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Different colleges and universities have very different expectations for your high school preparation in math. An engineering school like MIT will expect more preparation than a predominantly liberal arts college like Smith. However, a difficulty arises because the recommendations for high school preparation in math are often unclear, especially when you're trying to distinguish between what is "required" and what is "recommended."

High School Preparation in Math - From College Websites

Here's how several different colleges phrase their requirements:

MIT: "A strong academic foundation in high school both improves your odds of getting into MIT and will help you make the most of the Institute when you're here. We recommend that your high school years include...math through calculus"
(http://www.mitadmissions.org/topics/before/recommended_high_school_preparation)

Carleton College: "The strongest candidates for admission to Carleton have taken...three or more years of mathematics. ...At a minimum, applicants should have at least two years of algebra and a year of geometry"
(http://apps.carleton.edu/admissions/overview/rqments/)

Smith College: "There is no typical applicant to Smith and no typical academic program, but it is strongly recommended that a student prepare for Smith by taking the strongest courses offered by her high school. Where possible this should include...three years of mathematics"
(http://www.smith.edu/admission/firstyear_faq.php)

University of Texas at Austin: "3 units (4 recommended) at the level of Algebra I or higher: algebra, plane geometry, trigonometry, analytic geometry, elementary analysis, probability and statistics, solid geometry, calculus with analytic geometry, or number theory. Informal geometry, pre-algebra, and mathematics of money are below-achievement-level courses and may not be counted toward the mathematics requirements.

Strongly recommended: If you’re interested in studying architecture, business, geosciences, natural sciences, or other technical fields, you should prepare by taking math every year of high school."
(http://bealonghorn.utexas.edu/freshmen/admission/hs-courses/index.html)

Harvard University: Well, check out their requirements on the Harvard website. Essentially, in over 500 words they say that it's more important to think deeply about math than it is to take calculus.


What Does This All Mean?

Very few colleges have a definite requirement of calculus or four years of math. A college doesn't want to be in a position where they have to reject an otherwise well-qualified applicant because of a lack of calculus.

That said, take the "strongly recommended" guidelines seriously. For most colleges, your high school record is the single most important component of your application. It should show you've taken the most challenging courses possible, and your success in upper-level math courses is a great indicator that you can succeed in college.

A 4 or 5 on one of the AP calculus exams is about the best evidence you can provide of math readiness, but most students don't have that score available at the time applications are due.