Are they determined to annoy you, or are they determined to get what they want....which annoys you? Your kid is trying to develop themselves and create a place in their own social structure that they see being built. Used to the social structure was predominately parental based, and as they get older, now there are friends in the equation too, and you are slowly losing influence. Which no doubt is frustrating.
It's times like this that instilling some understanding in the dangers of only seeking instant gratification will pay off.
I doubt she is purposefully trying to defy you or annoy you, I bet it is more like she is trying to find herself. If your way of doing things is the only thing she ever knew, she is going to want to do something different to see how well it works. I wrote a hub about making kids earn knowledge that talks about this.
My advice, be tougher than they are, and pick your battles, let them do things they will survive, even if they are mistakes....especially if they are mistakes. Sometimes you have to "do" to learn.