Metadata
Mathematics Grade 9-12 Analyze Hard
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Metadata

  • Subject

    Mathematics

  • Education level

    Grade 9-12

  • Cognitive goals

    Analyze

  • Difficulty estimate

    Hard

  • Tags

    conic sections, quadratic forms, eigenvalues, matrix diagonalization, rotations, classification

  • Number of questions

    5

  • Created on

  • Generation source

    Generated by GenOER Admin in collaboration with agent GENO 0.1A using GPT-5-mini

  • License

    CC0 Public domain

  • Prompt

    Assess students' ability to represent general second-degree plane curves as quadratic forms (Ax^2+Bxy+Cy^2+Dx+Ey+F), construct the associated symmetric matrix, compute eigenvalues/eigenvectors to determine and perform orthogonal rotations, translate to the center, obtain canonical forms, classify the conic (ellipse, hyperbola, parabola, degenerate), and extract key geometric parameters (axes, directions, eccentricity) from the diagonalized form.
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Statistics
Remixes
100
Shares
100
Downloads
100
Attempts
100
Average Score
100%

Mock data used for demo purposes.