Self Studying AP Chinese

I am going to be a senior next school year, and would like to start preparing for the AP Chinese exam next spring. I grew up speaking and listening to my parents in Mandarin. However, I have never gone to Chinese school and I don’t know much complex vocabulary, culture, or reading/writing. Do you guys think I can be prepared come next spring? Also what are study materials/textbooks that could assist me in the studying process?

If you already can speak the language and just need to expand your knowledge of vocabulary, culture, and the written language, it would definitely be possible to be prepared for the exam by next May.
When you learn more characters, keep in mind that the exam is typed, so you don’t necessarily need to learn how to handwrite the characters for the purposes of the exam. I think recognizing ~2000 words in writing should be enough to have little difficulty on the reading portion of the exam.
For the culture, keep in mind that you are not expected to know a great number of details about all possible topics in Chinese culture, just some general knowledge about important topics. The cultural presentation prompts are all very broad so that you can bring up what you have learned from your own experiences/study.
To prepare, I think working with authentic materials is the best, even if most passages on the AP exam aren’t at the level of, for example, Chinese newspapers or other authentic text. I’ve found the Chinese version of BBC news online to be useful in preparing for the exam, as it helped me learn vocabulary and writing. The Barron’s prep book will probably over-prepare you if you do all of it; in particular, the culture section has a lot of detail and advanced vocabulary (even my Chinese teacher, who is a native speaker, didn’t know one of the words they put in there!). If you want a textbook that focuses on basic-intermediate vocabulary and fundamentals, I suggest Integrated Chinese from Cheng-Tsui publishing.
Good luck!