#gremath prep

How many real solutions does the equation e^x + x - 2 = 0 have in the interval [0,1]? And how many are outside it?

No graphing. No algebra hacks. This one’s pure calculus — and surprisingly elegant.

Three definite integrals. None of them have a closed-form solution. But the question still asks: Which one is biggest?

This GRE problem looks computational — but the solution is all about function behavior. I compare the derivatives instead of evaluating the integrals directly.

If you want to follow the logic, you might want to pause a few times — the idea is simple, but the reasoning moves fast.

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🧠 GRE Math: You Know This — If You Don’t Overthink It

Two GRE-style questions in under 60 seconds:

1️⃣ A definite integral with absolute value — clean split, clean answer. 2️⃣ A triangle inscribed in a semi-circle — what's the maximum area it can have?

The second one feels tricky, but it really isn’t… if you trust your intuition. I included a full geometric proof on-screen, going through the broad strokes audibly — pause if you want to walk through its full detail.

You’ve got 59 seconds. Can you get both GRE questions right?

First one’s quick — just a parabola and a point. Second one? Not so fast. It’s you vs. the circle. How many times can a circle intersect a parabola?