Naomi, I don't know if you still need this or not, but I had to write a few tests last year, which were administered to someone in a room with no laptop, no mobile device, etc.
The tests would say something along the lines of "you have Table A, table B, table C, here are the columns, here are 5 sample rows.....and you need to produce the following output result set....which of the four SQL statements would produce the correct result?" The questions would test things like whether the person knew things like...
- what you can put in a HAVING (and when a HAVING is appropriate)
- difference between an outer and inner join
- what you can put in a WHERE
- aggregation
- identity keys (some of the questions would be 4 different statements to do an insert)
- subqueries
Unfortunately, I can't really provide the questions (NDA, etc), but hopefully this will spawn some ideas (assuming you still were looking for something)