grammaticality - Omitting the last "to" in "All {I need to / have to / must} do is (to?) do something"

I remember I learned a structure like the one that this post’s title mentions:

All I {need to do | have to do | must do} is do something.

But is it correct to use "to do something" after the "is" — as compared with just plain "do something" without the "to"?

Or to be more specific, which of the following sentences in each pair is correct, or are both version correct? The second one in each case adds "to" to the formula:

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Pair #1:

1. 
   

   All I must do is prepare myself for the test.

   
   


2. 
   

   All I must do is to prepare myself for the test.

   
   

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Pair #2:

1. What we should do is teach children how to think.


2. What we should do is to teach children how to think.

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As far as I could remember, both forms should be fine. But it seems that all the materials, texts, and articles I've read so far use the first form only.

Furthermore, I'd really appreciate it if you could show me some references, like webpages or some book, where I could find more information about this point.

Answer

Both are grammatically correct. The first is the one I'd use and is the idiomatic one. The second sounds fine and there's nothing wrong with it, but only less idiomatic and that's why you don't see it in your written materials. In addition to that, the to in there is unnecessary and doesn't really add anything to the overall meaning of the sentence. Most grammar books should cover these topics, but personally I am not aware of one. On top of that, that part of your question seems a bit off topic on this site. Good luck with your grammar.

Edit

Here's a link to Google Ngram that supports my assumption. Thanks to Peter for providing that.