Graphs Transformation

Pls click on the above pics for the full size

Also pls note that the order of TSRRST is also applicable for both the forward & backwards....meaning for eg. (backwards) to get y=f(x) from y=D + Cf (Bx + A), we will still start wif translation (T) ferst in the brackets by getting rid of A first by forming the eqn y= D + C f(Bx + A -A). Hence, the order still follows just that everything is by eliminating the form to get back y=f(x).

How to remember what sort of transformation to do?

Simple, always remember that those transformation along the x-axis or those that are in the brackets are always opposite of wat they meant. For eg in translation, y=f(x + a) means a translation of a units in the negative x-axis direction (to the left by a units // to x-axis) while y=f(x-a) means a translation of a units in the positive x-axis direction (to the right by a units // to x-axis).

For scaling involving the x-axis it is always a reciprocal of the number. For eg, y=(2x) will mean a scaling along the x-axis by 1/2 times. If its y=(Bx), it will be a scaling along the x-axis by 1/B times meaning multiply the x-coordinates by 1/B. For reflection involving the numbers in the bracket like y=(-x), it means a reflection about the y-axis. In summary, it can be noted that any transformation in the bracket is always the opposite of what is meant (for translation), a reciprocal of the number (for scaling) & about the opposing axis (for reflection). Simply put, anything in the brackets is about OPPOSITES.

For those transformation involving outside the brackets or involving the y-axis are quite straight forward because they are usually written to be exactly what it means. For example a translation of y=f(x) + a means a translation of a units in the positive y-axis direction (move up) n the reverse for y=f(x) - a means a translation of a units in the negative y-axis direction (move down). For scaling, there is NO RECIPROCAL FORM NEEDED, when it is written as y= 2f(x), it simply means scaling of factor of 2 units along the y-axis meaning just multiply the y-coordinates by 2 NOT 1/2! Only reflection still follows the general rule of being the opposite whereby y=-f(x) actually means a reflection about the x-axis. Simply put, anything out of the bracket is straight forward and is all involving the y-axis EXCEPT for REFLECTION!!!

After mastering the transformation for graphs, it becomes quite standard for questions involving graphs transformation. Just ensure that there are no carelessness.

Mechanisms 1

Here are the mechanisms for 3 types of reactions. Free Radical Substitution for alkanes, Electrophilic Substitution for alkenes and Nucleophilic Substitution for Halogenoalkanes/Alkyl Halides.

Alkanes mainly go through Free Radical Substitution (FRS) reactions, combustion as well as cracking. Since i have not included any mindmaps on alkanes, i shall proceed to describe more about alkanes for our syllabus. Hydrogen atoms are substituted by halogen atoms in FRS.

Combustion reactions for alkanes have a general equation of:

C_xH_y + ( x + y/4) O₂ (g)→ xCO₂ (g) + (y/2) H₂O (l)

Typical alkane questions would usually involve the application of this equation so i think it's important to memorise it. There will be clues to helping you find the values of x and y in the equation. One particular type i noticed is that they like to do combustion then run the resultant gas through limewater to remove the CO_{2. From there, just determine the number of moles of CO2} and you have found the value of x! Note that water formed is in liquid state, not gaseous state in the equation.

Another reaction to remember that alkanes undergo is cracking, which involves the breaking up of a large molecule to smaller molecules. Hydrogen gas is produced from cracking reactions.

For more information about Halogenoalkanes or Alkenes, please refer to the Chemistry section and search for a post with the appropriate title.

Mechanisms for the 3 reactions:

I've got one arm longer than the other!

Tired from studying? Looking for cheapthrills? Look HERE!

It would be weird to see one arm shorter than your other arm wouldn't it? Try this!

1) Stretch both arms out. Ensure they're of equal lengths

2) Bend either arm (your choice) back and forth as if you're lifting invisible weights for about 30 seconds. (Rmb to do this for only ONE arm)

3) Stretch both arms out and check their lengths. One arm should be longer than the other now!

Juice stains

Did you know?
Sometimes we spill juice on our shirt and have a tough time scrubbing them out. What do you do?!
Try using milk to make the cleaning easier! Lipids in milk can help "loosen" the juice from the shirt to make the cleaning easier.

Iodoform test

The iodoform test (or tri Iodomethane test) is used to identify the presence of 2 particular structural units:

1)RCH(OH)CH₃

2)RCOCH₃

*R denotes H, alkyl or aryl group

In positive tests, the reaction will produce a yellow precipitate of CHI₃.

Equations:

*Click on picture for a clearer and bigger view
Any compound which contains the above mentioned structural units will result in a positive iodoform test. Ethanol is the only first degree alcohol to give a positive iodoform test.

Learning Biology with a Passion

Why learn Biology?

Everyone has to read a manual someday.. whether its a new electrical appliance or your new handphone, everything's accompanied by a little booklet which desires to be read..

Biology is that little booklet to life..

What better manual would you read than the one that tells you how your body operates? The passion for learning Biology comes from realising the need to know how your amazing body is designed.

Studying Biology is often seen as memorising parts and pieces of the body... but do we really need to know all that? I personally feel it is more important to know the function of the body parts- simply because when one can understand the function, one can understand why the part is named so.

