18 percent of easy-labeled items have no answer choices, against 39 percent of hard-labeled ones

College Board says about a quarter of digital SAT Math is student-produced response, where you type the answer instead of picking it. That is a section-level figure, and it says nothing about where those questions sit.

We counted 819 Math questions in College Board's released question bank, sorted by the difficulty label College Board attaches to each one. The student-produced share is not flat across those labels:

A chi-square test of response format against difficulty label gives 30.7 on 2 degrees of freedom, p about 2 in 10 million. The odds of a hard-labeled item being student-produced are about three times the odds for an easy-labeled one.

Everything here is a property of the public question bank. The last two sections cover what that does and does not let you conclude, and one of those limits is larger than we expected when we started.

The pattern is not a side effect of which topics are hard

The obvious objection is composition. If geometry uses the typed-answer format more often, and geometry is over-represented among hard items, you would see this pattern without difficulty having anything to do with it.

It is not that. Hard sits above easy within all four Math domains:

Counts in brackets are the items in each cell. Problem-Solving and Data Analysis does not rise in order: 8 of 46 easy, 18 of 39 medium, 17 of 52 hard. Its easy-to-hard endpoints still point the same way, and on that domain alone the difference would not be significant.

Reweighting each difficulty group to a common domain mix leaves the figures at 17, 28 and 39 percent. Doing the same across the 19 individual skills gives 16, 30 and 38 percent. Removing near-duplicate questions, so repeated variants of one template cannot count several times, gives 17, 29 and 40 percent.

Most hard-labeled questions still have choices

The change is in the odds, not in what you will usually meet. Sixty-one percent of hard-labeled items in this sample still offer four options. Elimination and testing the choices remain useful on most of the section, including most of the hard part of it.

What changes is how often the technique is simply unavailable: about one time in six on easy-labeled items, about two in five on hard-labeled ones.

The multiple-choice questions shift too

Among the items that do keep four options, what the correct answer is also moves.

On easy-labeled items, 63 percent of correct answers are something you can compute and then match: a number, an ordered pair, a table of values. On hard-labeled items that falls to 49 percent, and that difference is significant (p is about 0.004). Answers that are an equation or a function rise from 22 percent to 30 percent, which on its own is not significant (p is about 0.07).

The distinction matters because of what it does to backsolving. An option that answers "which equation represents this situation" cannot be plugged back into itself the way a candidate number can. You can often still test an equation against a given point, a stated condition, or a value from a table, and graphing candidates is a legitimate move. But the cheap version, substitute each option and see which survives, has less to work with.

Sorting by size gets less help too. One released hard item asks which equation must be true for a 30-sided polygon, and offers 5n + 6 = 30, then 6n + 6 = 30, then 8n + 3n + 4n = 30, then 8(5n) + 3n + 4(6) = 30. There is no largest or smallest to reason about.

Across all formats together, no clear trend

Ask how often the answer to a Math question is a computable value, counting student-produced and multiple-choice items together, and this sample gives 70 percent easy, 67 percent medium, 69 percent hard. No monotonic trend.

That is a weaker statement than it looks, in two ways worth being explicit about. The easy-to-hard difference is about one point, with a 95 percent interval running from roughly seven points down to nine points up. The data cannot show a large shift and cannot rule out a moderate one. And the measure is partly arithmetic: a typed answer is a computable value by construction, so a rising student-produced share mechanically offsets the falling multiple-choice share. This combined number reconciles the two earlier results more than it adds a third.

Our first version of this count left the student-produced items out, because they have no options to classify, and produced a larger effect pointing a different way. Our first count did exactly the thing this section exists to warn about.

What this suggests about practicing

Read these against the last section, which explains why 39 percent is not a forecast for your test.

Check where your practice material puts its typed-answer questions. A set that concentrates them at the easy end is drilling the format where it costs least. Include hard-labeled ones.

Practice finishing problems. Narrowing to two options and picking the likelier one is legitimate and efficient, and there is no guessing penalty. It is also unavailable when there are no options, and only one of those two skills gets exercised by default.

Read what the question asks for before you start solving. "Which equation represents this situation" and "what is the value of n" can come from the same setup and reward different work.

How we counted, and the two things this cannot tell you

The numbers come from 819 Math questions in College Board's released question bank, pulled in September 2026, sampled without replacement at random within each difficulty label. The eligible pool holds 1,925 Math items: 685 easy, 630 medium, 610 hard. We drew 257, 260 and 302 of them, so sampling fractions were 38, 41 and 50 percent, with hard oversampled. Percentages are within-label, so the uneven fractions do not bias them. We did not assign the difficulty labels. College Board did.

For the duplicate check we dropped 49 near-duplicates from the 819, which otherwise includes them: 23 easy, 11 medium and 15 hard, matched on the first 90 characters of the question text. Of the 57 skill-by-difficulty cells used for the skill adjustment, 3 were empty and 7 held fewer than five items, so read that adjustment as a check on the domain result rather than as a finer one.

The direction of cause is not settled, and this is the largest limit. College Board's difficulty labels are empirical, derived from how test-takers actually performed. A four-option question gives a random guess a one-in-four chance of being correct. A student-produced response has no comparable fixed guessing baseline. Response format can therefore affect observed performance, and these data cannot tell us how much that contributes to the labels. So there are two explanations for everything above: College Board may write its harder questions without choices, or questions without choices may earn a harder label partly because they are harder to get right without knowing the answer.

One piece of evidence says the labels are not purely an artifact of format. Among the multiple-choice questions alone, where every item carries the same one-in-four guessing floor, the labels still track a real property of the question: the drop in computable answers from 63 to 49 percent. Whatever else the labels are doing, they are tracking something beyond whether choices are present, though answer type also affects how easily the choices can be tested. That does not resolve the question for the format result itself.

The question bank is a practice pool, not an assembled test. Random sampling from it gives you a property of that pool, and College Board could stock a practice bank with a different format mix from its live forms. The released full-length practice tests in Bluebook are the only public place to count an assembled adaptive module directly, and there are only a handful of them. Anyone quoting you a precise figure for your own second module is extrapolating from those, not from this bank.

Reweighting our student-produced share to the bank's difficulty mix gives 27.7 percent, near the roughly 25 percent College Board publishes for the section. That is a rough consistency check on the overall rate. It does not show that the bank reproduces the exam's joint distribution of format and difficulty, which is the thing this post is about.