Linear Programming

Click on the link below for the tutorial:

https://docs.google.com/file/d/0B9veYrYAicH_NWNFaUhmamMxZ28/edit?usp=sharing

Motion in a Straight Line

Click on the link below for the tutorial:

https://docs.google.com/file/d/0B9veYrYAicH_bGZJTEJrWlVZdnc/edit?usp=sharing

Probability Distributions

Click on the link below for the tutorial:

https://docs.google.com/file/d/0B9veYrYAicH_VEkxVDFjX0wzbU0/edit?usp=sharing

Probability

Click on the link below for the tutorial:

https://docs.google.com/file/d/0B9veYrYAicH_ZlVpRi1mSkMySVE/edit?usp=sharing

Permutations and Combinations

Click on the link below for the tutorial:

https://docs.google.com/file/d/0B9veYrYAicH_QV9RUXRVTjRJQWs/edit?usp=sharing

In Malaysia, registration numbers are generally made up of a maximum of 3 letters on the left and a maximum of 4 digits on the right, as shown in the diagram above.

The first letter indicates the state in which the motor vehicle is registered. The list below shows the first letters and their corresponding states:

A: Perak
B: Selangor
C: Pahang
D: Kelantan
J:  Johor
K: Kedah
L: Labuan
M: Melaka
N: Negeri Sembilan
P: Penang
Q: Sarawak
R: Perlis
S: Sabah
T: Terengganu
W: Kuala Lumpur (KL)

Note that "H" is for taxis and "Z" is for the military.

"H" means "taxi", while "B" means "Selangor", so it's a taxi registered in Selangor

The letters (except for I, O and Z) and numbers are issued in a sequence (from A to Y and from 1 to 9999). Let's take KL as an example. 

- The 1st phase starts from W 1 and ends with W 9999

- The 2nd phase starts from WA 1. Then it's on to WA 9999, WB 1 to WB 9999 and so on until WY 9999.

- The 3rd phase starts from WAA 1 and ends with WYY 9999.

The same case applies to the other states. Using permutations, the 1st phase allows for a maximum of 9999 vehicles, the 2nd phase 23 x 9999 = 229 977 vehicles and the 3rd phase 23 x 23 x 9999 = 5 289 471 vehicles. So, in total, there can be a maximum of 5 529 447 vehicles for each state.

You might think that's a lot, considering that the population of Malaysia is still less than 30 million. However, guess what? KL will reach the end of the 3rd phase before the end of 2013! What happens next?

No wonder KL's about to enter phase 4 of the registration number series!

Answer: KL enters the 4th phase, which will start from W 1 A. Then it will go on until W 9999 A, W 1 B,... W 9999 Y, WA 1 A,... WY 9999 Y, WAA 1 A,... and end with WYY 9999 Y. This phase will allow for 127 177 281 (which is roughly the population of Japan) extra vehicles.

An example of Kuching's 3rd phase registration number 

In Sabah and Sarawak, the system is slightly different. For both states, the 2nd letter indicates the division/ district in which the car is registered. For examples, QA indicates (Sarawak - Kuching), QM (Sarawak - Miri) and SA (Sabah - West Coast, which includes Kota Kinabalu).

So, taking Kuching as an example, its 1st phase starts with QA 1 and ends with QA 9999. The 2nd phase starts with QAA 1 and ends with QAY 9999.

In 2011, Kuching reached the end of the 2nd phase and its 3rd phase, unlike KL, started with QAA 1 A and will end with QAY 9999 Y. So, the maximum number of vehicles in Kuching division will be 5 529 447.

The 1st and 3rd phases for Sabah are the same as that for Sarawak, but not the 2nd phase.. Taking the West Coast for instance, the 2nd phase begins with SA 1 A and ends with SA 9999 Y (instead of starting with SAA 1 and terminating with SAY 9999).

So far, only Kuching and Sabah's West Coast have entered the 3rd phase. Miri, Sibu and Tawau are coming close, though.

The first 2 characters of Chinese license plates form the "area code". For example, 陕A is for Xi'an city while 苏E is for Suzhou city

The picture above shows some license plates in China, where the Chinese character indicates the state/ province and the letter after it the district or city in which the vehicle is registered. These two characters form the "area code", and there are 5 more "places" after it. A few decades ago, all 5 places used to be filled with numbers only (from 00000 to 99999), giving each district a maximum of only 10 000 vehicles.

