Math 19
Fall 2015

Home Course Schedule Homework Exams Office Hours Resources

This page might be updated as the course progresses, including both review materials and lectures and sources to help with new material.



Here are some handouts that you might find useful during this class. Note: to access these, you need to be enrolled in this course. Is there another handout you'd be interested in having? Let us know and we'll see what we can do!

Office Hours and Tutoring

You are welcome to come to office hours with any kind of question -- we are here to help you and ready to explain the same thing as many times as necessary. You can also email your instructor or a Course Assistant if you have any concerns.

The Office of the Vice Provost for Teaching and Learning offers free drop-in and individual appointment tutoring in the following Math courses: Math 19, 20, 21, 41, 42, 51, 52, 53. To schedule an individual appointment, visit To view our drop-in schedule and to view information about tutoring for other courses, visit

Some graduate students also offer their services to tutor for Math 19, you can find their names and email address on the list of private tutors maintained by the math department. Beware, private tutors tend to be expensive.

Old Exams

Material covered for a given midterm in the past does not necessarily correspond to the material covered in Math 19 this quarter (even in Fall 2014), so bear this in mind when using these to study for exams.

For more guidance about which exams or problems to focus on in these past exams, visit the exams page.

We will not provide solutions other than the ones already available here, but you are welcome to ask any instructor or course assistant to show you correct solutions to any problem.

First Midterms

Second Midterms

Final Exams

Precalculus resources

The Stanford Math Department has developed two mini-courses to help you review or learn trigonometry, and exponentials and logarithms. The mini-courses are a quick and to-the-point review of certain areas of precalculus that a sizeable proportion of students need to brush up on before taking calculus. They consist of short videos followed by supplementary videos and exercises from Khan Academy. While they typically will not cover every single important aspect of a topic, they are a fast way to get to a good place before starting calculus.


The Stanford Math Department has developed an online learning tool to help you acquire the precalculus skills you will need for the Math 20 series. This resource is an in-depth, time-intensive survey of most precalculus topics you will encounter at Stanford. It is recommended for students who feel that they need extensive extra practice across a wide range of precalculus topics, or who need to learn precalculus topics from scratch. There is a fee for use of the software ($34 for 6 weeks of help, $82 for 18 weeks of help).

The precalculus topics go through Module 12, but you might want to also work on the topics of Modules 15 and 16 as they will be important for us this year.

Khan Academy

Another interesting resource for this class is Khan Academy, a website which hosts short, very helpful lectures. We highly recommend you spend some time looking through their Algebra lectures. We also expect their Calculus lectures will be very helpful throughout the course. They have a very popular sequence hosted at iTunesU. Some sample sessions are given below. You may not need all (or any) of these or you may need more. Try some out and don't hesitate to contact any member of the teaching staff if you have any questions. If you are feeling either bold or highly confused, you can start from the beginning with a very thorough set of diagnostic exercises that can help pinpoint where you should be focusing. To do the diagnostic exercises, start at the exercise dashboard (and be patient, it starts with arithmetic and finishes at calculus).

The following is a list of video topics we think will be particularly helpful to Math 19-20-21 students. This list may or may not be updated as the course progresses.

Fall 2015 -- Department of Mathematics, Stanford University