More Maths.

(Please, try and solve the questions if you want)

The first thing I would like to rant about is this question.

Actually, I tried to do this question again later that day. I mean, this question had negative exponential, not to mention an irreducible denominator. Of course, as leaving the question blank during the exam, I HAD to try this at home in my own sweet time.

I proceeded to write down the question first.

Then stare at it blankly for a few moments.

After which, I lifted the marker and tried to see how far it leads too. After 10 minutes of agonizing, I got this.

What an idea! Bring the negative number down of course, for 1/e is actually e^-1. So it will end up like the above. So... Then what?

Ok...maybe this is not the way. A dead end has been approached. Erased it.

No wait!

How about:

Ok fine that is SO wrong. You cannot cancel exponentials like that. I know you had to do some substituting, but it looks from here it can't! The "u" is supposed to cancel out the "x", which doesn't here.

After 40 minutes, I quit. To solve for another day.
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"This is retarded" I thought to myself when Ms. Lee (Adv. Maths lec.) gave the answer.

The secret was to change 1+e^(-x)=u by bring over the 1 so that you get u-1=e^(-x)

WHAT THE HELL.

Then of course, you proceed to substitute accordingly. Working is below.


Another question for you to try.

Not many got this correct.
Try and list your working :)


This question is easy (Well, after the exam it was). Just use long division.
This one is a mad one. "Manipulate the question to your liking" Its like how in the world am I supposed to think so far ahead with this question? I dont think 4-x looks like 2x+10 seriously. I would need to multiply by 2 and +18 to the equation. what is this. MANIPULATION.


And finally this one. I was surprised when I got it right lol. Cause this does look more complicated then most of the above questions.