However, as urban populations increased, this became insufficient. So now, the first 3 places can each be either a letter (except I and O) or a number. The remaining places will consist of numbers only. This system thus allows for a maximum of 34 x 34 x 34 x 10 x 10 = 3 930 400 vehicles per district.

Even then, it's still not enough for mega-cities like Beijing, Shanghai and Tianjin. In view of that, while most districts in China have only one area code each, Beijing has 9, Shanghai 7 and Tianjin 12! Using simple maths, the maximum possible registration numbers in the 3 cities are 35 373 600, 27 512 800 and 47 164 800 respectively! In comparison, the most populated city in China (Shanghai) has just over 20 million people.

In China, registration numbers are not issued according to any sequence. Instead, they are randomly generated by computers.

References:
1. http://en.wikipedia.org/wiki/Vehicle_registration_plates_of_Malaysia (retrieved 10/08/13)
2. http://en.wikipedia.org/wiki/Vehicle_registration_plates_of_the_People's_Republic_of_China (retrieved 10/08/13)
3. http://en.wikipedia.org/wiki/List_of_cities_in_China_by_urban_population (retrieved 12/08/13)
4. Zuhrin Azam Ahmad (2013) "KL Car Number Plates to Bear 'W1A'", The Star, 24 May [Online].. Available at http://www.thestar.com.my/News/Nation/2013/05/24/KL-car-number-plates-to-bear-W1A-Ministry-announces-new-vehicle-registration-series.aspx (accessed 10/08/13)

Trigonometric Functions

Click on the link below for the tutorial:

https://docs.google.com/file/d/0B9veYrYAicH_ZnNfLVZsZlJIMms/edit?usp=sharing

Note: You may need to download this file in order to view the embedded Power Point slides.

Vectors

Click on the link below for the tutorial:

https://docs.google.com/file/d/0B9veYrYAicH_dkIzV25FdGR1clk/edit?usp=sharing

Note: You may need to download this file in order to view the included Power Point slides.

Integration

Click on the link below for the tutorial:

https://docs.google.com/file/d/0B9veYrYAicH_N2g0ZnJxb3V1Nk0/edit?usp=sharing


You probably have heard about the story in which "Isaac Newton discovered gravity after an apple fell from a tree onto his head". Well, there's actually a lot more to the story than this (and not all of them are pleasant).

Isaac Newton (1642 - 1727) and the falling apple

The change in position of several objects due to gravity can be worked out using calculus (differentiation and integration). Evidently, calculus was developed (independently) by Newton and another mathematician named Leibniz. Yeah, you probably have never heard of the latter, because Newton stole all the credit for himself and even accused Leibniz of stealing his ideas. 

Gottfried Wilhelm von Leibniz (1646 - 1716)

The symbols for differentiation and integration we use today were invented by Leibniz. On the other hand, Newton just used whatever symbols he could think of on a certain day. 

With calculus, Newton managed to describe accurately the movements of the planets known at that time. Guess what? Unlike the other planets, the presence of Neptune was predicted using equations for gravity long before it was observed!

Neptune - the first planet to be mathematically predicted before observed. Wind speeds during thunderstorms on this plant may exceed 2 100 km/h!

All bodies exert gravity, and the larger the body, the larger the gravitational force. Prior to the first sighting of Neptune, scientists had observed irregularities in the orbit of Uranus, which was due to the gravitational influence by the gas giants Jupiter and Saturn. However, even after incorporating the mass and motion of those two planets, the resulting equation still couldn't explain the behaviour of Uranus. 

So, scientists hypothesized that there must be another planet influencing Uranus's motion and, using calculus, predicted where the "new" planet might be. Finally, in 1846, Neptune was sighted - almost exactly at the predicted position! 

The orbit of Uranus is significantly affected by those of Jupiter, Saturn and Neptune - the clue to the discovery of Neptune

Today, we know that our universe is made up of four forces (all of which are calculus-based):

1. Gravitational force
2. Electromagnetic force
3. Weak nuclear force
4. Strong nuclear force

All these forces interact with each other, and as of now, scientists have managed to explain (with very high accuracy) how the last three forces interact. In view of that, the ultimate goal of Physics is to find an equation which incorporates ALL four of them, and when that day comes, it will open our eyes to a multitude of new technologies which are way beyond current imagination!

