years

REAL LIFE APPLICATION

interest can be used to count the “rewards” or the “loss” that took place. for example if you are saving on a bank, you would want to know the amount of money which you will obtain in total after a few years of storing it there and this action is possible through the help of using either simple or compound interest. another example is that if you are to sell your used car of 5 years, the sale price will definitely decrease, and to calculate the decrease in value of the car, we are able to use the compound interest formula through the diminishing/decreasing formula.

Topic 4 : Trigonometry

trigonometry can be used to find unknown angles or unknown length of mainly triangles.

CIRCLE THEOREM

when all vertices touches the circumference, right angle triangle will be formed

angle at the center is twice the angle touching the circumference

angles at the centre O is twice the angle touching the circumference as they both have the same base

cyclic quadrilateral, is where the corners of the quadrilateral touches the circumference. opposite sides equals to 180 degrees. therefore in the picture above p = 30 degrees

Topic 5 : Functions

looks so extra and complicated right? no worries we wouldn’t be going in too much depth. just the basics 🙂

for example you are given the function

f(x) = 2x + 5

and you are supposed to find f(3)

first thing to do is to actually just replace the “x” with 3

so you will get f(3) = 2(3) + 5

so f(3) = 11

moving on, what if we are given two functions

f(x) = 2x + 5

g(x) = 7 – 3x

and you are to find fg(5)

first don’t mind the f

so you’re left with g(5)

g(5) = 7 – 3(5)

g(5) = -8

now that you found g(5) = -8

f(g(5)) will be the same as f(-8)

and all you have to do is substitute the x in function f with -8 and your final answer will be

fg(5) = 2(-8) + 5

which will give you fg(x) = -11

easy right? now let’s carry on to a slightly challenging one

you are to find f^-1 (x) which can be read as inverse of function f

first things first, substitute f(x) with y

so you will get the equation y = 2x + 5

next, replace y with x and replace x with y

your equation should look like this x = 2y + 5

then, you mke y as the subject of your formula

2y = x – 5

but you’re not done just yet

simplify it so the you get only one y

y = (x-5)/2

NEVER forget to switch the y back to the function f^-1 (x) as you wouldn’t be awarded any marks if you didnt change it to this form

so your final inverse function should look like this

f^-1 (x) = (x-5)/2

and that’s it!!!

Topic 6 : Mensuration

this is something you should know before starting this topic

180 degrees equals to pi radians

so 360 degreed equals to 2pi radians

and here’s a few important formulas that are usually being asked in exams 🙂

Topic 7 : Similarity Test

how to find if triangles are similar

• all their angles are equal
• corresponding sides are in the same ratio
• AA, SAS, SSS

that’s the end of this blog! i hope i helped you understand these topics..all the besttt:)

at some point, we would want to know why are we studying about this. like, what’s so important that i really have to know it. or things like am i ever going to need it in my life. these are few examples of how geometry and trigonometry is applicable in real life and why learning about it isn’t a waste of time.

this picture is an example of trigonometry used in real life. how? by looking at the angle of elevation. imagine being at the peak or being at the bottom. have you ever wondered how high a building or something is. well, by using trigonometry, it isn’t hard to find the nearest estimated height. in this picture, we are able to find the height of the mountain at its highest peak by simply using trigonometry and the data given there.

a dome? that’s right a dome. this is where we need geometry in real life. geometry can help find the size, shape, positions, dimentions of the things you would want to know. geometry helps in building this dome because by the help of geometry, the workers would know where the middle point is and how they are supposed to shape it correctly or in this case symmetrically. how to make it look alive like 4-d like buildings.

in conclusion, trigonometry and geometry both are useful in our lives. it might now be useful now, but it might be in your future.

“the mathematician does not study pure mathematics because it is useful; he studies it because he delights in it because it is beautiful.” – Georg Cantor

realization of silly mistakes that could’ve brought me to a higher mark 🙂

from this journal, i have learned that i must be more careful, and should really check my work carefully. i should try and manage my time during a test in order to not be in a hurry finsihing the papers.

Thanks for joining me!

Good company in a journey makes the way seem shorter. — Izaak Walton