What is this called in English?
3) blank page
I'm a little confused about the acceptable name.
Context: "Do you want one (here is one of this three options) to write down the exercise?"
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Are you talking about a single piece of paper, that's not attached to a book? If so, don't use either "page" or "blank page", because a page is a sheet of paper bound inside a book. Technically, a page of paper is only one side of a sheet. If you wanted to talk about the sides of a single loose piece of paper, you'd just say the "side of the paper". Thus "page" is not used in the context of single pieces of paper.
You could use:
And because "sheet" is so specific of a word, sometimes people drop "of paper" in "sheet of paper"
I guess you could technically do the same with "piece of paper", but "piece" is too vague, so people don't usually drop "of paper".
P.S. Wikipedia tells me the technical term is a "leaf of paper", but nobody says that in daily use.
In American English, one would most likely say
Do you want a (blank) piece of paper.
Do you want a (blank) sheet of paper.
Notice I said a and not one. When we are offering people just one of a particular thing, we usually say/use the indirect article if we name the thing, as in this case. If we don't name the thing, we say Do you want one?
Note that the object shown in the photo is also called a (blank) page, but one would not ordinarily ask for a page in your context.
The object is also one piece/sheet/page of loose leaf paper if all the pieces/sheets/pages are separate and not attached to each other, as they are in a bound notebook.
There isn't a single word for this unless you exclude "paper" from the count. But both "lined paper" and "notebook paper" should be understood to mean this type of paper. Without the lines, it is is typically called "blank paper" or "copy paper" (used to be "typewriter paper", but I doubt it is called that by many nowdays).
Any piece of paper used for writing would be called a sheet.
If you look at a package of such paper, it will say (for example) 1000 sheets.
page generally refers to an already printed piece of paper, such as in a book or magazine. If a page in such book or magazine were blank (no printing), that would be a blank page.
This is called "loose leaf paper".
Typically loose leaf paper has straight blue lines with pink margin lines. This type of paper is normally sold in packs of 100 or 200 sheets and are not necessarily sold loose which means they can be torn out of notebooks with perforations. Loose leaf generally has three holes so that the piece of paper can fit into a three-ringed binder.
Weird name? Yes, but that is what it is. At least, in English.
(I have also heard it casually called "notebook paper" but that is more vague, and could mean anything. Loose leaf paper would imply the holes and the lines you are speaking about more specifically.)