Tackling the Hardest SAT Math Problems

The SAT math section makes a lot of students nervous, but it shouldn't. Read on to learn what basics you need to know and how to tackle the most difficult questions you'll encounter.

First things first: I should define what exactly I mean by “hard.” There are scads of ways something can be difficult, and comparing them doesn’t always make sense. Compare, for example, a Rubik’s cube and running a mile in under five minutes. It’s tough to say which is harder, because a.) they’re both ridiculously hard in the first place and b.) they’re completely different skills, so it depends on who you are and what you’re good at.

SAT math is so straightforward a test that only one skill is tested. There are a few different aspects, so the hardest questions can be hard in different ways.

Knowing your stuff

If you don’t already know what’s on the SAT, this part might come as a relief. The test doesn’t go deep into high-level math. There’s no trigonometry, no precalculus, no statistics—nothing that you get in advanced math classes during your last year or two of high school. The most advanced math on the SAT are functions and parabolas, but even then you’ll see just a couple related questions on your test and you only need to know the bare minimum about how they work.

That said, you really have to know your rules when it comes to algebra, geometry, and number properties. There’s nothing particularly advanced, but there is a lot of detail. If you’re not confident with the first few sets of Pythagorean triples or aren’t sure what a negative exponent means, then you have some brushing up to do. The toughest questions do rely on those details, but that’s not what makes them really tough.

Being experienced (and working quickly)

Even if you do know the exponent rules well, how quickly and confidently can you apply them to a question like this one?

If k, n, x, and y are positive numbers satisfying x^(-4/3) = k^(-2) and y^(4/3) = n^2, what is (xy)^(-2/3) in terms of n and k?

It’s easy to slip up if you’re working with rules that you don’t use often, and that’s precisely what this question relies on to make it difficult. (This is a real SAT question from a past test, by the way.) All of the math that goes into it is relatively straightforward, but if you’re not used to answering questions that work with tricky exponents, then you’re in danger of faceplanting.

Being creative

This is what makes the SAT special, and it’s why people find themselves actually enjoying SAT questions more than they might expect. The math is part puzzle, really. When a question is really tough, you have to do more than just know the rules and apply them. You also have to figure out the fastest way to arrive at an answer and see unexpected questions between the information.

The hardest SAT math is not based entirely on what you’ve learned or memorized; it wants you to explore and find patterns for yourself. Check out some examples to see what I mean—can you find shortcuts, when they’re possible? Can you remember all the rules you need to and apply them when working under pressure?

Like what you’re reading?

Join the CollegeXpress community! Create a free account and we’ll notify you about new articles, scholarship deadlines, and more.

Join Now

Tags:

About Lucas Verney-Fink

Lucas Verney-Fink is a resident TOEFL and SAT expert at Magoosh. Standardized tests and English grammar are two of Lucas’s favorite things, and he’s been teaching both since 2008. Between his time at Bard College and his time spent teaching abroad, he’s tried to learn a total of three other languages. He speaks none of them well.

You can follow Lucas on Google+.

 

Join our community of
over 5 million students!

CollegeXpress has everything you need to simplify your college search, get connected to schools, and find your perfect fit.

Join CollegeXpress

College Quick Connect

Swipe right to request information.
Swipe left if you're not interested.

University of Miami

Coral Gables, FL


Kyla McClain

Kyla McClain

High School Class of 2024

I found CollegeXpress when you partnered with Bold.org for a scholarship. I found your website, put my information in, and got connected. I only wanted to stay in North Carolina [for college] and not move far from home, but you all opened a door up for me. I started researching colleges you suggested for me. On your social media platforms, you also give really good test-taking tips that I used and suggested others to do the same. It helped me a lot on my exams, so thank you.

Sarah Armstrong

Sarah Armstrong

High School Class of 2022

I am a deaf student, and I had always dreamed of going to Gallaudet University. CollegeXpress helped me search though other qualified universities. They helped me know for sure that Gallaudet University was the right choice for me!

Nikole Dixon

Nikole Dixon

$500 Refer-a-Friend Scholarship Winner

Toward the beginning of last year, I was searching for scholarships to apply to through my school, town, websites online, and anything else I could find. I asked tons of questions [online] about scholarships and the best places to find them because I was desperate and needed as many as I could find. I came across a ton of bogus websites, but as soon as I found CollegeXpress, I knew I had to tell other people about it. It was definitely the most helpful site I came across, so I told my friends about it. CollegeXpress is definitely a website worth giving as a source.

Kayla

Kayla

High School Class of 2021

CollegeXpress helped me organize the schools I wanted to choose from in one place, which I could then easily compare and find the school that was right for me!

Jada Bohanon

Jada Bohanon

High School Class of 2021

CollegeXpress has helped me find scholarships for the colleges I applied to. It was very hard for me to find scholarships in the beginning that I was qualified for. My teachers recommended this website to find some, and not only did I find some scholarships but I also got to look into some schools I hadn’t heard of before. I was very happy to have discovered this website, especially with the coronavirus spreading all over as I can’t really go visit many colleges.