You don't need to open the app to do this - it's all done very cleverly from the superb search options we have built into BlackBerry 10.
For us folk that like to be productive and get things done with the shortest amount of effort this is one of the places where BlackBerry 10 really shines.
To quickly add a note to the Remember app simply follow these steps:
The same applies for adding a task to Remember - just follow the above steps but type the word 'task' instead or 'note'. It doesn't get much easier than that. Once again - another example of how fast and fluid the whole BlackBerry 10 experience can be.