'Scratch paper' does exist. It's low-grade paper manufactured specifically for rough work, notes and so on. 'Scrap paper' refers to paper which has been used or partially used and then discarded. Perhaps you've already printed on one side of it. 'Rough paper' could also be used in the context of an exam, to distinguish this paper from the paper where the students write the answers to be marked.

Scrap paper. There is no such thing as scratch paper. " At school we keep some paper for recycling, and we give students this scrap paper for them to take notes on. What do you call this kind of paper? " Hope this helps!

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