The big thing for Sec 4 A-Math ( Oh yar, since this blog has quite a number of visitors from other countries, I think it is important for me to mention that Secondary 3 - 4 is known as Grade 9 - 10 in other countries) is CALCULUS.
Well, you will hardly find this word in your A-Math textbook but you see a bulk of the chapters dedicated to Differentiation & Integration. These 2 topics are like freezing and melting processes.
Why? Because they are simply opposite of each other !
I am going to talk about the techniques of differentiation.
There are 3 main types for Sec 4 level ; you ought to learn these techniques real well and know when to apply each one of them as application problems follow after the basics.
- Chain Rule
- Product Rule
- Quotient Rule reserved for fractions. * But some fractions can skip this rule
My personal favourite is No. 2 - Product Rule. Well, let's see the technique in action.
Differentiate 
with respect to x:
Now to do this, you can apply Product Rule - Differentiate Copy + Differentiate Copy
so 
Now from this example, we notice some patterns, if you have a constant ( a fixed number) in front, you can simply focused on differentiating the portion with x involved. For example in this case, Focus on Differentiating 
so now, we don't even have to use product rule :
- Leave the constant in front
- Differentiate the portion with x involved by Power Front - Power Down by 1-Differentiate within also known as your Chain Rule. BINGO!
By realizing this pattern, it will save you some time and less pen ink as well.
Certainly hope it is useful.
:-)
alwaysLovely
Photo by just another paul