🎯 Algebra Mastery Guide — AMC 10 & AMC 12

🗺️ Quick Navigation

📚 Reference Materials

• Scope Map — AMC10 vs AMC12 coverage matrix
• Notation Cheatsheet — Symbols, functions, domains, intervals
• Concept Atlas — One-paragraph primers with AMC appearance cues

📖 Topic Guides

• Algebra Basics — Order of operations, factoring patterns, identities
• Linear Equations & Inequalities — One-variable, interval notation, graph sense
• Absolute Value — Piecewise setup, distance view
• Quadratics & Parabolas — Vertex/axis, discriminant, completing square
• Polynomial Theory — Division, remainder/factor theorems, Vieta
• Rational Expressions — Domains, asymptote sense, extraneous roots
• Radicals & Exponents — Rational exponents, conjugate/rationalize
• 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
• 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

🧩 Problem Types

• Factoring Templates — Classic patterns, Sophie Germain, grouping
• Discriminant & Parameter Sweeps — Count solutions, range of parameters
• Rational Equations — Cross-multiplying safely, domain first
• Radical Equations — Isolate, square, verify, conjugate tricks
• Absolute Value Casework — Breakpoints, symmetry, sum of distances
• Systems Linear & Nonlinear — Line-circle, parabola-line, substitution flows
• Symmetry Substitutions — $u=x+\frac{1}{x}$, $t=x^2$, cyclic sums
• Sequence Closed Forms — Finite GP/AP sums, telescoping
• Functional Equation Templates — $f(x+a)/f(-x)$ invariances, injectivity tests
• Exponential & Log Tricks — Compare growth, base alignment, logs of both sides
• Word Problems — Work/rate/mixture, ratio/proportion, units

📏 Essential Resources

• Essential Formulas — Compact formula bank with micro-examples
• Problem-Solving Tips — Heuristics, checklists, timing strategies

🧮 Practice Problems

• Algebra Problems — Example problems and techniques for AMC 10 Algebra topics
• Practice Hub — Comprehensive AMC-style practice with mixed sets, topic drills, and mock exams

⚡ Quick Facts

• AMC10 Focus: Core algebra, basic polynomials, simple systems
• AMC12 Extensions: Complex numbers, advanced inequalities, functional equations
• Common Pitfalls: Domain restrictions, extraneous solutions, sign errors
• Key Success Factors: Pattern recognition, algebraic manipulation, strategic substitution

Next: Geometry | Back: AMC 10/12