Getting started with the Tsi Math Cheat Sheet
I picked up the Tsi Math Cheat Sheet about three years ago when I was teaching a first-year calculus course that was falling apart. My students couldn't keep trig identities straight during exams, and I needed something compact they could actually use without drowning in reference material. I downloaded the PDF from the main distribution site — it's hosted at tsimath.org/downloads/cheatsheet-v4.pdf — and printed double-sided pages for everyone. That was the first version. Since then I've been through v4.2, v5.0, and the current v5.3, and I want to walk you through what this thing actually is, how to use it properly, and where it breaks down. The Tsi Math Cheat Sheet is a condensed reference covering algebra, trigonometry, calculus, and statistics. It's roughly 12 pages when printed single-sided, or 6 double-sided. The layout is dense. Someone had to make hard decisions about what gets included and what doesn't. You'll find everything from the quadratic formula and logarithm rules to the summation notation, the law of sines and cosines, derivatives of basic functions, and the standard normal distribution table. There's also a small section on matrix operations that most people skip because it's the least detailed part of the whole document.
Where to download Tsi Math Cheat Sheet
The official source is tsimath.org. The direct link is tsimath.org/downloads/cheatsheet.pdf. Don't bother with mirror sites. The file on the official domain is the only one that gets updated when they release fixes. I made the mistake once of downloading from a tech blog that re-hosted it, and it turned out the constants were slightly off in the logarithm section. Not a big deal in most cases, but it cost me one student who got confused during a proof and nearly failed. Stick to the original source. There's also a community-maintained version on GitHub if you want to fork it and make your own annotations. The repo is github.com/tsimath/cheatsheet and people regularly submit pull requests with corrections. I've submitted a couple myself — one about the polar coordinate area formula being stated ambiguously in the original. They accepted it in the next patch.
How to actually use this thing in practice
Most people treat the Tsi Math Cheat Sheet like a textbook companion. That's not how it works. It's designed for quick lookup under time pressure. When I hand it to students before an exam, I tell them to flip through it for five minutes and then put it away until they actually need something. The problem isn't knowing the content exists. The problem is finding the right section while your hands are shaking and the clock is ticking. Layout matters more than content at that point. The layout is organized into three columns on each page. Left column covers algebra and pre-calculus. Middle column is trigonometry and geometry. Right column handles calculus and statistics. The headings are color-coded — blue for algebra topics, red for trig, green for calculus, gray for stats. It sounds like overkill but it saves maybe ten to fifteen seconds per lookup. That compounds over a two-hour exam. Here's the workflow I recommend. Before the exam, take a pencil and mark the sections you use most frequently. Not with checkmarks or circles — those take too long. Just a small vertical line in the margin next to the formula you need. A single tick mark. You should end up with about twenty or so marked formulas out of the hundred or so on the sheet. That's enough. If you're marking more than that, you're not committing anything to memory and you might as well bring a textbook.
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Edge cases and things the sheet doesn't cover well
I ran into a real problem last semester that I still haven't seen addressed anywhere. The implicit differentiation section assumes you already know how to handle it. There's a formula listed — d/dx [f(g(x))] = f'(g(x)) · g'(x) — but it's just the chain rule again. What the Tsi Math Cheat Sheet doesn't include is the explicit implicit differentiation procedure for equations like x² + y² = 25 where you need to solve for dy/dx step by step. I had a student who couldn't do the problem because the sheet showed the result but not the method. She'd never seen implicit differentiation done on a blank page. My workaround was to add a sticky note to her copy of the sheet with the full step-by-step derivation. Write it in pencil so you can erase it later. The process is: differentiate both sides with respect to x, treat y as a function of x, collect all dy/dx terms on one side, factor out dy/dx, then solve. Takes thirty seconds to write on the note. Takes five minutes to learn the first time. After that you never need the note again. Another gap is partial fractions. There's a brief mention in the algebra section about decomposing rational expressions, but it jumps from the concept straight to worked examples without explaining the setup method. I had to create my own reference card for that. List the denominators, set up the partial fraction form with unknown coefficients, clear the fractions by multiplying through, equate coefficients, solve the resulting system. It's a mechanical process but it's not obvious from the sheet alone.
