We named every wrong answer we could in our ACT Math bank, then counted the categories. The smallest one surprised us.

Wrong answers that are plain arithmetic, where the method is right and only the number is off, account for 30 of 1,138 labelled wrong answers. That is 2.6 percent.

That is a count of the wrong answers our writers built, not of mistakes students make. What it says is that when our writers wanted a tempting wrong answer, an arithmetic slip was almost never the way to get one.

The largest group swaps one definition for a neighbouring one

239 of 1,138, or 21 percent, replace a rule or definition with an adjacent one. Real examples from our review notes: permutations counted where combinations were needed, the coefficient of x read as the amplitude, a sum formula used where the formula for a single term was needed, additive reasoning applied to a proportional relationship.

In these choices the computation itself is typically sound. What is wrong is the quantity being computed, so re-checking the steps can confirm the arithmetic and still leave the choice looking right.

Sign errors are the second largest group

Dropped or flipped signs account for 185 of 1,138, which is 16 percent, six times the size of the arithmetic group.

Whether a sign error belongs under arithmetic is a fair objection, and it is exactly the kind of boundary that moves a headline. We separated them because the choice offered is a sign-flipped version of the right value rather than a miscalculation of it. Merge the two and the arithmetic share goes from 2.6 percent to 19 percent. We are telling you that because the categories are ours, not the exam's.

Together the two largest groups account for 424 of 1,138, or 37 percent.

Checks that match how these choices are built

Since a definition-swap choice is a correct calculation of the wrong quantity, verifying the steps will not separate it from the right answer. Naming which quantity the question asks for, before computing, is a check that does distinguish them, because it tests the one thing the two choices disagree about.

The pairs worth writing down are the ones you personally mix up rather than a general formula sheet. Permutation against combination. Area against perimeter, surface area against volume. Mean against median. The nth term against the sum of n terms. Radius against diameter. Slope against intercept.

For signs, mark a negative when it enters and look for the mark on each rewrite. In our own drafting review, sign losses showed up more often between lines than inside the reasoning.

Paper testers can annotate the booklet. On the computer-based test you are given authorised scratch paper, and the software provides its own tools as well.

One thing the headline does not cover

A student who picks the right method and then adds wrong makes an error that never appears in the answer choices at all. The 2.6 percent counts what our writers built, so it says nothing about that.

The pairs are a shorter list than the formulas

Designed arithmetic traps are rare here and definition swaps are the largest group. That points at where a cheap check has something to catch, and the pairs you personally confuse make a much shorter list than the formulas you already know.