Your math teacher is suggesting the AP course because it will look better on your college resume. Colleges give a higher value to students that take honors, AP, and dual credit classes over regular course classes. Both courses will help you in the long run, but the AP designation with a good grade will look better on your college application.
Here is some generic college advice:
Leadership is a MUST on college applications! A job helps. My daughters were lifeguards, led vacation bible school, taught swimming lessons, were presidents of clubs, secretary or treasurer for other clubs etc. Peer tutoring looks good too. I have known students with and ACT of 35 that were not accepted into their preferred university because they did not have leadership activities.
Start college visits by fall of your junior year. You want to visit while school is in session if possible. Granted classes are in session in summer too, but it is better to see the campus when the majority of students are there so you can see how crowded it can be. You can see what campus food really tastes like. Remember that search engines like Google are your friends. You will get answers to your questions about those universities faster if you type them into a search engine rather than waiting for someone to reply to your question. Bloomberg Business Week and US News & World Report can give you information on the best universities for your degree program. About.com provides some useful information too. The university admission offices/websites are your best source in the long run about specific information. You can see residency guidelines that explain how to qualify for in-state tuition on the websites for each university as well so you can figure out what to do to reduce your costs if you what to go some where out of state.
By the end of your junior year arrange to do an internship in the degree field that you are planning to apply to at the university. Internships of 40 hours or more impress the admittance counselors. Even if your internship proves to you that you no longer want to get a degree in that field, it will still look good on your applications and give you something to talk about on your essays. High school guidance counselors can write recommendations and perhaps make suggestions on who you can ask about interning at their business. My daughters began asking businesses about internships in March of their junior year and it was worth it. Both of my older daughters did two-week internships in May of their junior years at Pharmacies. The oldest did it at a hospital and the middle did it at a retail setting. When we went to the oldest's college registration day last June, the counselor was amazed with her application/resume. She had already completed many of the things that they encouraged incoming freshman to attempt. If she keeps it up he told her she had a sure shot into their Pharm'd program. My senior in high school daughter has been accepted everywhere she has applied with half-tuition scholarships and she knows from her internship that she does not want to be a pharmacist so she was able to use that experience in her college essay writing for business school. I am hoping to get her to internship in business for a few weeks this summer to help her get a further leg up on her classmates.
Community service looks very good on applications. Try to do community service that allows you to actually work with people instead of just collecting things for others to disperse.
Begin taking your college exams your junior year of high school because you want to be finished taking them by September of your senior year for your initial college applications that are due before November 1st if you want to be considered for merit-based scholarships. An ACT score of a 27 can make you eligible to earn a half-tuition merit scholarship. An ACT score of 33 can make you eligible to earn a full-tuition merit scholarship. Never take either the ACT or SAT more than 3 times. After the third attempt many Universities begin to average your scores. Some Ivy League schools and certain degrees programs can require SAT subject tests. Math SAT subject tests are popular for business degrees and engineering degrees. Some schools require face-to-face interviews too.
You must choose a college major for your college application. Scholarships are usually handed out based on your field of study. Undecided is a bad choice! Many schools will automatically enter you into the race for some scholarships based on the information in your college application. Remember that most college students change their major 2 or 3 times before earning their undergraduate degree so it does not matter if you change your mind after you start at college. Just do not change it until after that first semester or year of college is over so they do not revoke the scholarship.
Complete your college applications between August 1st and October 1st of your senior year so that you are considered for merit-based scholarships. Due date is actually November 1st but the people you will be asking recommendations from may get swamped if you ask too late. If you set the goal of October 1st as your latest date, you give yourself breathing room if they do not write the recommendation that you want written...then you can find someone else. My older daughter completed hers before the end of September and was not stressed at all, but my middle daughter put hers off until mid October, which is also mid-term time. She was completely stressed out and so was I when she finally turned them in on October 27th, because we were unsure if all of her recommendations would get turned in on time. If you decide to apply to school after November 1st, those merit scholarships that are based solely on your college application will no longer be available and you will be stuck with trying to find other funding.
Between January 1st and March 1st of your senior year, you and your parents will need to go to the FAFSA website, get a pin, and complete a FAFSA application. This puts you in the running for financial need based scholarships/grants/loans. If you do not fill out the FAFSA you are not eligible for this funding. Federal Tax information is required for FAFSA. https://fafsa.ed.gov/
This article about FAFSA helps explain it well
http://www.moneytalksnews.com/2014/01/23/yes-you-can-afford-college-completing-the-fafsa/
Money-saving-tips for college
http://www.moneytalksnews.com/2014/01/27/yes-you-can-afford-college-6-money-saving-tips/
The article above is very worthwhile if you are you are worrying about paying for school. I would have paid for my older daughter to CLEP out of some college classes to add more college credits to the dual credit classes that she took in high school. As a result of this article, I now have a plan for my middle and youngest, since the state we moved to doesn’t have dual credits like Indiana did.
http://www.fastweb.com/ Is a web engine that finds scholarship offers and suggests them to you based on the information you input into your profile. It is free and many of the scholarships that they find can be applied for prior to your senior year of high school and all the way through your doctorate if that is what you are going for with your degree. If you start applying for non-degree specific scholarships in your early years of high school, you might end up with a tidy sum to start college. My college sophomore uses fastweb to search for scholarships that relate to her specific degree to find funding.
Good Luck!