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Prerequisite Diagnostic

Allow 30–45 minutes. This checks arithmetic, careful reading and basic programming from the launchpad/orientation. Quantifiers and induction are taught here; you do not need them to enter. Write an attempt before opening the feedback below.

  1. Calculate 2(-3)+5, and expand (x+1)^2 without choosing a value of x.
  2. Find integers k satisfying 12=3k and 7=3k. Explain why the second fails.
  3. List the values visited by for i in range(3) and the final sum starting at 0.
  4. Trace a loop that counts values greater than zero in [-2,0,4,1], then in [].
  5. Explain the difference between an input, an expected result and an observed result.
  6. Run a small Python file from the terminal and record the command and output.

Feedback and repair​

  1. −1; x^2+2x+1. If expansion is unstable, distribute both factors and check x=0,1,−1; those checks diagnose arithmetic but do not establish an identity.
  2. k=4; no integer k solves the second equation. Review integer division and remainder.
  3. 0,1,2; final sum 3. Explain why the stop value is excluded.
  4. Counter states 0,0,1,2; empty input leaves 0. Revisit launchpad tracing if needed.
  5. Expected results come from the specification; observed results come from a run.
  6. Any small reproducible script suffices. Use the launchpad terminal/Python setup.

Begin the mathematical lessons if items 1–2 are reliable. Repair items 3–6 before the coding labs; they need not delay the logic lessons. No aggregate score hides a missing prerequisite. Record assistance and reattempt the missed skill with different values. Prior proof knowledge can shorten practice only after a fresh competency assessment demonstrates it.