The Hardest SAT Math Problems of 2025 (and How to Solve Them)
- Laura (Heslin) Whitmore
- 1 day ago
- 3 min read
By Laura Whitmore
If you're aiming for a top score on the SAT Math section—whether that's a perfect 800 or something north of 700—you already know that the second module often ends with some of the hardest math problems on the test! These are the ones that trip up even strong students, especially under timed conditions.
Our tutor team has taken the SAT multiple times (yes, officially!) and earned perfect scores on the math section. We’ve recently put together a collection of the most difficult SAT math problems we’ve seen so far in the new digital format. Check out the highlights here to help you tackle each of these challenging concepts head-on.
Not up for reading? Watch my YouTube video instead!
1️⃣ Using Desmos for Systems of Equations | Tutor Andy
Andy shared a problem involving two spheres with radii in a 12:13 ratio and a known difference in surface areas. Rather than manually solving a system of equations to find the radius, Andy recommends using Desmos to graph and identify the point of intersection. Once the smaller radius is known, the volume becomes a simple plug-and-chug.
This problem is a great reminder: when allowed, Desmos can be a powerful tool to speed up your work and minimize mistakes!
2️⃣ Geometry & Scale Factors | Tutor Luis
Luis walked through a geometry problem where you’re given measurements from a triangle nested inside a larger one. He used the Pythagorean Theorem to find the height of the smaller triangle, then used a scale factor to calculate the area of the larger triangle.
Key takeaway: when two triangles are similar, their area increases by the square of the scale factor—not the scale factor itself. A small detail that makes a big difference!
3️⃣ Simplifying Complicated Functions | Tutor Shayda
Shayda tackled a function problem that at first glance looked like a nightmare: absolute values, squared expressions, unknown constants. But by simply plugging in the x-values provided, she noticed that both outputs simplified to the same value. That meant the difference between the two (which the question asked for) was zero—making the final calculation easy.
Moral of the story: Don’t panic when a function looks messy. Sometimes substitution is all you need.
4️⃣ Piecewise Functions in Real-World Contexts | Tutor Maria
Maria explained a problem involving bird population growth, which changed at the two-week mark. The key was setting up two separate linear functions: one for the first two weeks and another for the time after. She then used those to build a third function that tracked how many birds were still needed to reach the goal.
It’s a classic piecewise function setup, and it reinforces the importance of understanding how to model real-world changes in behavior over time.
5️⃣ Circle Equations & Regression | Laura
I love this math problem because it looks intimidating—students often think they need to complete the square. But when you're given the center and radius of a circle, you can quickly identify three points on the circle and plug them into Desmos to generate the full equation using regression. This approach is faster, cleaner, and avoids careless errors.
It’s a great example of how knowing the right tools can make tough problems much more manageable.
Each of these problems is pulled directly from our brand-new SAT Math Workbook, which we’re currently offering as a free download on our website. You can grab your copy and follow along with the problems above—or use it to continue your practice on your own.
And if you're looking for more targeted help with test prep, we offer personalized 1:1 tutoring with expert tutors who specialize in both SAT and ACT.
We hope these strategies help you approach the hardest SAT math problems with more confidence and clarity. Keep practicing, and as always—happy prepping!
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