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.
Compute the sum of the infinite geometric series 1 + 1/2 + 1/4 + 1/8 + ... Give the exact value.
Is the repeating decimal 0.999... equal to 1? State the exact value and justify using a geometric-series argument.
Compute the number of permutations of 7 distinct objects taken 3 at a time, P(7, 3). Give the exact integer.
Compute 6! (six factorial). Give the exact integer.
Compute the binomial coefficient C(8, 3). Give the exact integer.
State the smallest prime factor of 1001. Give the exact integer.
Compute the greatest common divisor of 252 and 198 using the Euclidean algorithm. Give the exact integer.
A fair coin lands heads five times in a row. State the probability that the next flip is heads, and explain why it is not affected by the previous flips.
A prior P(H) = 0.2 and likelihood P(E|H) = 0.8, with P(E|not H) = 0.1. Compute the posterior P(H|E) using Bayes' theorem. Give the exact value.
Compute the limit of (x^2 - 4) / (x - 2) as x approaches 2. Give the exact value.
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.