# 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.

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?

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.

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

Victoria

High School Class of 2019

CollegeXpress has helped me by opening my eyes to new opportunities. I learned about such easy ways to get financial help to achieve my dreams while also learning about myself and who I truly am. I know this isn't a very long explanation of what CollegeXpress has done for me, but nonetheless, I believe it's crucial to how I developed as a person throughout my time as a college student.

Bri'Yana Brown-Dunn

High School Class of 2022

CollegeXpress helped me gain interest in many colleges/universities and many scholarships. I would say the most helpful thing CollegeXpress has done for me is sending me emails that tell me certain types of colleges are interested in me as well as emails about scholarships that I can look at and possibly apply for.

Kamal

Student, University of the People

I registered with CollegeXpress and filled all my necessary and relevant information as well as the course I wished to study. A few days later, an email was sent to me with a list of schools offering the course; amongst them was the University of the People, the school I got admitted to.

Monica

High School Class of 2023

Being a sophomore in high school, I never really worried about college. I thought it wasn't important to worry about until senior year. Through this program opportunity I came across, I realized how important it is to start looking at colleges early and start planning ahead. CollegeXpress has opened my eyes to what colleges require, what colleges are near me, and what they offer. The daily emails I get from CollegeXpress really help me look at the different options I have and what colleges I fit into. Without this website, I would not be taking the time out of my day to worry about what my future will be nor what opportunities I have. I could not be more grateful for such an amazing and useful website. It's thanks to CollegeXpress that not only me but my family now know how much potential I have in to getting into these colleges/universities that we thought were out of my reach.

Katelyn

High School Class of 2021

CollegeXpress gave me options of schools with my major and from there I was able to pick what was most important to me in a school. Everything was so organized that I could see all the information I needed.

College Matches
X

## Colleges You May Be Interested In

SUNY Maritime College

Throggs Neck, NY

Monmouth University

West Long Branch, NJ

Iona University

New Rochelle, NY

Hendrix College

Conway, AR