For Mathematics see the Mathematics Syntax page which has several slideshows of examples with their resulting queries.
The WolframAlpha Tour includes a useful Basics section, see also Examples. Note that one can subscribe to WolframAlpha hence the Personalise and Pro sections but free use offers an unlimited number of queries every day (and additionally in Mathematics three step by step solutions).
From h+ Magazine a comprehensive Users Guide to WolframAlpha
Mathematics Lesson Plans from WolframAlpha for Educators
10 questions younger children could try – Wolfram Alpha blog entry
10 more fun questions kids can answer with WolframAlpha – WolframAlpha blog entry