Taxonomy Distribution Report

Overview

• Total Concepts: 380
• Number of Taxonomies: 17
• Average Concepts per Taxonomy: 22.4

Distribution Summary

Category	TaxonomyID	Count	Percentage	Status
Applications	APPL	39	10.3%	✅
Analytical Tools	ANAL	34	8.9%	✅
Limits	LIMIT	30	7.9%	✅
Derivative Basics	DERIV	30	7.9%	✅
Derivative Rules	DRULE	29	7.6%	✅
Integration Basics	INTEG	28	7.4%	✅
Implicit & Inverse	IMPL	24	6.3%	✅
Fundamental Theorem	FTC	23	6.1%	✅
Optimization	OPT	21	5.5%	✅
Foundation Concepts	FOUND	20	5.3%	✅
Continuity	CONT	20	5.3%	✅
Chain Rule	CHAIN	16	4.2%	✅
Higher-Order Derivatives	HIGH	15	3.9%	✅
Asymptotes & End Behavior	ASYM	14	3.7%	✅
Curve Sketching	CURV	14	3.7%	✅
Riemann Sums	RIEM	12	3.2%	✅
Integration Techniques	TECH	11	2.9%	ℹ️ Under

Visual Distribution

APPL   █████  39 ( 10.3%)
ANAL   ████  34 (  8.9%)
LIMIT  ███  30 (  7.9%)
DERIV  ███  30 (  7.9%)
DRULE  ███  29 (  7.6%)
INTEG  ███  28 (  7.4%)
IMPL   ███  24 (  6.3%)
FTC    ███  23 (  6.1%)
OPT    ██  21 (  5.5%)
FOUND  ██  20 (  5.3%)
CONT   ██  20 (  5.3%)
CHAIN  ██  16 (  4.2%)
HIGH   █  15 (  3.9%)
ASYM   █  14 (  3.7%)
CURV   █  14 (  3.7%)
RIEM   █  12 (  3.2%)
TECH   █  11 (  2.9%)

Balance Analysis

✅ No Over-Represented Categories

All categories are under the 30% threshold. Good balance!

ℹ️ Under-Represented Categories (<3%)

• Integration Techniques (TECH): 11 concepts (2.9%)
• Note: Small categories are acceptable for specialized topics

Category Details

Applications (APPL)

Count: 39 concepts (10.3%)

Concepts:

• 1. Related Rates
• 1. Related Rates Setup
• 1. Implicit in Context
• 1. Rate Variables
• 1. Related Rates Diagram
• 1. Ladder Problem
• 1. Balloon Problem
• 1. Shadow Problem
• 1. Conical Tank Problem
• 1. Distance Rate Problem
• 1. Linear Approximation
• 1. Tangent Line Approx
• 1. Linearization Formula
• 1. Error in Approximation
• 1. Differential
• ...and 24 more

Analytical Tools (ANAL)

Count: 34 concepts (8.9%)

Concepts:

• 1. Mean Value Theorem
• 1. MVT Statement
• 1. MVT Conditions
• 1. MVT Conclusion
• 1. Rolle's Theorem
• 1. Rolle's Conditions
• 1. MVT Applications
• 1. Average vs Instant MVT
• 1. Extreme Value Theorem
• 1. EVT Statement
• 1. EVT Conditions
• 1. Global Maximum
• 1. Global Minimum
• 1. Local Maximum
• 1. Local Minimum
• ...and 19 more

Limits (LIMIT)

Count: 30 concepts (7.9%)

Concepts:

• 1. Limit
• 1. Limit Notation
• 1. Intuitive Limit
• 1. One-Sided Limit
• 1. Left-Hand Limit
• 1. Right-Hand Limit
• 1. Two-Sided Limit
• 1. Limit Existence
• 1. Limit Laws
• 1. Sum Rule for Limits
• 1. Product Rule for Limits
• 1. Quotient Rule for Limits
• 1. Constant Multiple Rule
• 1. Power Rule for Limits
• 1. Direct Substitution
• ...and 15 more

Derivative Basics (DERIV)

Count: 30 concepts (7.9%)

Concepts:

• 1. Rate of Change
• 1. Average Rate of Change
• 1. Instantaneous Rate
• 1. Difference Quotient
• 1. Secant Line
• 1. Tangent Line
• 1. Slope of Tangent
• 1. Derivative Definition
• 1. Limit Definition Deriv
• 1. Derivative at a Point
• 1. Derivative Function
• 1. Derivative Notation
• 1. Prime Notation
• 1. Leibniz Notation
• 1. Differentiable Function
• ...and 15 more

Derivative Rules (DRULE)

Count: 29 concepts (7.6%)

Concepts:

• 1. Derivative Rules
• 1. Constant Rule
• 1. Power Rule Derivative
• 1. Sum Rule Derivative
• 1. Difference Rule Deriv
• 1. Constant Multiple Deriv
• 1. Linear Combination
• 1. Polynomial Derivative
• 1. Derivative of x to n
• 1. Negative Exponent Deriv
• 1. Fractional Exponent
• 1. Derivative of Root
• 1. Product Rule
• 1. Product Rule Formula
• 1. Quotient Rule
• ...and 14 more

Integration Basics (INTEG)

Count: 28 concepts (7.4%)

Concepts:

