Here's how the Horizons math placement test works. If a student successfully completes the readiness test for Level 3, then the student should be placed into Math Level 3. Begin testing at the grade level the student should be in next. If the student does poorly, have them take the test for the previous level.

Fortunately, Horizons Math provides ready placement tests (which they call Readiness Evaluations) for each level. These are printable PDFs that contain a few straightforward math questions (10-15) to determine if a student has the necessary skills required to start a particular level.

Both Horizons Math and Saxon Math, helpfully, have free placement tests available for their respective curricula. Horizons Math placement tests are available on the AOP website, and can largely be found on any retail website that sells the curriculum. Saxon Math placement tests are available pretty much wherever the program is sold online.