Blog · 5 October 2026 · 6 min read
We graded 18,529 calculus answers. Here's what students actually get wrong.
Across 18,529 typed calculus answers in Asymptote's first month, the most-missed problems were integration by parts (63% right), derivatives of square roots (67%) and limits by plain substitution (77%), which players got wrong more often than L'Hopital's rule (84%). The hardest part of calculus, it turns out, is often the algebra around it.
Asymptote is a calculus game where you type your answers instead of picking them, so every answer tells us something. In its first month, with players signed up from 81 countries, 18,907 answers were typed in. We set aside the 378 the checker could not read (sorry, "idk"), which leaves 18,529 graded answers and an overall accuracy of 82%. These are the rules that drag that number down.
1. Integration by parts: 63% right
No surprise at the top. Integration by parts was the least-solved rule we track, and the slowest: the median correct answer took 110 seconds. The formula itself is short,
but the misses are almost never about the formula. They are about choosing u badly (pick the part that gets simpler when you differentiate it - LIATE exists for a reason) and losing a minus sign in the second integral.
2. Derivatives of square roots: 67%, against 85% for the power rule
This is the one that surprised us. The plain power rule was answered correctly 85% of the time across 1,173 attempts. Put the same thing under a square root and accuracy fell to 67% over 906 attempts. The calculus is identical:
The 18 points are lost converting the root into a power and back, and in the fractional exponent: 1/2 minus 1 is -1/2, not 1/2, a fact that has been ruining afternoons since Leibniz.
3. Limits by substitution are missed more than L'Hopital
The "easy" limits, where you just plug the number in, were answered right 77% of the time (1,211 attempts). L'Hopital's rule problems, which look much scarier, came in at 84%. Our best guess: nobody relaxes on a 0/0, but everybody relaxes on a substitution, and arithmetic is where relaxed people go to make mistakes.
4. Exponentials forget the chain rule: 74%
Derivatives of exponentials like were right 74% of the time, while chain rule problems with trig functions were right 90% of the time. Same rule, different costume. With trig, the inside function is visible; with the 3 hides up in the exponent, and it is very easy to write back down as the derivative instead of .
5. The quotient rule loses to the product rule: 76% vs 84%
The quotient rule is the product rule with an order that matters and a denominator to square, and both extra steps cost points. If you blank on it under time pressure, writing f/g as f times g to the power -1 and using the product rule is entirely legal.
What holds up best
Limits at infinity of rational functions (92%, and quick: a median of under 8 seconds), standard derivatives like (93%) and simple antiderivatives (94%) are close to solved. The pattern across the whole list is the same: players know the rules. What they miss is the algebra in between.
How we measured it
Every number here comes from answers typed into Sprint and Diverge between 1 September and 5 October 2026, grouped by the rule each problem is built on and counted only where a rule had at least 100 attempts. Answers are checked as maths, so and both count. Times are for correct answers only. We will update this post as the numbers move.
Want to see where you land? A five-minute Sprint is free and needs no account, and the formula sheet has every rule above on one page.