SAT Math Is Old Math

But that doesn't mean it's easy.

If you’ve taken Algebra 1 and Geometry, you’ve probably worked with at least 95% of the concepts on the SAT. If you’re scoring below a 750, it’s not some exotic concept that’s blocking you – it’s probably stuff you forgot or never fully learned. This has many important implications for how students should study…but first I should explain how I got that number.

If anything, 95% might be low. I tagged every question from the Bluebook tests in multiple ways. For example, a single question might get tagged with terms like quadratic, -b/2a, and vertex y-coordinate. Then I made a list of every tag in the Mathchops system that refers to a concept that a student would not learn before Algebra 1 and Geometry – things like logarithms, vertical asymptotes, and matrices. Then I counted how many times one of these ‘advanced’ tags appeared in an SAT question.

I was pretty conservative when applying that ‘advanced’ label. For example, circle equations, radians, fractional exponents, and special right triangles were all considered advanced, even though many students actually do learn them before 10th grade. If you assume students have seen those concepts, the number jumps to 98%. And even that number might be low – many questions involve an advanced concept (like a cubic equation) but can be solved without knowing much about the concept (by using Desmos, for example). All of which is to say…a very strong student could score 700+ on the SAT after taking Algebra and Geometry. Even an 800 is not out of the question. (By contrast, it would be almost impossible for that student to score a 36 on the ACT – there are just too many unfamiliar concepts.)

This doesn’t mean the SAT is easy. Any math topic can have difficult questions, as you can see from these Mathchops examples:

Those are mostly what I’d call “750+” questions – you could miss all of them and still get a 740, as long as you got everything else right. But getting all those other questions right isn’t so easy either. You have to remember lots of nuances – things like percent increase (change over original), solving linear inequalities with negatives (flip the sign when you divide by a negative), and exponent rules (power to a power means multiply).

They aren’t hard to learn or apply, but they’re hard to remember if you haven’t used them recently. It’s sort of like driving around a city. When you drive every day, you’re familiar with which routes have less traffic at rush hour, which lights are long, which lanes disappear, and where the one-way streets are. You use this knowledge easily, almost without thinking. But if you haven’t driven in that city for years, you forget some of those details.

I say some of those details, but which ones in particular? You may hear ‘quadratic equations’ and think you already know it. But maybe your school didn’t cover an important topic, like discriminants. Or maybe they did cover quadratics, but you never fully understood a key concept, like factoring. Most SAT math prep consists of filling in gaps – all those things you forgot or never learned. You have to systematically cover all of the most common material, learn the parts you haven’t mastered, and then practice them repeatedly over long periods of time, making sure to shuffle the concepts and come at them from all different directions, so that you aren’t just memorizing but are truly understanding.

This is very different from school math prep, because the content is so diffuse. As I argued in an earlier post, we’d much rather be hunters than gatherers. It’s simpler to focus on one difficult topic: learn everything about it for a short period of time, take the test, and move on. It’s much harder to pick up this variation here and that variation there, knowing that neither is guaranteed to appear on your test but that, if you pick up enough of these variations and keep them fresh with mixed practice, some of them definitely will show up.

Unsatisfying as this process can sometimes be, it does have one silver lining. When you fill in all those gaps, so that your math foundations are completely sound, you start to notice that you’re (somehow?) much better at math! And not just at SAT math, but at all math, even the new material you’re working on at school.