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.

Alabama State University

Montgomery, AL


Cameron Lee

Cameron Lee

High School Class of 2022

I used CollegeXpress to search for colleges. It helped me narrow down the schools on the West Coast and which schools had Construction Engineering programs. I made my decision to go to OSU and I am so excited about it.

Melanie Kajy

Melanie Kajy

High School Class of 2021

CollegeXpress has helped me tremendously during my senior year of high school. I started off using the college search to find more information about the universities I was interested in. Just this tool alone gave me so much information about a particular school. It was my one-stop shop to learn about college. I was able to find information about college tuition, school rank, majors, and so much more that I can't list it all. The college search tool has helped me narrow down which college I want to attend, and it made a stressful process surprisingly not so stressful. I then moved to the scholarship search tool to find scholarships to apply for because I can't afford to pay for tuition myself. The search tool helped me find scholarships that I was eligible for. The tool gave me all the information I could ever need about a particular scholarship that was being offered. The CollegeXpress scholarship search tool is so much better than other tools offered, like the Chegg scholarship search. Thanks to CollegeXpress, I was able to apply to tons of scholarships in a relatively easy way!

Rose Kearsley

Rose Kearsley

High School Class of 2021

CollegeXpress has seriously helped me out a lot, especially when it comes to scholarships and studying for tests like the ACT. I also really love the financial help. It’s a little harder to pay because I live with a family of eight, so any help is appreciated. Thanks for this opportunity!

Christina

Christina

High School Class of 2021

CollegeXpress helped me find Allegheny College with the super-user-friendly search tool for both schools and scholarships. Using CollegeXpress, I was able to search for programs I was interested in studying and find colleges that offered those programs. Also, once you search for the college, CollegeXpress can get you connected!

Katelyn

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.