#gremath

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.

This one’s got everything:

• A solid of revolution • An improper integral • An antiderivative that turns into arctangent • And a final step that makes you think about where arctangent actually goes at the extremes

Direct integration works — but only if you’ve internalized the key formulas and can recognize where inverse tangent shows up.

One GRE question tests how well you know your calculus theorems — continuity, integration, differentiability, all in one.

The other looks complicated — vector spaces, matrices, linear transformations — but it collapses with a single line of reasoning if you know what to look for.

Two very different problems. One minute. No calculator.

Three GRE-style questions in 60 seconds:

• A geometry problem on maximizing area with limited fencing • A number theory question: what’s the units digit of 7^25? • A polynomial root-counting challenge — no graphing required

All three come fast — but each one tests something different: reasoning, pattern recognition, and algebraic structure.

Three questions. One minute. No calculator.

1️⃣ A derivative graph — where is the function largest? 2️⃣ An approximation — how close can you get to √1.5 × (266)^(3/2)? 3️⃣ A matrix — can you spot the guaranteed eigenvector?

Each one uses a different kind of reasoning, and all three go by fast — but you can pause if you want to dig in.

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?