Today, rockets are powered by fossil fuels. Who knows? In the future they could well be propelled by nuclear power, laser beams, ionized atoms, superheated hydrogen or even antimatter!

References:
1. Michio Kaku, 2008, Physics of the Impossible, Doubleday Publishing
2. Stephen Hawking, 1988, A Brief History of Time, Bantam Dell Publishing Group.
3. http://www.uiowa.edu/~c22m025c/history.html (retrieved 08/08/13)
4. http://csep10.phys.utk.edu/astr161/lect/history/perturbations.html (retrieved 08/08/13)

Linear Law

Click on the link below for the tutorial:

https://docs.google.com/file/d/0B9veYrYAicH_amxQOGRIUEp0Zkk/edit?usp=sharing

Progressions

Click on the link below for the tutorial:

https://docs.google.com/file/d/0B9veYrYAicH_VHhwcWtRN1FURUE/edit?usp=sharing


In the 18th century, a primary school master in Germany asked his students to find the sum of the numbers 1 to 100. This certainly kept the students busy until the end of the lesson - except for one boy.

Karl Friedrich Gauss (1777 - 1855)

In just a few seconds, Gauss wrote the correct answer (5 050) on his slate (a small blackboard) and handed it up to his teacher. The teacher was certainly dumbfounded, and when Gauss was asked how he got to the answer so quickly, he replied:

"I noticed that 1 + 100 gives 101,  2 + 99 gives 101 and  3 + 98 also gives 101. There are 50 such pairs of sums so 101 x 50 = 5 050!"

So, did Gauss pave the way for the formula below? What do you think? 

Biography reference: http://www.math.wichita.edu/history/men/gauss.html (retrieved 07/08/13)

Index Numbers

Click on the link below for the tutorial:

https://docs.google.com/file/d/0B9veYrYAicH_VU01Q0RDNTRLOU0/edit?usp=sharing


Ever heard of the term "stock" or "share"? It's actually the amount of ownership of a company.(usually a public limted company @ syarikat awam berhad). For example, a new company tenders 1 million shares for sale. If you buy 10 000 of them , then you own 1% of the company.

When a newly-established company opens its shares for sale for the very first time, the value of each share will normally be RM 1.00 or RM 0.50. This initial value is known as the par value. As time passes, the price of the share will increase or decrease, depending on how well the company is performing.

Take for instance Public Bank, which was listed as a public limited company in 1967. At that time, the price for each share was RM 0.50. Over the years, it expanded and became more successful and as of 4 Oct 2013, its share price has shot up to RM 17.90 (only a very small percentage of public limited companies in Malaysia have share prices exceeding RM 10).

The share price (in RM) of Public Bank for 4 Oct 2013 (upper graph) and for the past 1 year (lower graph)

A stock index is a composite index of a few selected stocks (of different corporations) and their respective weightages. It is frequently used by investors to determine how much profit they can get from their investments in a region. In Malaysia, the stock index is Bursa Malaysia (for Hong Kong, it's Hang Seng while for New York, it's Dow Jones).

The typical view inside a stock market office. The large electronc boards display the real-time share prices 
for many different companies

As a matter of fact, the general formula employed to calculate the stock index is no different from what you'll be learning in this chapter:

However, the conditions are different. For example, the base year (for Bursa Malaysia) is 1964 and the value of the index keeps changing every second (it is not static). Take a look at the chart below:

The value of Bursa Malaysia between 30 Sept and 4 Oct 2013 (upper graph) as well as between Oct 2012 and Oct 2013 (lower graph)

References:

1. http://www.klse.info/counters/chart/stock/1295 (retrieved 5 Oct 2013)
2. http://www.pbebank.com/corporate/ (retrieved 5 Oct 2013)
3. http://en.wikipedia.org/wiki/Stock_market_index (retrieved 5 Oct 2013)
4. www.bursamalaysia.com (retrieved 5 Oct 2013)
5. http://finance.yahoo.com/q/bc?s=%5EKLSE (retrieved 5 Oct 2013)

Solutions of Triangles

Click on the link below for the tutorial:

https://docs.google.com/file/d/0B9veYrYAicH_eU9nZ3hkbncyREU/edit?usp=sharing

Differentiation

Click on the link below for the tutorial:

https://docs.google.com/file/d/0B9veYrYAicH_dkxZV3JYYWE3eFU/edit?usp=sharing

Note: you may need to download this file in order to view the embedded Power Point slides.

