Math 21
Autumn 2026

Precalculus information

As the name might suggest, precalculus is a prerequisite for calculus. However, the term "precalculus" applies to a variety of topics. For Math 19-20-21 at Stanford, we mean:

  • Ability to manipulate algebraic expressions
  • Familiarity with the concept of a function
  • Mastery of working with lines (for example, how to find the equation of a line, meaning of the slope of a line)
  • Knowledge of a number of basic functions
  • Familiarity with sine, cosine, and tangent

We have developed an online Precalculus Refresher in Canvas consisting of videos and associated exercises that are available for use at any time. It goes through the core skills in algebra, graphing, functions, and trigonometry that are necessary for learning and using calculus. We strongly encourage you to spend some time using this resource to brush up on these topics and skills.

Additional handouts

In addition to the resources in the precalculus refresher, we also think you might find these handouts helpful:

More practice

We have a more in-depth Precalculus practice quiz on the course canvas site which you can take as many times as you like. Each time you take the practice quiz, you will get a fresh set of similar problems for practice. The skills covered on this practice quiz are fundamental in your future STEM courses. Some of the problems on the practice quiz are challenging. Please feel free to come to office hours to discuss any of these practice quiz problems with the Math 21 teaching team.

Autumn 2026 -- Department of Mathematics, Stanford University.