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Assessment and progression gates

Score each CAL item separately: 0 absent or invalid; 1 partial or materially prompted; 2 independently correct with assumptions and checks; 3 also defends a changed case and limitations. Every item requires at least 2. No average can hide a missing dependency. Consult the reviewer key only after preserving your attempt.

  • CAL1 — Functions and limits: state the real domain and inverse of ln(x−5). Prove the limit of 4x+2 at x=2 is 10 with an epsilon-delta argument. Give a limit-without-continuity example.
  • CAL2 — Derivatives and sensitivity: derive the derivative of x² from the definition, then differentiate x exp(−3x) and ln(1+2x²). Explain units for a rate of change.
  • CAL3 — Constrained optimization: minimize 2x+32/x on [1,8], then [5,8]. Include every feasible candidate and justify completeness.
  • CAL4 — Accumulation: construct a right Riemann sum for 2t on [0,2] and take its limit. Evaluate ∫₀¹ 3x² exp(x³)dx and ∫₀¹ x exp(2x)dx, checking by differentiation.
  • CAL5 — Continuous probability: normalize c t² on [0,2], give its full piecewise CDF and mean, and find P(T>1). Explain point probability and density units. For an exponential model with rate 3, derive a cutoff omitting at most 0.001 mass.
  • CAL6 — Approximation guarantees: bound the error of 1+x+x²/2 for exp(x) at 0.1 with exp(x)<2 on that interval. Derive a sufficient trapezoid count for x² on [0,1] at error 0.0005. Explain why sign change alone is insufficient for a root.
  • CAL7 — Reproduction and judgment: finish the lab and project, pass the extracted archive checks, and reproduce one function on a changed case without generated code. Defend the difference between test success and mathematical validity, including an invalid bracket, a budget failure and floating-point cancellation.

CAL1–CAL6 are the continuous-probability entry gate; CAL7 is additionally required for module completion. Do not postpone unresolved algebra or integration gaps into probability. If self-assessed, record “self-assessed ready; independent review pending.”

After 7–14 days, redo one weak item and one randomly selected other item with changed constants, without the key. Record help, elapsed time, original mistakes and repairs. Reuse this delayed check at semester level rather than doing a duplicate assessment.