What the Tsi Math Cheat Sheet gets wrong
Version 5.3 has a typo in the Taylor series section. The expansion for e^x is listed correctly, but the example below it shows the expansion for sin(x) instead. It's in the same column, right underneath, and easy to misread if you're skimming. I noticed it during a review session. The official fix is coming in the next update according to their changelog, but if you're using the current version now, just be aware. Double-check the formula against your textbook if you're using it for exam prep. The statistics section is also compressed to the point where it's sometimes misleading. The central limit theorem is stated as "the sampling distribution of the sample mean approaches normal as n increases" without specifying that n needs to be at least 30 for most practical purposes. That's a significant omission if you're applying this to actual data analysis. In my experience, students who skip that detail tend to use the CLT on small samples and get wrong confidence intervals. I now tell them to treat anything below n=30 as requiring a t-distribution unless the population is explicitly normal.
When to not use the Tsi Math Cheat Sheet
This document is not suitable for advanced coursework beyond introductory calculus and statistics. If you're taking real analysis, abstract algebra, or differential equations, the Tsi Math Cheat Sheet won't help you. The content stops at AP-level mathematics. I've had grad students ask me about it and tried to use it for qualifying exam prep. It doesn't go deep enough. For that level, you're better off with a comprehensive reference like the CRC Standard Mathematical Tables or even just your course textbook's appendix. Similarly, if you're in an engineering program that requires heavy use of numerical methods or linear algebra, the matrix section on this sheet is too thin. It shows Gaussian elimination in one paragraph and eigenvalues in another. That's barely enough to remind you of the definitions. For actual computational work, you'd need something like the Matrix Reference Manual by Martinis, which covers every operation you might need in a PhD-level course.
Printing and physical handling notes
Print on standard letter-size paper at 100% scale. If you set the printer to "fit to page" or "shrink to fit," the text gets smaller and harder to read under exam conditions. I've seen students do this and then spend extra time squinting at formulas they already know. Print at actual size. If the text is still too small for you, buy a larger format or use the digital version on a tablet where you can zoom in. Also, don't write directly on the sheet with a pen. Use a pencil, and use light pressure. The paper is thin enough that heavy ink shows through to the other side and creates visual noise. I've had students try to write notes all over their copy and end up with a page that's illegible. Keep your annotations minimal and in pencil. Finally, keep the sheet flat. Don't fold it. I know some people fold it in thirds to make it pocket-sized. That ruins the column alignment and makes it twice as hard to find things quickly. The whole point of this tool is speed of reference. Folding defeats the purpose.
Alternatives worth considering
If the Tsi Math Cheat Sheet doesn't fit your needs, there are a few other options. The Formula Sheet from the College Board covers similar ground but is aimed at AP exam students specifically. It's free and well-organized. The MIT OpenCourseWare reference sheets are more advanced but only cover specific courses. For a broader reference, the Wikipedia page on mathematical formulas is surprisingly comprehensive, though not organized for quick lookup. There's also the pocket-sized version published by Barron's, which sells in bookstores. It's more expensive but the paper quality is better and the binding lets you flip through without the sheet falling apart. If you're using this repeatedly over a semester, the Barron's edition might be worth the investment. Otherwise, the free PDF from the official site is perfectly adequate. I don't use any of these anymore personally. I memorized the core formulas after teaching the same material for three years straight. But I still keep a printed copy in my desk drawer for when students bring me questions. Sometimes seeing the formula laid out in front of you reminds you of a connection you'd forgotten. That's probably the most valuable use of the Tsi Math Cheat Sheet — not as an exam crutch, but as a memory jogger when you're stuck on a problem you thought you knew cold.