Circular Measure

Click on the link below for the tutorial:

https://docs.google.com/file/d/0B9veYrYAicH_ekRqekh5dzdhTHM/edit?usp=sharing

Statistics

Click on the link below for the tutorial:

https://docs.google.com/file/d/0B9veYrYAicH_RnZ6ZHdTYU1ab3M/edit?usp=sharing

Coordinate Geometry

Click on the link below for the tutorial:

https://docs.google.com/file/d/0B9veYrYAicH_WEZodFZRWGFxQmc/edit?usp=sharing

Indices & Logarithms

Click on the link below for the tutorial:

https://docs.google.com/file/d/0B9veYrYAicH_a19SVzZTUHp5Mms/edit?usp=sharing

Simultaneous Equations

Click on the link below for the tutorial:

https://docs.google.com/file/d/0B9veYrYAicH_ZVhsZlVobmZZOGs/edit?usp=sharing

Quadratic Functions

Click on the link below for the tutorial:

https://docs.google.com/file/d/0B9veYrYAicH_YzhtOExmNENLX3c/edit?usp=sharing

Quadratic Equations

Click on the link below for the tutorial:

https://docs.google.com/file/d/0B9veYrYAicH_NHYtX2ljUW1IRlk/edit?usp=sharing

Functions

Click on the link below for the tutorial:

https://docs.google.com/file/d/0B9veYrYAicH_N1hkZVNTQ0UxUHc/edit?usp=sharing

Introduction

Hello and welcome to Add Maths - PWNED!. Before getting started, please be informed that the main purpose of this blog is to help you enhance your prowess in Add Maths and as such, basic knowledge in all topics in your syllabus is expected. However, do not rely on the content in this blog alone, as it's definitely not going to be enough.

I doubt that this blog would be helpful to those scoring 50% or below, but to all others, it is sincerely hoped that upon completion of this blog, it would be able to help you boost your memory in the methods for tackling questions. With luck, the material contained here will be able to make Add Maths a "no-need-to-study-for" subject so that you can divert the extra precious time to other "tougher" subjects like Bio or Chem. Trust me, with sufficient understanding, Add Maths can be a very easy subject indeed; it's one of the very few subjects where you can technically score full marks.

Every tutorial in this blog will contain some of the following sections:
A. Introduction; which elaborates on the general properties in the chapter concerned
B. Essentials; which highlights the important stuff you need to know in the chapter. It's rather like a chapter summary.
C. Explanations
D. Logic chip, which explains the logic behind formulae or workings (these are usually extra info)
E. Calculator-smart; where you'd learn how to get the most out of your calculator for that chapter.
F. Check-smart, where you can get the lesser-known or alternative ways to verify the correctness of your answers.
G. Brain squeezers, or in normal terms, exercises.

Fonts of different colour will be used throughout the tutorials... and they have the following meanings:
Yellow: Sections in the tutorial
Orange: Important info
Pink: Examples
Green: Buttons on your calculator
Blue: Things to watch out for/ common pitfalls 

Take note that there will hardly be any exercises in the tutorials... you can easily get them from your workbooks and practice papers. Besides, the examples provided here are more aimed at promoting your understanding of a subject matter, and may not reflect the way exam questions are set.

For your very first tutorial, click on the link below (since i can't easily make tables or write equations on Blogger). 

https://docs.google.com/file/d/0B9veYrYAicH_Z3hKU3ZtbHZoLUk/edit?usp=sharing

Feel free to air your views about the effectiveness of this blog later on. Also, I'm not an active "blog-walker" so don't be offended if I don't go around liking or commenting on your respective blogs (if any). I've tried my best to ensure that the content in the tutorials is compatible with that in the syllabus and so will not be liable for any untoward occurrences resulting from direct or indirect reliance on the information presented in this blog. 

In the meantime, have fun! :)