Math - Laws of Indices

As I stated before, my school is quite slow at teaching Maths (at least thats what I think). Currently in Year 9, we have started algebra - 2 unknown variables. We have learnt the Law of Indices application is very important, not only are its uses limited only to scientific notation, but it also extends to algebra.

Here are the rules for the 6 different laws of indices.

Rule 1: a^m x aⁿ = a^m+n 

The first rule implies when two bases are the same, but indices are different. This cannot occur when the bases are different. The rule for multiplying is to add the two powers together, and not multiply the bases. 

Ex.1) 9² x 9⁵ =9⁷

Ex.2) 7⁶ x 7⁹ = 7¹⁵

What not to do: 4³ x 4⁶ = 16¹⁰ 

Rule 2: a^m ÷ aⁿ= a^m-n

The second rule implies in division, the bases must be the same but indices may be different. When dividing similar bases with different indices, you subtract indices. 

Ex.1) 10² ÷ 10⁷ = 10^{-5 =} 0.00001

Ex.2) 8⁹ ÷ 8³ = 8^{6 =} 262144

What not to do: 9⁹ ÷ 9⁴ = 1⁵ 

Rule 3: (a^m)ⁿ = a^mn 

For this rule, do not times the number in the brackets by the power. You must first times the power inside the brackets by the one on the outside. After multiplying the powers, then you may multiply the base by the power.

Ex.1) (7³)² = (7)^{6 =} 117649

Ex.2) (3⁷)² = (3)¹⁴ = 4782969

Rule 4: a⁰ = 1 (a≠0)

This rule is simple, whatever number the base is does not matter. If the power is 0, the base is out of the equation. The answer to any number to the power of 0 will be 1. 

Ex.1) 9998324230948324⁰ = 1

Ex.2) 5⁰ = 1

Rule 5: a^-m = 1/a^m

This rule implies whenever the power is a negative number. Simply put the base to the power over 1.  

Ex.1) 5^-3 = 1/5³ = 125

Ex.2) 8^-6 = 1/8⁶ = 262144 

Warning: Do not put the negative sign in front of the power.

Rule 6: a^1/m = 

The last rule implies when the power appears in a form of a fraction. 

Ex.1) 9^1/2 = 2√9 = 3

Ex.2) 125^2/3 = (³√125)²  = 5² = 25

CAS Week Revisited

About 3 weeks ago, our school attended an event called CAS. You may or may not have heard about it, CAS stands for;
Creativity, Action and Service. As students progress through their secondary years and reach about Year 11, they will be required to do CAS, 50 hours for each.

Year groups under Year 11, teachers and staff aim to assist and guide students towards what is coming for them in the upcoming years.

Most of the time, CAS is done as camp; a week from where you leave all of your terrible daily habits; computers, television, telephone, etc.

Camping is a good way to 'promote' CAS, as there are certain skills needed for CAS; such as teamwork, respect, communication, leadership, risk-taking, sacrifice, etc.

During camp, classmates were challenged to do activities such as: Surfing, canyoning, hiking, building camp-fires, developing first-aid techniques, etc.

In these types of activities, you just can't work on your own. You have to use all available resource around you. Every pair of hands help.

At first, my attitude towards this trip was: Why do we have to do this again? We did this last year.. This year it's so much more expensive, and we don't have as much fun... Its unhygienic, etc.

But after I came back, I had brought back with my a whole new set of skills, new knowledge, and a whole new respect for my peers, and the people around me.

Drama Soliloquy - Inferiority

In our life, no matter who you are, there will be at least once in your life that you will or have felt inferior. We have various reasons for getting inferior, your colleague getting credit for what he hasn't done, for someone getting a medal which you think you should have gotten, for someone getting a new toy you were dying to buy. 


It was a unique experience for me in class, since we every student had to create their own soliloquy, and it was interesting how different people had different experiences to share/ make up.


Below is a soliloquy I wrote for Drama, showing my understanding of what being inferior feels like. Of course, this was not based on a true event, and was only made up for fun.


Soliloquy - Why does she get more than me? Why does she get more time than I do? She's no different, she's just a student. Unless, I'm better than her. That's right, you bloody know it, you know damn right I'm better than her!

