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Prerequisite Diagnostic

Allow 40–50 minutes. This checks arithmetic, elementary functions, proof and code tracing from earlier work; elimination, orthogonality and conditioning are taught here. Save an attempt before consulting the feedback.

  1. Solve 3x+2=11 and explain why subtracting two from both sides preserves equality.
  2. Simplify 1/2+1/3 exactly, then distinguish that rational value from a rounded decimal.
  3. Evaluate f(g(2)) for f(t)=2t and g(t)=t+1. Compare g(f(2)).
  4. Negate “every nonzero vector satisfies this inequality.” State the domain.
  5. Prove that if two real numbers have the same difference from five, they are equal.
  6. Trace a loop computing sum(row[j]*x[j] for j in range(2)) for row=[2,−1], x=[3,4].
  7. Run a short Python script; record input, prediction and observed output separately.

Feedback and repair​

  1. x=3; adding the same quantity is reversible. Repair equation manipulation first.
  2. 5/6; a finite displayed decimal is generally an approximation. Use fractions for the exact lab and state when converting to floating arithmetic.
  3. f(g(2))=6; g(f(2))=5. Composition order matters before matrices enter the story.
  4. Some nonzero vector in the specified space fails the inequality. Repair quantifier negation through Module 1.
  5. From a−5=b−5 add five to both sides. State the permitted algebraic operation.
  6. 23−14=2; check indexing and multiplication before the matrix labs.
  7. Any reproducible script suffices; repair environment setup independently of handwritten lessons. Python 3.10+ is sufficient for the offline kit.

Reattempt missing skills with new numbers. There is no aggregate score that excuses a missing arithmetic or reasoning prerequisite.