Before Calculus

These are post about topics that students usually study before studying calculus. Some go back to Algebra 1 or earlier. You may want to share these ideas with the teachers of the courses that come before your calculus course.

AP Calculus Prerequisites From the 2019 CED

Teaching How to Read Mathematics (4-12-2013) Some suggestions on reading textbooks

The Unknown Thing (8-10-2012) A video about x.

Axioms, Theorems, Definitions, and Proof. Don’t leave high school without them!

Theorems  What students (and teachers) need to know about theorems and how to teach them.

Theorems and Axioms   Theorems ,axioms and related statements – contrapositive, converse, and inverse.

Definitions   What students (and teachers) need to know about definitions and how to teach them.

Definitions   How to write and therefore how to read and understand definitions.

For Any, For Every, For All There all the same!

Proof Why study proofs.

         Then there is this – Existence Theorems

Algebra class.

The Opposite of Negative (5-19-2013) Comments on the m-dash (a/k/a the minus sign)

Absolutely  (7-27-2012) Absolute value – so simple and so difficult once variables get involved.

Absolute Value (5-23-2013) More on absolute value and variables.

Stamp Out Slope – Intercept Form! (1-20-2013) This is NOT the way to write the equation of a line.

Inequalities (12-8-2012) Solving non-linear inequalities is an import calculus skill that student learn before calculus. This post contains this link to an explanation of the easy way (as in no arithmetic) to solve inequalities.

 A Note on Notation (8-6-2012) Which is better sin x or sin(x)?

         A quick thought on the Intermediate Value theorem: The tallest person in the world was at one time the same height as every other person.

Intermediate Weather  (7-2-2014) The intermediate Value theorem

Amortization ((2-9-2015) How to find your mortgage payment using (finite) series and no calculus.


Inverses (11-5-2012) The basics and the problems. (Part 1 of a series of 5 posts.)

Writing Inverses (11-7-2012) What happens if, after switching the x and y you can’t solve for y? (Part 2 of a series of 5 posts.)

The Range of the Inverse (11-9-2012) The inverse of a function is not always a function. What to do? (Part 3 of a series of 5 posts.)

The Calculus of Inverses (11-12-2012) Working with inverses once you get to calculus (Part 4 of a series of 5 posts.)

Inverses Graphically and Numerically (11-14-2012) Graphical considerations for pre-calculus with some calculus considerations.

Logarithms (2-6-2013) Logarithms are defined by a definite integral. Save this for later.


This is a series of posts that could be used when teaching polar form and curves define by vectors (or parametric equations). They might be used as a project. Hopefully, the equations that produce the graphs will help students understand these topics. Don’t let the names put you off. Except for one post, there is no calculus here.

Rolling Circles  (6-24-2014)

Epicycloids (6-27-2014)

Epitrochoids (7-1-2014) The most common of these are the cycloids.

Hypocycloids and Hypotrochoids  (7-7-2014)

Roulettes and Calculus  (7-11-2014)

Roulettes and Art – 1  (7-17-2014)

Roulettes and Art – 2 (7-23-2014)

Limaçons (7-28-2014)