Mixed module checkpoint

Quadratics, complex numbers and polynomials: mixed checkpoint

Use this mixed precalculus checkpoint after studying the core topics in Module 5. It samples quadratic structure and optimization, model comparison, power functions, complex arithmetic, polynomial roots, division and inequalities through fresh combinations of skills.

The questions are intentionally interleaved rather than arranged as a lesson or labeled by the method to use. Work independently on paper, select all supported statements in multiselect items, and consult the explanations after committing to an answer. All needed data are supplied; no regression software or calculator is required.

Interpret errors by skill, not only by total score. A mistaken endpoint, an omitted domain restriction, an unjustified model claim or a lost root can identify different practice needs. Return to the relevant topic and its algebra or function prerequisite, then use a fresh problem to reassess.

This checkpoint uses new item families rather than copies of the associated practice sets. It samples the core module and excludes optional extension theorems. One short bank cannot exhaustively establish mastery. Its recognition-based evidence should later be combined with written solutions, graph construction and delayed retrieval after intervening study.