I have outlined the things in three categories Input, Writing and Visualization. You see a picture or a homework, you see it i.e. you store it to your brains -- or you can scan it with your iPad or iPhone. You realize you want to add some material to it so you may add a photo -- vizualisation -- or write something.
I. Readdle Scanner: photocopy & edit to adjust lightness etc and to store physical
II. Mathematical Apps such as Quick Graph, Sage Math and TouchDraw to process mostly mathematical ideas
III. Conceptual tools such as general-graph-tool iThoughtsHD and linguistic-analysis-tools such as Wordflex
I. TeX Writer
II. Business apps such as Pages, Numbers and Keynotes to generate things fast
I. PDFPen (if you need only merging, check PDF Merger)
III. GoodReader (somewhat limited editing tools)
II. Echograph for generating short GIF videos from images
I have tried most collage apps in iPad and iPhone but I only like the following
I. MyFrames app
II. FrameArstist app
Somewhat-marketed apps such as Layout have bugs in writing and developer not responding and apparently not developing anymore.
Personally, I use a massive amount of different editing tools. You can see some results here. It is sometimes slow when missing the right tool but generally I really like doing one thing well even though it may take a bit more time.
It is pretty easy: you see something, you process it somehow and in every step you may need a specific app for your purpose. For brainstorming, you may want to have a look in
input part while editor may want to look at
vizualization part and
writing part. I use the above tools but my tools will change because the environment changes. When I started with iOS, I had no OSx but later I got it making some steps easier -- however I am able to write long essays with photos and graphs in iOS without touching a proper desktop. It is not however the most efficient way of doing things so I use nowadays iOS besides OSx.