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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.
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.
Compute the area of a circle with radius 7. Use pi to 2 decimal places.
Find the derivative of f(x) = x * sin(x) using the product rule.
Solve the system: 2x + 3y = 12 and x - y = 1.
Evaluate log base 2 of 32 and show your reasoning.
Find the prime factorisation of 360.
Compute the indefinite integral of 6x^2 + 4x dx.
Differentiate f(x) = (3x^2 + 1)^4 with respect to x.
A right-angled triangle has legs of length 5 and 12. Find the length of the hypotenuse.
Factor the polynomial x^2 - 7x + 12 and explain the steps.
State the quadratic formula for solving ax^2 + bx + c = 0 and show how to use it to solve 2x^2 + 5x - 3 = 0.