THE 100 HARDEST
SAT® MATH
QUESTION types,
FULLY EXPLAINED.

For students aiming for a perfect 800 and admission to the Ivy League and other top-tier universities. Each question type is worked step by step, then shown again in different variations, so you learn the pattern instead of memorizing one answer.

Got a question? See our FAQs or contact us.

Where some of our SAT students study now

WHAT'S INSIDE

For students aiming for 800 — and the parents supporting them.

Only the hardest 100

Hand-picked from the problems that separate a 700 from an 800. No easy filler — only the questions that decide top scores.

Fully worked solutions

Not an answer key. Each problem is solved step by step — the reasoning, the traps to avoid, and the fastest path to the answer.

Built for the 800 track

Written for students and parents serious about top-tier admissions who want the last, hardest points on the math section.

Watch a walkthrough

Watch Will walk through one question type

In this walkthrough Will takes one of the 100 questions and shows the full thought process: what the question is really testing, the trap most students fall for, and the cleanest route to the answer.

Thirteen years spent getting students the last, hardest points.

Will has tutored the SAT full-time since 2013, coaching students into Harvard, MIT, Oxford and beyond. The 100 questions in this guide are the exact problems he pulls out when a student is stuck between a strong score and a perfect one.

10K+

hours spent analizing the SAT content

1-on-1

Weekly sessions behind the method

1000+

Students coached

13 years

Of tutoring the SAT​

Every hard corner of SAT Math, mapped.

Not a random pile of problems — a deliberate spread across the topics that actually cost top scorers points.

Heart of Algebra

18Q

Linear systems, absolute value, and the traps in "solve for" phrasing.

Passport to Advanced Math

18Q

Quadratics, exponentials, and manipulating nasty algebraic expressions.

Problem Solving & Data

Ratios, percentages, and the statistics questions that hide the trick.

18Q

Geometry & Trigonometry

Circles, angles, and the trig identities that show up in the last five questions.

18Q

Nonlinear Systems

Where lines meet curves — discriminants, intersections, and edge cases.

18Q

100 questions

Each with a complete worked solution — nothing left as "left to the reader."

A sample from the guide

What changed for our students

These students started at different scores, worked on different problems and needed different amounts of time. The numbers show the result. Their own words explain the rest.

Get the last, hardest points.

100 questions, a full worked solution for each. One download, yours for good.

One hour with a high-end private SAT tutor typically runs $180–$400. This is the whole method, once, for less than a single session.

$100

Instant PDF · Pay once

Questions, answered

Everything students and parents ask before buying

A PDF covering 100 SAT math question types, the ones that separate a 700 from an 800. Each one is worked step by step: what the question is testing, the trap most students fall for, and the cleanest way to the answer. Most question types also come with 2 to 5 variations, so you see the same idea show up in a different form and learn to recognize it, not just memorize one problem.

Students who are already scoring well and want the last 50 to 100 points. If you’re still missing questions in the 500 to 650 range, this guide will feel too advanced. It’s built for the gap between a 700 and an 800.

Yes. This guide covers the hardest math questions on the SAT. If you’re looking for Reading and Writing, check our free guides below.

Instant PDF download after purchase. You’ll create a free account to get it, which also unlocks every free guide we publish.

Yes. Nothing is skipped and nothing hand-waved. Every problem is broken into the same steps Will uses when he’s sitting across from a student: what’s actually being asked, where the trap is, and the exact path to the answer.

Yes, scroll up to see a full sample question with the worked solution. That’s exactly the format used for all 100 question types.

Free SAT Guides

Each guide is built to give you more than just a starting point. They’re detailed, carefully written, and designed to walk you through the parts of SAT prep that actually matter: how to plan, how to study, and how to approach a school like Bocconi with a strategy that makes sense.

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