📖 Topic Guides — Algebra Mastery

Detailed guides for each algebra topic, organized for systematic study.

🎯 Core Topics (AMC10 Essential)

🔢 Fundamentals

Algebra Basics — Order of operations, factoring patterns, identities
Linear Equations & Inequalities — One-variable, interval notation, graph sense

🎯 Quadratic Systems

Absolute Value — Piecewise setup, distance view
Quadratics & Parabolas — Vertex/axis, discriminant, completing square

🧮 Polynomial Theory

Polynomial Theory — Division, remainder/factor theorems, Vieta

🔄 Rational & Radical

Rational Expressions — Domains, asymptote sense, extraneous roots
Radicals & Exponents — Rational exponents, conjugate/rationalize

🎲 Systems & Advanced

Systems of Equations — Substitution/elimination, 2×2, 3×3, nonlinear pairs
Inequalities & Optimization — Sign charts, AM-GM/Cauchy, bounds
Sequences & Recursions — Arithmetic/geometric, simple recurrences, telescoping

🚀 Advanced Topics (AMC12 Extensions)

🧮 Advanced Algebra

Functional Equations — Substitutions, symmetry, injective/surjective checks
Exponential & Log Equations — Equation/ineq solving, change-of-base
Complex Numbers — Algebra, quadratic roots, Arg basics
Equations with Parameters — Number of solutions via discriminant/degeneracy

📚 How to Use These Guides

Study Order

Start with Core Topics — Master AMC10 essentials first
Practice Each Topic — Work through examples and problems
Connect Topics — Notice how concepts build on each other
Add Advanced Topics — For AMC12 preparation

Each Guide Contains

Key Ideas — Core concepts explained clearly
Micro-Examples — Quick practice problems
Traps & Fixes — Common mistakes and how to avoid them
AMC-Style Examples — Contest-level worked problems
Cross-References — Links to related topics

Study Tips

Read actively — Don’t just skim, work through examples
Practice immediately — Try problems as you read
Make connections — See how topics relate to each other
Review regularly — Come back to reinforce learning

⚡ Quick Reference

Topic	AMC10	AMC12	Key Skills
Algebra Basics	✅	✅	Factoring, identities
Linear Systems	✅	✅	Solving, graphing
Quadratics	✅	✅	Formula, vertex, discriminant
Polynomials	🔶	✅	Vieta, remainder/factor
Rational	🔶	✅	Domain, extraneous
Radicals	🔶	✅	Isolate, square, verify
Systems	✅	✅	Substitution, elimination
Inequalities	🔶	✅	Sign charts, AM-GM
Sequences	✅	✅	AP/GP, telescoping
Functional	❌	🔶	Substitution, symmetry
Exponentials	🔶	✅	Change of base
Complex	❌	🔶	Conjugates, modulus
Parameters	🔶	✅	Discriminant analysis

Start with Algebra Basics to build your foundation!

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