Attributes of an Entrepreneur

There are many many many, entrepreneurs who fail. But if you become a successful entrepreneur, you can be a billionaire! But an entrepreneurs journey is painful, and lonely. Are you that type of person with these characteristics? :

Famous inspirational entrepreneurs who I personally  am inspired by are:
•Sir Richard Branson (Known for his own enterprise Virgin)
• Duncan Bannatyne. Net-worth £430m.
• Sam Walton, although deceased Sam Walton started from scratch to build up an empire of Wal-Mart.
• Steve Jobs, deceased, passed away few days ago. He said in one of his speeches, 'Stay foolish, Stay Hungry'.


Even though you may have the attributess of an entrepreneur, are you capable of becoming one? An entrepreneur has to require quite a lot of luck. Lets take Sir Richard Branson for instance, narrowly escaping death 4 times. Once on the Virgin Atlantic Challenger attempting to break a world record of crossing the Atlantic Ocean. On his second attempt on the Atlantic Ocean crossing, in reward for the Blue Riband he successfully beat the world record. His other 3 death stories all come along in a hot air balloon. Once trying to fly around the world in a helium-propelled hot air balloon, and twice trying to cross the Pacific Ocean.

But not only has he managed to narrowly escape his fate, he has also successfully started his company Virgin Airlines, even though previous airline, Lakers Airways was brought to an abrupt failure in competing against (at the time) British Airways. But Virgin Airlines successfully overcame all odds, and astonished the whole world, including Sir Freddie Laker himself.

Justice

What is justice? What is the right thing to do? Do we always have to put moral and ethics in front of us? The video explains a Harvard Professor lecturing students about what the right things are for certain scenarios.



You don't need to watch the whole thing, but just go through 10 minutes of it. After watching the 10 minutes, come back here and post what you would do in the scenarios that were provided.

Personally, there would be 1 scenario I would do differently to everybody else in the lecture. If the cart could be stopped by me pushing a big (no offense intended in anyway) man to say 5 other people, I would certainly push the man down. My reason being would be, because if I could save 5 man for sacrificing 1 it saves more people. But if I save the man who is next to me, I would feel guilt for knowing I could have saved more lives if I pushed him down.

Whereas on the other hand, if you were to ask me to do the same thing in the doctor's scenario, I would not possibly do that. I would be violating the law to take one healthy person (who is only here for a checkup)'s life, to save 5 others' I would not be able. Unless the one healthy person agrees to sacrifice his life to save the other 5.

Comments are appreciated.

Computer Systems

Technology is involved in our every day life. The most used piece of technology are; cars, computers, telephones, WiFi etc. We use the technology around us, but do we know what the function of them are? How they work?

Over the last 3 IT lessons, we have learnt about the 6 key components and one of the few operating systems, in our case Linux (Ubuntu). We also took apart a desktop PC, and located the 6 key components, consisting of:

Motherboard
RAM (Random Access Memory)
Harddrive (HDD)/ (SSD)
CPU (Central Processing Unit)
Powersupply
Case

The 6 key components are included in all computers, Macs, PC's, Desktops, Laptops, Netbooks, etc.

But computers don't just work by the 6 Key Components themselves, we use the 4 layer model to describe the system.

Hardware - The mechanism of the computer. The 6 key components of a computer.

Software - The system that it uses, the way it runs. Software coding, different applications from one another etc.

Network - Wireless LAN, WiFi, connecting from one person to another such as ping-ing

4. People - Without people the computer is useless. People create the applications, social networking sites, websites, etc.

Each of the 6 key components have their own unique jobs.

Motherboard - The job of the motherboard is to 'connect' all the wires, cables, components etc altogether. The motherboard also is a structural support system for the RAM (to hold it in place) and CPU, etc.

(The large green beef jerky)

RAM - The RAM is a temporary memory storage system. In order for the RAM to be enabled to use the memory, you have to first open some applications from the HDD or SS, and then the applications then move to the RAM. The less RAM you have, the less applications it can handle. Thus causing lag. The RAM is a much faster in-comparison to the HDD/ SSD.  

(The green beef jerky)

Harddrive - The Harddrive is the permanent computer memory. Once the computer is booted up, the Harddrive launches the OS in our case a Linux OS 'Ubuntu'. Once the laptop/ desktop is booted up, you can launch your applications from there. It passes on the information or applications that are being used to the RAM, which then get transferred to the CPU. The Harddrive is a very slow piece of equipment. Thus, we now have developed a new component called the Solid State Drive (SSD). 

