Answer Key — Advanced topics
Real analysis
Do not share with students before practice tests.
Worksheets — Sets 1–10
| Set | Guidance | | --- | --- | | Set 1 | Advanced topics — verify written work and accept reasonable drawings. | | Set 2 | Advanced topics — verify written work and accept reasonable drawings. | | Set 3 | Advanced topics — verify written work and accept reasonable drawings. | | Set 4 | Advanced topics — verify written work and accept reasonable drawings. | | Set 5 | Advanced topics — verify written work and accept reasonable drawings. | | Set 6 | Advanced topics — verify written work and accept reasonable drawings. | | Set 7 | Advanced topics — verify written work and accept reasonable drawings. | | Set 8 | Advanced topics — verify written work and accept reasonable drawings. | | Set 9 | Advanced topics — verify written work and accept reasonable drawings. | | Set 10 | Advanced topics — verify written work and accept reasonable drawings. |
Worksheets — Sets 11–20
| Set | Guidance | | --- | --- | | Set 11 | Advanced topics — verify written work and accept reasonable drawings. | | Set 12 | Advanced topics — verify written work and accept reasonable drawings. | | Set 13 | Advanced topics — verify written work and accept reasonable drawings. | | Set 14 | Advanced topics — verify written work and accept reasonable drawings. | | Set 15 | Advanced topics — verify written work and accept reasonable drawings. | | Set 16 | Advanced topics — verify written work and accept reasonable drawings. | | Set 17 | Advanced topics — verify written work and accept reasonable drawings. | | Set 18 | Advanced topics — verify written work and accept reasonable drawings. | | Set 19 | Advanced topics — verify written work and accept reasonable drawings. | | Set 20 | Advanced topics — verify written work and accept reasonable drawings. |
Review tiers 1–10
- Checklists are parent-judged.
- Written items: verify against practice set patterns.
- Standard text: Sequences and series of functions; pointwise vs uniform convergence Power series and analytic functions (introduction) Metric spaces (optional capstone): definitions and examples
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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