Below is a compilation of websites and curriculum publishers offering free (or mostly free) downloadable and online assessments that you can use to help you place your child in a suitable grade, purchase appropriate course materials, or identify subject-based skills your child has mastered or needs to learn. You can filter this list by subject or grade level.
Sonlight's online reading assessment for grades K-4.
The Texas Education Agency’s STAAR assessments and answer keys.
Institute for Excellence in Writing’s The Phonetic Zoo spelling placement tests.