(The heavy, slow, faulty Hard Disk Drive)

CPU - As the name speaks for itself, the CPU (Central Processing Unit) is the central area of processing data, which gets projected on your laptop/ desktop screen. The CPU also processes applications, games, etc. which then is projected onto the screen.

(Metal flap is the shield of the CPU. Little 'hook' on the left of the image)

(CPU Chip. If you flip the CPU chip over, you can see a little gold triangle in one of the corners)

The 'little golden triangle' is for you to make sure you insert the CPU back into its shield the right way.


Powersupply - Again, the name tells you all about it! The power supply supplies the main components with electric currents. 

(The large wire is the powersupply wire coming out from the powersupply unit)

Case - The function of the case is simple, to protect the internal competents, and to act as a external barrier and infrastructure. The case is built with many holes around, the 'holes' can be audio jacks, USB ports, Ethernet ports etc. 

(The case of the PC is located to the left, and has already been removed)

How to take apart a PC (Desktop)
Steps:
1. Unscrew all screws that are holding down the case.
2. Get a camera to record each step, and each process.
3. Start unplugging all the wires slowly and cautiously. If there are some wires that are hard to pull, do not forcefully pull them out. 
4. Then slowly, lift a hook-like object which holds down the CPU, and then carefully take out the CPU chip. Note - CPU looks like a SD Card, and is covered by metal. 
5. Then locate the RAM, the RAM looks like 3 long pieces of green beef jerky. There are 2 levers, after lifting the two will release the 2 / 3 pieces of RAM
6. Locate all the screws that are holding the Motherboard down, and unscrew all of them. Note - The motherboard looks like a large piece of green beef jerky. The motherboard is the component that is at the bottom. 
7. Basically, that's all to it! ... 
8. Except, after you finis taking apart your PC, and finished reassembling it. You may also consider installing an OS (Operating System), we used an Linux OS called Ubuntu. All you need to do for installing an OS, is simply click on your mouse, and wait. 
9. Enjoy the process! 


After having fun taking apart your PC and venturing through all the different components, and after you finish installing your OS. Then you can connect to an network, and start interacting with other people on the web.


Connect to a Router - "Use an RJ45 cable to connect your computer to a router."


Talk to Another Computer - 
"Open up Terminal
Find your IP Address 
Ping a friend/ colleague etc. - ping (classmate IP)"


Pinging websites - 
Open up Terminal
type in: host www.(whatever website you wish to go to).com
Terminal should then unfold 6 or more lines with numbers that read 72.14.203.106 etc. Not all of them will be the same, since the website may have multiple server locations
After that, you can simply copy '72.14.203.106' to your web browser and it should lead you to Google
That is to find the host server location
To cancel the 'requests' press Control C (On Mac) 
Then type: ping www.(whatever website you wish to go to).com and numbers should flow out again. 
You can also use them for connecting to the website you so wished for.


My Personal Experience with Computers
Being honest with you, I've never understood a computer. I've never been good at using one, and probably never will be as good as other classmates of mine. I've always been inept about how they work and how to use them. 


I only learn the primary things about them, such as how to use documents, how to save your work, how to access your e-mail and so on. 


So I have gained valuable knowledge and experiences throughout this whole entire unit, although it has not finished yet. I've learnt more in-depth about how computers work, how they are built, and how the interior looks. In fact, I've never thought once before outside of school, how does a computer connect to a network, (seriously, no joking). If I would have not been involved in this unit, I would never have acquired the knowledge about the 6 key components of a computer, and how they work. Ironically, all of those 6 key components are used in things such as mobile phones, televisions, printers, etc. 

What we do in Music Class

On this blog, I've never introduced what we do in music class. Although we won't be attending any more music classes this year, last year we had lots of fun.

Eagles - Wasted Time

For one of our projects, we used a file like the above, and copied it into a software called Finale Notepad. And then, we had to add our own tracks to it such as Riff, Harmony, Melody, etc. And it was a fun process for me to translate the notes from Scribd to the actual Finale Notepad document as we had to punch out every note individually with our trackpad. And I ended up making 4 more extra tracks, and it sounds really well!