Math 152

MATH 15200 is a University of Chicago calculus course. There are two versions of the course. One is as part of a 151-152-153 sequence. This version continues where 151 left off, completing applications of derivatives, and then proceeding to integration and its applications (but excluding integration by parts, radicals, and partial fractions). Math 151 and 152 together are equivalent (syllabus-wise, not credit-wise) to the Advanced Placement AB curriculum. The starter 152 is intended for people who come in with some prior calculus credit or placement test performance, and includes a quick review of limits and differentiation before commencing on integration.

The material below is from the most recent version of Math 152 I taught. This was a starter Math 152 in Autumn 2011.

Alternative learning recommendations

If you’re interested in recommendations for learning single-variable calculus, see Cognito Mentoring’s single-variable calculus learning recommendations page, to which I was a primary contributor.


The textbook for the course was Calculus: One Variable (Tenth Edition) by Salas, Hille, and Etgen. In the lecture notes and quizzes, it may occasionally be referred to as the “book” or “textbook” or “text” — however, it is not necessary to buy or own the book in order to make sense of the lecture notes or quizzes. The book is not very different from other standard calculus texts such as the book by Stewart.

Full downloads

Later in this page, links to each of the lecture notes, quizzes, and review sheets are available. If, however, you want to download all the lecture notes or all the quizzes, saving each link can be a pain. The links below can be useful if you want to download in bulk. Note that page numbers as shown on the pages are for individual files, not for the combined file.

Lecture notes plus quizzes

On the topics for which videos exist, the videos were created after the last time I taught the course, and were therefore not available to students.

For solutions to any quiz, add -solns to the part of the URL just before the .pdf at the end of the URL. For instance, the solutions file for the quiz with URL has URL

Notes Sections in textbook (Salas et al) Related quiz(zes) Related video(s)
Functions: a rapid review (part 1) 1.5, 1.6 Quizzes: warmup, main
Functions: a rapid review (part 2) 1.6, 1.7 (see above)
Informal introduction to limits 2.1, parts of 2.4 Limits (first video of playlist below)
Formal definition of limit 2.2 Limits Limit: first time college playlist
Limit and continuity theorems (plus an additional note on composition theorem for limits) 2.3-2.6 Limit theorems
Introduction to derivatives 3.1-3.3, 3.5 Derivatives: 1, 2, 3
Trigonometric limits and derivatives 3.6
Derivative as rate of change, plus implicit differentiation 3.4, 3.7
Rolle’s theorem, mean-value theorem, increase/decrease, extreme values 4.1-4.4 Increase/decrease and maxima/minima Playlists: 1, 2, 3
Max-min problems 4.5 Max-min problems
Concave, inflection, cusp, tangent, asymptote 4.6-4.7 Concave, inflection, cusps, tangents, asymptotes
Graphing 4.8
Integration and definite integral: introduction 5.1, 5.2 Integration basics
Definite integrals, fundamental theorem of calculus, antiderivatives

5.3. 5.4 Integration
Chain rule, u-substitution, symmetry, mean value theorem 5.6-5.9 Integration: first, second
Area computations using integration 5.5, 6.1
Volume computations 6.2, 6.3 Volume
One-one functions and inverse functions 7.1 One-one functions
Logarithm, exponential, derivative, and integral 7.2-7.4 Logarithm and exponential
Exponentiation with arbitrary bases, exponents 7.5

Lecture notes on background material related to the syllabus

These notes corresponded to material not directly covered in class but used in the course:

Other quizzes

Review sheets

Basic review sheets are unions of executive summaries of the corresponding lecture notes. Advanced review sheets include error-spotting exercises and other practice material. For midterm 1, the basic and advanced sheets were not separated.

Review sheet for … Sections of book covered
midterm 1 1.3, 1.5-1.7, 2.1-2.5, 3.1-3.3, 3.5, 3.6
midterm 2 (basic) 3.4, 3.7, 4.1-4.8, 5.1-5.9
midterm 2 (advanced) 3.4, 3.7, 4.1-4.8, 5.1-5.9
final (basic) 6.1-6.3, 7.1-7.5
final (advanced) 6.1-6.3, 7.1-7.5

Basic information