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:
sat SAT Math standardized tests test prep

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
Alexandria

Alexandria

High School Class of 2021

For a long time, I've been searching everywhere to find the perfect website I can get scholarships and information from. Needless to say, I could never find the right one. That was, until I found CollegeXpress. Through my journey of finding the right scholarships for me, I was able to find articles about different things. They've all been helpful, especially in times like this! I was even able to connect with some of my favorite colleges! I love CollegeXpress. Thank you!

Keaun Brown

Keaun Brown

$2,000 Community Service Scholarship Winner, 2020

As I transition to furthering my education, I can say with certainty that it simply wouldn’t be possible without the help of generous organizations such as CollegeXpress. Those who initially founded CX had no idea their platform would give a plethora of information to a first-generation homeless kid native to the ghettos of over half a dozen states. Everyone at CX and Carnegie Dartlet gave me a chance at a future when the statistics said I had none. And for that, I thank them.

Hailey Riddile

Hailey Riddile

High School Class of 2021

CollegeXpress has helped me find scholarships to apply for and look into more colleges. While there are many websites similar to CollegeXpress, every website is different, and I've found a lot of good insight on this website. Receiving emails from CollegeXpress about scholarships is extremely useful, and getting insight about colleges near, far, and anywhere in between helps me narrow down my choices to what I want, which is also super helpful. The articles are always really good reads, and I can't stress enough how helpful this website has been to me. Anything related to college is beneficial to me as a senior, and I have learned lots of useful things to help me on my college journey this year.

Maurice Whan

Maurice Whan

$2,000 Spring Scholarship Contest Winner, 2021

This year has been tough for my family and myself, so receiving this scholarship has been a blessing in disguise! CollegeXpress has been an excellent resource in helping me prepare financially for college. Thank you again for this amazing opportunity!

Heaven Johnson

Heaven Johnson

Back to School Scholarship Winner, High School Class of 2023

I’d like to thank everyone on the CollegeXpress team for their generosity. Not only have I been awarded this scholarship, but CollegeXpress makes it easier to apply and gives amazing tips for schools and scholarships. I am extremely grateful as this will help with my schooling and allow me to be able to enter into the field I’ve been dreaming of all my life. 

College Matches