Public viewer
The journey of every round
Every round-trip in the corpus is public. Open one to see the prompt, the zero-point index, the baseline response, the enhanced response, and how each grader read the difference. Leave a comment if a grader's reading lands — or doesn't.
Evaluate the definite integral of (2x + 1) from x = 0 to x = 3. Give the exact value.
Differentiate g(x) = sin(3x^2 + 1) using the chain rule. Give the exact derivative.
Evaluate the indefinite integral of 3x^2 + e^x with respect to x. Give the antiderivative and include the constant of integration.
Differentiate f(x) = 4x^3 - 5x^2 + 2x - 7. Give the derivative f'(x) as a polynomial.
Simplify the rational expression (x^2 - 9) / (x^2 - x - 6) and state any restrictions on x. Give the simplified form.
Solve the linear system 3x + 2y = 16 and x - y = 2. Give the exact values of x and y.
Expand (2x - 3)(x + 5) and give the result as a polynomial in standard form.
Factor the cubic polynomial x^3 - 6x^2 + 11x - 6 into linear factors over the rationals. Give the factored form.
A game show host shows you three doors. Behind one is a car, behind the other two are goats. You pick door 1. The host opens door 3, revealing a goat, and offers you the chance to switch to door 2. Should you switch? Why?
Ice cream sales and drowning incidents both rise in summer. Does buying ice cream cause drowning? Explain what is really going on.
Given f(x) = x + 1 and g(x) = x^2, is f(g(x)) the same as g(f(x))? Show both and explain.
A student writes: "-3 - (-7) = -10 because two negatives next to each other stay negative." Is the student correct? Show the correct working.
A medical test for a rare disease is 95% accurate. The disease affects 1% of the population. Someone tests positive. What is the probability they actually have the disease?
A fair coin has come up heads ten times in a row. Is tails more likely on the next flip, less likely, or the same? Explain.
Is 0.999... (repeating forever) equal to 1, or just very close to 1? Explain your answer.
Explain in plain terms what a confidence interval is and what it is not.
Describe the geometric meaning of the dot product of two vectors.
Why does the integration-by-parts formula take the form it does? Explain in your own words.
What is the relationship between the derivative and the slope of a tangent line? Explain in plain language.
Explain how mathematical induction works as a proof technique. Give a small example.
Compare and contrast the mean and the median as measures of central tendency. When is each preferred?
Describe an intuitive way to understand the chain rule for differentiation.
Explain what it means for two events to be independent in probability. Give a real-world example.
Why does completing the square work as a method for solving quadratic equations?