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.
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?
Explain why a function and its inverse reflect across the line y = x.
Describe how to find the limit of (sin x) / x as x approaches 0. There is more than one valid approach.
Explain the difference between a permutation and a combination. When would a student choose one over the other?
What is the most elegant way to prove that there are infinitely many prime numbers?
Why is the integral of 1/x equal to ln|x| rather than something else? Give an intuitive explanation.
Explain in your own words what a derivative represents. Use an example if it helps.
Explain why the Pythagorean theorem holds. You may use any proof method you prefer.
Find the equation of the line passing through (1, 2) and (4, 11).
Given the data set {4, 8, 6, 5, 3, 7, 8}, compute the mean, median, and mode.