Math 101/102

Calculus I with Precalculus Review

Two-semester treatment of (mostly) differential calculus. Includes an introduction to integration as well. Compared to MAT103, which covers the same calculus topics, the slower pace of MAT101/102 allows more in-class review of fundamental precalculus material including basic trigonometry, the graphs and properties of standard functions (e.g. logarithms, exponentials), inverse functions, algebraic techniques for solving equations (e.g. factoring, completing the square), equations for ellipses, hyperbolas and parabolas.

103 Topics: limits, continuity, definition of derivative, standard differentiation formulas, implicit differentiation, applications of the derivative (related rates, optimization, curve-sketching), linearization, antiderivatives, L'Hôpital's Rule, the definite integral, Fundamental Theorem of Calculus, area between curves, integration by substitution.

101 typically covers somewhat more than the first half of 103. 102 begins with a review of differentiation and applications of the derivative and finishes up with definite integrals and the fundamental theorem of calculus.

Textbook: Thomas' Calculus, Early Transcendentals, Single Variable with Second-Order Differential Equations (Customized for Princeton University) by Thomas, Weir & Hass, Pearson: Addison-Wesley, (12th edition).


Who Takes this Sequence?

Placement and Prerequisites

General information about placement and contact information for the placement officer can be found on the Math Placement Page.

Sample Problems

Working problems from these sample exams can give you a good idea of the expectations and content in these courses as you think about which course is right for you. Just reading the questions or the solutions can be very misleading however. Try the problems yourself!

Once you have tried the problems, you can check your answers:
101 Midterm Exam Solutions, 102 Midterm Review Solutions 102 Sample Final Exam Solutions.

It may also be useful to look at the sample exams posted for 103.


  1. How hard should I expect to work?
    • These courses require a steady time commitment. We expect that the weekly problem sets will take at least 3 hours to complete. To do well on exams, you need to work a lot of extra problems from old exams. So all in all you should be ready to spend a minimum of 10 hours/week outside of class, on average.
  2. What if I decide later that I need more calculus? Will this sequence get me ready for MAT104?
    • If you did well (at least B+) in 101/102 and you are motivated enough to work hard, then you should know enough to take 104. You may need extra practice working through problems in order to do well in 104 just because the other students there may be more highly motivated and/or mathematically seasoned than your classmates in 101/102 were. With work it is certainly feasible.
  3. How hard is it to get an A in this class? I absolutely have to get an A so I can go to medical school!
    • Sigh. There are no guarantees, and we hope that you will still be able to go to med school, even if you sometimes get a B in a difficult math or science course. You won't get the full benefit of your four years at Princeton if you limit yourself to classes where you can be sure of an A. To answer the question, grades in the math classes are curved, so your grade depends on how your work compares to that of the other students in the class. Generally speaking, in the larger courses like MAT103, the top 25% of the class gets an A or an A-. The middle 45% gets some kind of B and the remaining 30% mostly get C's, but we do regularly give D's or F's if necessary. In smaller classes like 101/102 we don't follow this curve as strictly, but we use it as a guide. Our aim is that students will only get an A in MAT102 if they have learned the first semester of calculus well.
  4. I have more questions that are not answered here. What should I do?
    • First check the general Math FAQ page for more information. (There is a whole section there on how Princeton's calculus courses work.) If you still have questions, representatives from the math department will be available at freshman registration.