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Answer Key — Vector calculus

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Calculus III

Do not share with students before practice tests.

Worksheets — Sets 1–10

| Set | Guidance | | --- | --- | | Set 1 | Vector calculus — verify written work and accept reasonable drawings. | | Set 2 | Vector calculus — verify written work and accept reasonable drawings. | | Set 3 | Vector calculus — verify written work and accept reasonable drawings. | | Set 4 | Vector calculus — verify written work and accept reasonable drawings. | | Set 5 | Vector calculus — verify written work and accept reasonable drawings. | | Set 6 | Vector calculus — verify written work and accept reasonable drawings. | | Set 7 | Vector calculus — verify written work and accept reasonable drawings. | | Set 8 | Vector calculus — verify written work and accept reasonable drawings. | | Set 9 | Vector calculus — verify written work and accept reasonable drawings. | | Set 10 | Vector calculus — verify written work and accept reasonable drawings. |

Worksheets — Sets 11–20

| Set | Guidance | | --- | --- | | Set 11 | Vector calculus — verify written work and accept reasonable drawings. | | Set 12 | Vector calculus — verify written work and accept reasonable drawings. | | Set 13 | Vector calculus — verify written work and accept reasonable drawings. | | Set 14 | Vector calculus — verify written work and accept reasonable drawings. | | Set 15 | Vector calculus — verify written work and accept reasonable drawings. | | Set 16 | Vector calculus — verify written work and accept reasonable drawings. | | Set 17 | Vector calculus — verify written work and accept reasonable drawings. | | Set 18 | Vector calculus — verify written work and accept reasonable drawings. | | Set 19 | Vector calculus — verify written work and accept reasonable drawings. | | Set 20 | Vector calculus — verify written work and accept reasonable drawings. |

Review tiers 1–10

  • Checklists are parent-judged.
  • Written items: verify against practice set patterns.
  • Standard text: Vector fields, line integrals, and circulation Fundamental theorem for line integrals; conservative fields and potential functions Green's theorem in the plane; curl and divergence (introduction) Surface integrals; flux and the divergence theorem (introduction) Stokes' theorem (introduction) and connections among the major theorems

Practice test scoring

| Tier | Pass guidance | | --- | --- | | 1–3 | Most oral tasks smooth; majority of written correct | | 4–6 | 7/10+ total with clear understanding | | 7–8 | 9/12+ with explanations | | 9–10 | Near-perfect; ready to move on |

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