hello everyone

I have a resit exam in a month on economic theory treated mathematically. for some reason i cant get my head around this course. I am working on the following problem:

"The utility function of a consumer is given by U = x1^alpha * x2^alpha ("alpha" is a positive constant) The individual has a fixed income M and is faced with fixed prices p1 and p2.

i.Calculate the demand fuctions of the 2 good, check whether they are homogeneous of any degree in prices and income and whether the goods are normal or inferior.

ii. Obtain the form of the indirect utility function and explain how it depends on p1.

iii. (this part i will leave for now)"

In theory i know how to do this and it should be easy but i never seem to get through one of these question. first off for the first order conditions do i just get the derivatives of the U equation or do i use monotonic transformation ( a big problem is that i never know when to use monotonic transformation, I know what it is supposed to do and its definition and everything but i still never impliment it correctly!) Once i know this i think i can do the rest (but will probably be back with more questions!)

What would really help would be too see some sample questions with model answers but these are hard to find on the web... anyone got any links? Thanks!!