Ultimately, the career prospects that Biology offers is often misunderstood as being a Doctor a Brain surgeon or a lab person. But in reality, many biologist don't find place in these careers. They settle in other professions because their study of biology helped them realise their interest for their profession.

When you know your physical self well enough, a greater desire to understand the mental and ultimately spiritual self will arise. This is the reason why the debate over evolution's credibility is always heated, and will be explored in issues to come.

Simply put, the study of biology is practical because, if one studys and not Mugs (studying without thinking), one will defintely have to think and consider the meaning of life. And it often calls for every biologist to take a stand: for evolution or against evolution. To believe in science, or not to. This questions will satisfy the deepests of all insecruities life could bring.

I sincerely hope I have depicted the essense of studying biology as one of purpose, and not of mindless memory work. Indeed, the human boday and mind is the greatest secret anyone can behold!

Aldehydes and Ketones (carbonyl compounds)

Aldehydes and ketones are carbonyl compounds which undergo Nucleophilic Addition. The oxygen atom bonded to the carbon is electronegative, hence, the C atom becomes slightly positive. The slightly positive C atom is thus the target of nucleophiles. It is easy to remember the reactions that aldehydes and ketones undergo. The most important thing to remember for this chapter is the identification of aldehydes and ketones. This is done so by carrying out a variety of tests which you have learnt in the syllabus. It is also important to be able to draw the compounds that are formed when the respective tests are carried out, especially for Brady's test. I have not included the equations for the Iodoform test clearly in the mindmap below. Do not that the equations of the Iodoform test are just as important to memorise.

How to remember the special angles without the need to memorise or use the calculator

In math, there are group of angles known as special angles. They are 0, 30° (p /6 ), 45 ° ( p/4), 60° (p /3) & 90° (p/2) . These angles are usually needed in math topics such as trigonometry and complex numbers. Usually a calculator can be used however some answers require candidates to give it as the exact form meaning as a fraction. In this case there is no other way than to derive the sin, cos or tan of the special angles which often means memorising. However, there is a quicker way to derive it other than memorising as shown in the table below.

The key to using this type of table is simply the order in which for sinq is from left to right which is from 0 to p/2 radians with the exception that at 0 radians...the sin must be 0. From p/6 to p/2 radians onwards, the sin for that angle will be a fraction of denominator 2 with the numerator, the square root of 1 to 4 corresponding to the respective consecutive special angles. Obviously, some of the fractions can be simplified. Now once, the sin of the number can be derived, to find cos of the special angles is the opposite or reverse order from right to left. Whatever respective numbers that you have written for the sin q from left to right is now the cos q of the angles from right to left. For example, sin 0 = cos p/2 & sin p/6 = cos p/3 . Hence, it is very simple, to derive both sin & cos of the special angles. To find the tan of the special angles, you just have to know the formula that tan q = sinq / cosq and then you can use your already find the tangent based on the sin & cos of the corresponding angles that you have derived earlier. If you are used to the table, it can saved you time and as you get familiar with the table, you can sketch the table by around a min.

Does this table works for obtuse angles or larger angles?

As long as the angles can give basic angles which are the special angles, it will work. However, you must remember the quadrant rules,in which in the 1st quadrant all the Sin, tan & cos are positive, 2nd quadrant where only the sin is positive, the 3rd quadrant where only tan is positive and the 4th quadrant where only the cos is positive. I will illustrate with an example, 135° , the basic angle here is 45° and this angle lies in the 2nd quadrant and it happens that the basic angle is also a special angle. If you want to find the cosine it will be a negative since only sin is positive in this quadrant. So, based on the table, we find the cosine corresponds to 45° in the table and then add a - in front due to quadrant rule explained earlier on. This will give you the correct exact cosine of 135°. It also works for any other angles in the other quadrants as long as the basic angles are the special angles.

This table is quite useful as you can also use it for the inverse of sin, cos & tan to find the specific special angles. So really, it is useful if you guys could master this table.

Halogenoalkanes (alkyl halides)

Halogenoalkanes, otherwise known as alkyl halides, consists of one or more halide atoms bonded to a carbon. This is represented by R-X in the mindmap, where R is a carbon atom while X is a halide atom. Alkyl halides undergo 2 types of reactions, mainly Elimination and Nucleophilic Substitution. In Nucleophilic substitution( N.S), the halide atom is substituted by a nucleophile. Nucleophiles are molecules/ions with at least a bond pair. Common nucleophiles include cyanide ions, hydroxide ions and ammonia.

Summary of Alkyl Halide reactions:

Information in 1, 2, 3 steps!

To use this website more efficiently, here are some guidelines to make your search for information faster. The sidebar contains a categorial archive with various subjects under it.

1) Click on the desired subject you want to look at. Eg. Chemistry

2) Press (ctrl + F) to bring up a search box with your browser

3) Type a detailed word(s) which best describes what you are looking for. Eg. Alkenes. This will bring you to the post about alkenes.

There you are. Searching made easier. I hope the information will be useful.

Katakana/Hiragana table

Here for a quick post. This is the Katakana and Hiragana table. It is used in the Japanese language for writing. What else needs to be said. Refer to the table and start writing Japanese now! =)

As usual, please do not republish this image without permission.