From the archive, Saturday 22 August 2026
Math Review, 2 of 5, Graphs, Slopes, Areas, and Proportion
Today is about reading physics off a picture. A slope is a rate and its units name it, an area is an accumulation and its sign matters, and a proportion lets you predict a change without computing it. Three questions, each one harder than the last. You unlock the next one by answering the one you are on.
Level 1: PhD dropout
A pump fills a tank. The depth against time is a straight line: at t = 2.0 min the depth is 3.0 m, and at t = 10.0 min it is 5.0 m. Find the rate at which the depth rises, in m/min.
About 2 minutes. Watch out for dividing one reading by its own time, which is the mistake this question is built to catch.
Levels 2 and 3
Level 2, CalTech, opens once you have cleared Level 1, and it comes with every hint. Level 3, Lucasian, needs a class code. Nothing on an archived day is recorded, and nothing counts toward a leaderboard.
The interactive version of this day, with the tutor and the calculus companions, loads here when your browser runs the page script. See also today’s question and the rest of the archive.