HUNTERTUTORING

Answer Key — Groups

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Abstract algebra

Do not share with students before practice tests.

Worksheets — Sets 1–10

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

Worksheets — Sets 11–20

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

Review tiers 1–10

  • Checklists are parent-judged.
  • Written items: verify against practice set patterns.
  • Standard text: Binary operations, equivalence relations, and modular arithmetic Groups: definitions, examples (Z, Z_n, dihedral, symmetric groups) Subgroups and cyclic groups; generators and order Cosets, Lagrange's theorem, and index Normal subgroups and quotient groups Group homomorphisms and the first isomorphism theorem Direct products and simple groups (introduction)

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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