It is a good opportunity to get in touch with your professor to learn the material well. There are times where they will tell you what to exactly study. Making friends in class will also help. Bring a tape recorder to rewrite notes as needed.
TEAS was a lot of repetition when I took it. The math section tests middle school math. There were a lot of fractions, decimals, and mixed numbers that needed to be subtracted, added, divided, and multiplied. I would recommend using online worksheets if you need additional practice. I have also seen people use textbooks for practice problems.
Science contains more information about first semester biology 1 for bio majors. I would recommend a tutor, or a classmate majoring in biology for good review sources. It also tests on very basic chemistry such as concentration after 4 or 5 titrations.
Grammar has questions about punctuation, capitalization, and proper placement of colon, semicolon, and commas. There are a lot of online worksheets to practice from. Tutors are a good resource if you have trouble with punctuation.
Reading comprehension tests directly from short passages read. I found ATI concepts were helpful in answering most of the questions. You can also look into short high school reading passages.