Score Tiers

An explanation of why it's so much harder to predict 750+ SAT math scores now.

I’ve been having this debate with my tutor friends: What can students do to guarantee 750+ SAT math scores? Do they need to practice more of the super hard questions? Strengthen fundamental skills? Work faster so they have more time for hard questions?

As different as this new SAT seems at times, I think the answer has to do with the underlying score structure of standardized tests.

On most tests, roughly 90% of the material is predictable. Strong students will be able to master it. Some small portion (usually under 5%) is unpredictable and thus almost impossible to prepare for. And the rest is somewhere in between – not completely predictable, but not impossible.

Think about the ACT. At least 90% of the English questions are based on patterns and rules that appear over and over. Every test has a few question types so rare that they aren’t worth spending much time on. But they also have several questions that are just common enough to be worth studying – who/whom, the semicolon “supercomma”, affect/effect. All but a few ACT Reading questions are directly in the text or could be answered easily by a strong 8th-grade reader. The Science section might have 1 or 2 “outside knowledge” questions. Maybe there will be another 1 or 2 that ask something nuanced about how an experiment was conducted. But everything else is usually in the text or data.

Even the ACT Math, the hardest of the four sections, is like this. You expect ~50 questions to be very familiar, 5 or 6 to be rare-but-not-unheard-of (Law of Sines, ellipses, inverse trig), and maybe 3 or 4 to be unexpected. You see this pattern on ISEE math sections as well – roughly 85% of the math is within the reach of a smart 8th grader, 5 - 10% is totally out of reach for most, and the rest is somewhere in between.

The current SAT Math is no different. There are certain questions that have shown up many, many times on official practice tests. You’ve seen them in school many times as well. These questions account for about 90% of the material, and if you get them right, you’ll score at least a 700. Some of the questions are still hard. They may require strong foundational skills. And you may need to practice regularly (maybe even daily) to maintain all of these skills. But if you’re on the Calculus track getting As in your classes every year, then you can score a 700 on the SAT Math. You just have to find the material and work through it systematically.

Getting up to 750 is quite a bit harder – it’s that “in between” part I mentioned earlier. You have to get all that 700-level material PLUS some of their pet questions (and you have to do it all quickly, with no mistakes). These are questions that are not easy to predict and don’t show up quite enough to be obvious within a few tests. The discriminant was like this on the previous version of the SAT – it wasn’t on every test, or even half of the tests, but it did appear several times. If you could find, learn, and retain lots of questions like this, you could get your score up to a 750.

And that brings me to the last tier: 760 - 800. Sometimes you can break into this tier by handling the other questions perfectly, but you usually need to get a few ‘new’ questions right. These are questions that have never appeared before in quite that way, and will probably never appear again. The insane rectangular prism surface area question from BB 4 is a good example of this, for those of you who have seen it. It’s very hard to prepare for these questions. And it’s therefore very hard to predict where (or if) students might score in that range.

But it’s the “in between” part that we’re really talking about when we debate how to help students lock in high SAT math scores – the 700-level material is clear, and the 760+ material is permanently murky. Mastering this 700 - 750 material was easier when the College Board was releasing the QAS tests, because you could analyze all of the questions from dozens of tests. If something showed up 3 times in 20 tests, it would certainly make your list of things to know. As an overly simplistic example, suppose you found 30 question types like this and learned them all, and then 4 of them appeared on your test and you got them all right. Then your score would go up 40-50 points.

But we don’t have enough available practice tests to do this. We have 6 Bluebooks and a variety of random resources – PSATs, Educator Bank questions, linear versions, deprecated Bluebook tests – but it’s not the same as having 30 official tests. That makes it much harder to know what these infrequent-but-worthwhile questions are. And when you don’t know which questions to practice, it’s harder to predict scores.

So what can you do? I think it’s a mistake to pound the super hard questions. You can copy the ones you see in practice tests, but they’re unlikely to reappear on real tests. You can try to guess what the next super hard question might be, and there’s a small chance you’ll guess correctly, but you are guaranteed to find yourself spending large chunks of time explaining concepts and techniques that will never earn the student any points.

And ultimately, I don’t think most of these 700-750 questions actually are super hard. They are just harder to determine. When I don’t know for sure, and nobody else does either, I like to place a lot of reasonable bets. So I use questions from the old version of the SAT, Mathchops, current Bluebook tests, third party tests, and redos, and I generate score predictions from each resource. If a student can master 750+ material in all of these areas, I think they can hit that score on a real test also.