# Khaemenes Open-Age Algebra II & Advanced Functions

Course code: `KH-MATH-A2`  
Version: `1.0.0`  
Duration: 36 weeks  
Detailed lessons: 92  
Study sessions: 180  
Units: 13  
Pathways: Foundation, Core, Extended  
Mastery target: 80%

## Entry

This is a placement-based course. Recommended entry is completion of Algebra I or equivalent demonstrated mastery. The 40-question diagnostic is used to identify prerequisite review, not to impose an age or grade label.

## Course design

- Week 1: Algebra I readiness diagnostic and bridge planning
- Weeks 2–17: Units 01–06
- Week 18: midpoint synthesis, corrections, portfolio review, and 60-question midterm
- Weeks 19–35: Units 07–12
- Week 36: advanced modelling exploration, oral defense, comprehensive final, and record review

## Unit sequence

- Unit 01: **Advanced Functions, Transformations & Inverses** — 2 week(s), 6 lessons — How do notation, transformations, composition, and inverse thinking reveal the structure and behavior of functions?
- Unit 02: **Polynomial Functions & Complex Numbers** — 3 week(s), 8 lessons — How do polynomial structure, complex numbers, zeros, and end behavior work together to describe nonlinear change?
- Unit 03: **Polynomial Equations, Division & Graphs** — 3 week(s), 7 lessons — How can division, factor relationships, multiplicity, and graph features expose every important part of a polynomial model?
- Unit 04: **Rational Expressions, Equations & Functions** — 3 week(s), 8 lessons — How do excluded values, asymptotes, holes, and rates of change shape rational expressions and models?
- Unit 05: **Radical Functions & Rational Exponents** — 2 week(s), 6 lessons — How do radicals, rational exponents, inverse relationships, and domain restrictions describe quantities that grow by roots and powers?
- Unit 06: **Exponential Functions & Growth Models** — 3 week(s), 7 lessons — How do repeated multiplication, percent change, and continuous growth create exponential patterns and decisions?
- Unit 07: **Logarithmic Functions & Equations** — 3 week(s), 7 lessons — How do logarithms reverse exponential processes, compress scale, and reveal time, magnitude, and rate?
- Unit 08: **Nonlinear Systems & Matrices** — 2 week(s), 6 lessons — How can multiple equations, matrices, and graphical intersections describe systems with several interacting constraints?
- Unit 09: **Sequences, Series & the Binomial Theorem** — 3 week(s), 7 lessons — How do recursive and explicit rules describe patterns, accumulated change, and finite or infinite sums?
- Unit 10: **Trigonometric Functions & Periodic Models** — 4 week(s), 10 lessons — How do angle measure, the unit circle, graphs, and periodic functions model rotation, waves, cycles, and repeated behavior?
- Unit 11: **Trigonometric Identities, Equations & Oblique Triangles** — 3 week(s), 8 lessons — How do identities and triangle laws transform expressions, solve periodic equations, and determine unknown measurements?
- Unit 12: **Probability, Distributions & Statistical Inference** — 2 week(s), 7 lessons — How do counting, probability models, distributions, and sampling support responsible conclusions under uncertainty?
- Unit 13: **Advanced Mathematical Modelling Capstone** — 1 week(s), 5 lessons — How can a transparent, tested, and ethically communicated mathematical model support a real decision?

## Lesson architecture

Every detailed lesson includes:

1. learning objectives;
2. essential question;
3. governing relationship or formula;
4. concept development;
5. worked examples;
6. guided and independent practice;
7. Foundation, Core, and Extended pathways;
8. application laboratory;
9. misconception and correction;
10. mastery evidence;
11. reflection;
12. local completion and note storage;
13. print support and connected calculator route.

## Assessment model

- 40-question readiness diagnostic
- 13 randomized unit mastery checks
- 60-question midpoint examination
- 100-question comprehensive final
- 13 applied investigations
- weekly classwork, mastery, portfolio, and reflection records
- advanced modelling capstone with 100-point analytic rubric
- oral defense and revision
- printable completion record

## Weighted course record

- Coursework: 35%
- Mastery evidence: 20%
- Midterm: 15%
- Comprehensive final: 20%
- Capstone exploration and defense: 10%

An evaluator may adapt weights if clearly documented before instruction.

## Local-first privacy

Learner names, weekly scores, reflections, portfolio notes, assessment attempts, and certificate fields remain in browser storage unless explicitly exported or printed.