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AP Calculus Concept Taxonomy

This document defines the categorical taxonomy used to organize concepts in the learning graph.

Taxonomy Categories

TaxonomyID Category Name Description
FOUND Foundation Concepts Prerequisites from precalculus: functions, trigonometry, coordinate systems
LIMIT Limits Limit concepts, notation, evaluation techniques, and theorems
CONT Continuity Continuity definitions, types of discontinuities, and continuity theorems
ASYM Asymptotes Vertical/horizontal asymptotes, limits at infinity, end behavior
DERIV Derivative Basics Derivative definition, notation, differentiability concepts
DRULE Derivative Rules Power, product, quotient rules and derivatives of elementary functions
CHAIN Chain Rule Chain rule and composition derivative techniques
IMPL Implicit & Inverse Implicit differentiation, inverse functions, logarithmic differentiation
HIGH Higher Derivatives Second and higher-order derivatives, motion applications
APPL Applications Related rates, linear approximation, L'Hospital's Rule
ANAL Analysis MVT, EVT, critical points, first/second derivative tests
CURV Curve Sketching Complete curve analysis using derivative information
OPT Optimization Setting up and solving optimization problems
INTEG Integration Basics Antiderivatives, indefinite integrals, basic integration rules
RIEM Riemann Sums Riemann sums, summation notation, definite integral definition
FTC Fundamental Theorem FTC parts 1 and 2, accumulation functions, integral properties
TECH Integration Techniques u-substitution, long division, completing the square

Distribution Guidelines

  • Each category should contain approximately 5-8% of total concepts
  • No single category should exceed 15% of total concepts
  • Foundational concepts establish prerequisites
  • Categories progress from basic to advanced within each major topic area

Category Color Assignments

TaxonomyID Color Hex
FOUND LightCoral #F08080
LIMIT PeachPuff #FFDAB9
CONT LightYellow #FFFFE0
ASYM Honeydew #F0FFF0
DERIV PaleTurquoise #AFEEEE
DRULE PowderBlue #B0E0E6
CHAIN Lavender #E6E6FA
IMPL LavenderBlush #FFF0F5
HIGH Thistle #D8BFD8
APPL MintCream #F5FFFA
ANAL LightPink #FFB6C1
CURV Gainsboro #DCDCDC
OPT PaleGreen #98FB98
INTEG Aquamarine #7FFFD4
RIEM Plum #DDA0DD
FTC LightSteelBlue #B0C4DE
TECH MistyRose #FFE4E1