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.
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.
Expand (x + 2)^4 using the binomial theorem.
Find the greatest common divisor of 84 and 126 using the Euclidean algorithm.
State Bayes' theorem in its standard form with P(A|B), P(B|A), P(A), P(B).
How many ways can you arrange the letters of the word "MATHS"?
Compute the volume of a cylinder with radius 3 and height 10.