The preflight is often covered on the first or second lesson, and then CFIs put students in charge in determining if an aircraft is ready for a flight. And while a checklist should always be used, not everything is defined on a checklist.
In another article, I discuss the preflight on the CFI checkride, and things that applicants should specifically mention. I created a quiz (free printable PDF right here) which tests some of these things. The quiz is also below. It is by no means comprehensive, but designed to check some of the basics.
Piano Hinge Alternator Belt Oleo Strut
Beacon Light Cotter Pin Fuel Vent
Elevator Trim Tab Vertical Stabilizer Static Port
1. Alternator Belt
2. Piano Hinge
3. Oleo Strut
4. Cotter Pin
5. Vertical Stabilizer
6. Fuel Vent
7. Static Port
8. Beacon Light
9. Elevator Trim Tab