Does APA style require a cover page for short student papers? My students are required to use APA style. I'm familiar with the research paper format, which requires a separate title page (like a cover page). This makes sense for longer papers, but how should students format the first page of a one- or two-page assignment?

My question is: What do students do if the paper is one to two pages? How do they format their name and information w/o a title page?

In the style guides, I can only find information for research papers.
General points: APA style is principally designed for submitting manuscripts to academic journals. 

When it is used as a style guide for student assessments at universities, it is common for the requirements to be adapted. So for example, many people completing honours, masters, or PhD theses in the behavioural sciences will use APA style for referencing. But their university may have other requirements for the formatting of title pages, heading formats, line spacing, paragraph indentation and so on. Or these details may be left up to the student.

If you are setting the assignment, you are free to pick and choose which aspects of APA style you want students to follow. 

Your specific question: Note that APA style calls it a "Title Page" rather than a "Cover Page". Any manuscript submitted to a journal using APA style requires a title page (i.e., with title, author names, affiliations, author note, etc.). Those who create a university assignment based on APA style are free to adopt or not adopt aspects of APA style when it pertains to APA style. In some respects it doesn't even make sense to fully adopt APA style for Title pages on student assignments. For example, you wouldn't require them to provide a "corresponding author address" (a key requirement of APA style title pages), but you would require them to include their student number.