This varies depending on where you live, but in general you will need:
If your school system has different tiers of class difficulty, you will need the most difficult tier of each of these classes
grade 12 Biology
grade 12 Chemistry
grade 12 English
As optional classes or required for pre-vet admission you should also take:
grade 12 Math
grade 12 Social studies
Personally i would also recommend taking either a Latin course and a sports medicine course so that you may become comfortable with Latin terminology and anatomy
Biology, chemistry, zoology
Good grades of course
Your classes in Middle School will have little affect on your ability to become a vet. Get good grades in Middle School and High School so that you can get into a good college. Then take a pre-med or pre-vet major and hope you can get into Vet school, which is very hard to do, even harder then medical school.
There are no math classes per se in vet school, although calculations are part of most classes. To apply for vet school you need to pass Calculus I, and sometimes Calculus II depending on the vet school. An introduction to statistics as well as basic business accounting and financial statements are also helpful.
English, math and science.
The only high school classes that are required are those that any college would require for admission. To prepare for the classes required so that one may apply to veterinary school it would be good to take Algebra I & II plus Trigonometry.
How many classes have been failed? You can also talk to your school counselor.
vet schools typically don't look at high school grades. in high school you have to do the best you can taking classes that are challenging but that you can receive an A or a B in. This way the likelyhood of getting into a better college is greater. Vet Schools will look at college grades. Most schools will dismiss anyone with a College Cumulative GPA of 2.8. The average GPA is likely about 3.4-3.8. Vet school is very competitive so getting atleast a 3.8 will certanily increase your changes.
In the United States, you have to take a minimum of three years of undergraduate classes followed by four years of vet school. Even if you can get all the undergraduate classes finished during high school and are accepted to vet school on your first application, you won't have a vet degree until you are 21. Also, many vet schools are likely to reject your application because you don't have the time to get the experience and references you need to successfully apply straight out of vet school. In practice, the youngest you could become a veterinarian in the United States is 24. Graduate from high school at 17, spend 3 years in undergraduate and then 4 years in vet school.
You can take AP Chemistry, AP Biology, AP Physics, AP Calculus or similar courses, but this will only count towards your undergraduate college classes. In the United States, you have to complete at least three years' worth of undergraduate college classes and then take another four years of classes in vet school.
In undergraduate college, you should focus on taking science and math classes, as well as a broad selection of gen-ed classes. This will help you get into vet school - in the United States of America, having a strong science background in undergraduate is a prerequisite of applying for vet school. In vet school, you can and should take as many equine-focused electives as you can, or you can sign up for the equine track (in the vet schools that track).
Specific high school courses will have little to do with becoming a veterinarian. You will need good grades to enable you to get into college and good grades there in order to get into vet school. For entry into a pre-vet program, you should focus on the sciences, especially chemistry and biology. Once in college, you should expect a mix of biology, chemistry, math courses to dominate your schedule. Ask your advisor to help you design a path for your journey to vet school. Work hard, because vet school is not for the faint of heart!