🗺️ AMC Geometry Scope Map

This matrix shows which geometry topics appear on AMC 10 vs AMC 12, with frequency indicators and difficulty levels.

📊 Topic Coverage Matrix

TopicAMC 10AMC 12FrequencyNotes
Basic Triangles✅ Core✅ Core⭐⭐⭐SSS, SAS, ASA, AAS, isosceles, equilateral
Triangle Centers✅ Core✅ Core⭐⭐Centroid, incenter, circumcenter, orthocenter
Angle Chasing✅ Core✅ Core⭐⭐⭐Parallel lines, inscribed angles, exterior angles
Similarity & Ratios✅ Core✅ Core⭐⭐⭐Dilations, angle bisector theorem, area ratios
Circles & Power of Point✅ Core✅ Core⭐⭐⭐Chords, tangents, secants, PoP
Cyclic Quadrilaterals✅ Often✅ Core⭐⭐Opposite angles, Ptolemy’s theorem
Special Segments✅ Often✅ Core⭐⭐Medians, altitudes, angle bisectors
Length & Area Formulas✅ Often✅ Core⭐⭐Heron, Brahmagupta, Stewart, Apollonius
Coordinate Geometry✅ Often✅ Core⭐⭐Lines, circles, shoelace, distance
Geometric Probability✅ Often✅ Core⭐⭐Lengths, areas, random points
Transformations❌ Rare✅ Often⭐Reflections, rotations, homothety
3D Geometry❌ Rare✅ Often⭐Projections, volumes, cross-sections
Mass Points❌ Rare✅ Often⭐Ceva, Menelaus, concurrency
Tangency Configurations✅ Often✅ Core⭐⭐Incircles, excircles, tangent chains
Polygons & Tilings✅ Often✅ Core⭐⭐Interior angles, regular polygons
Inversion & Spiral Similarity❌ Never✅ Stretch⭐Advanced transformations

🎯 Difficulty Indicators

  • ⭐⭐⭐ = Very common, appears frequently
  • ⭐⭐ = Common, appears regularly
  • ⭐ = Less common, appears occasionally
  • ❌ = Rare or never appears

📈 AMC 10 Focus Areas

Must Master (Core + Often):

  • Basic triangle relationships
  • Angle chasing techniques
  • Similarity and ratios
  • Circle properties and Power of a Point
  • Coordinate geometry basics
  • Geometric probability fundamentals

Nice to Have:

  • Cyclic quadrilaterals
  • Special segments in triangles
  • Length and area formulas
  • Tangency configurations
  • Polygons and tilings

📈 AMC 12 Focus Areas

Must Master (Core + Often):

  • All AMC 10 topics
  • Advanced similarity applications
  • Mass points and Ceva/Menelaus
  • Transformations
  • 3D geometry
  • Advanced coordinate techniques

Stretch Goals:

  • Inversion and spiral similarity
  • Advanced transformation theory
  • Complex 3D problems

🎯 Study Priority by Level

AMC 10 Students

  1. Priority 1: Core topics (⭐⭐⭐)
  2. Priority 2: Often tested topics (⭐⭐)
  3. Priority 3: Nice-to-have topics (⭐)

AMC 12 Students

  1. Priority 1: All core and often topics
  2. Priority 2: AMC 12 specific topics (transformations, 3D, mass points)
  3. Priority 3: Stretch topics for advanced students

💡 Contest Strategy

  • AMC 10: Focus on geometric intuition and basic formulas
  • AMC 12: Master advanced techniques and coordinate methods
  • Both: Practice pattern recognition and quick formula recall

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