• 1. Antiderivative
• 1. Indefinite Integral
• 1. Integral Notation
• 1. Integrand
• 1. Variable of Integration
• 1. Constant of Integration
• 1. General Antiderivative
• 1. Particular Antideriv
• 1. Power Rule Integration
• 1. Constant Rule Integr
• 1. Sum Rule Integration
• 1. Difference Rule Integr
• 1. Constant Multiple Integ
• 1. Basic Trig Integrals
• 1. Integral of Sin x
• ...and 13 more

Implicit & Inverse (IMPL)

Count: 24 concepts (6.3%)

Concepts:

• 1. Implicit Function
• 1. Implicit Equation
• 1. Implicit Differentiation
• 1. dy dx Implicitly
• 1. Treating y as Function
• 1. Implicit Chain Rule
• 1. Solving for dy dx
• 1. Second Deriv Implicit
• 1. Tangent Line Implicit
• 1. Inverse Function Thm
• 1. Derivative of Inverse
• 1. Inverse Deriv Formula
• 1. Graphical Inverse Deriv
• 1. Derivative of Arcsin
• 1. Derivative of Arccos
• ...and 9 more

Fundamental Theorem (FTC)

Count: 23 concepts (6.1%)

Concepts:

• 1. Fundamental Theorem
• 1. FTC Part One
• 1. FTC Part Two
• 1. Evaluation Theorem
• 1. Accumulation Function
• 1. Integral as Function
• 1. Derivative of Integral
• 1. FTC Chain Rule
• 1. Net Change Theorem
• 1. Net Signed Area
• 1. Area Under Curve
• 1. Integral Properties
• 1. Additivity Property
• 1. Reversing Limits
• 1. Zero Width Integral
• ...and 8 more

Optimization (OPT)

Count: 21 concepts (5.5%)

Concepts:

• 1. Optimization
• 1. Optimization Problem
• 1. Objective Function
• 1. Constraint Equation
• 1. Primary Equation
• 1. Setting Up Optimization
• 1. Maximizing Area
• 1. Minimizing Distance
• 1. Minimizing Cost
• 1. Maximizing Volume
• 1. Fencing Problem
• 1. Box Problem
• 1. Can Problem
• 1. Closest Point Problem
• 1. Maximum Profit
• ...and 6 more

Foundation Concepts (FOUND)

Count: 20 concepts (5.3%)

Concepts:

• 1. Function
• 1. Domain and Range
• 1. Function Notation
• 1. Composite Function
• 1. Inverse Function
• 1. Graphing Functions
• 1. Piecewise Function
• 1. Even and Odd Functions
• 1. Function Transformations
• 1. Polynomial Function
• 1. Rational Function
• 1. Exponential Function
• 1. Logarithmic Function
• 1. Trigonometric Function
• 1. Unit Circle
• ...and 5 more

Continuity (CONT)

Count: 20 concepts (5.3%)

Concepts:

• 1. Continuity
• 1. Continuity at a Point
• 1. Three Conditions
• 1. Continuity on Interval
• 1. One-Sided Continuity
• 1. Continuous Function
• 1. Discontinuity
• 1. Removable Discontinuity
• 1. Jump Discontinuity
• 1. Infinite Discontinuity
• 1. Essential Discontinuity
• 1. Continuous Extension
• 1. Removing Discontinuities
• 1. Piecewise Continuity
• 1. Continuity of Composites
• ...and 5 more

Chain Rule (CHAIN)

Count: 16 concepts (4.2%)

Concepts:

• 1. Chain Rule
• 1. Chain Rule Formula
• 1. Composition Derivative
• 1. Inside Function
• 1. Outside Function
• 1. Nested Chain Rule
• 1. Leibniz Chain Rule
• 1. Derivative of f of g
• 1. Recognizing Composition
• 1. Power Chain Rule
• 1. Trig Chain Rule
• 1. Exponential Chain Rule
• 1. Log Chain Rule
• 1. Multiple Chain Rule
• 1. General Power Rule
• ...and 1 more

Higher-Order Derivatives (HIGH)

Count: 15 concepts (3.9%)

Concepts:

• 1. Higher-Order Derivative
• 1. Second Derivative
• 1. Third Derivative
• 1. nth Derivative
• 1. Second Deriv Notation
• 1. f Double Prime
• 1. d2y dx2 Notation
• 1. Velocity from Position
• 1. Acceleration
• 1. Jerk
• 1. Position Velocity Accel
• 1. Speed vs Velocity
• 1. Direction of Motion
• 1. Speeding Up Slowing
• 1. Higher Trig Derivatives

Asymptotes & End Behavior (ASYM)

Count: 14 concepts (3.7%)

Concepts:

• 1. Asymptote
• 1. Vertical Asymptote
• 1. Horizontal Asymptote
• 1. Oblique Asymptote
• 1. Limit at Infinity
• 1. End Behavior
• 1. Behavior Near Asymptote
• 1. One-Sided Infinite Limit
• 1. Comparing Growth Rates
• 1. Dominant Term
• 1. Rational End Behavior
• 1. Exponential Growth Rate
• 1. Logarithmic Growth Rate
• 1. Polynomial Growth Rate

Curve Sketching (CURV)

Count: 14 concepts (3.7%)

Concepts:

• 1. Curve Sketching
• 1. Complete Curve Analysis
• 1. f f Prime f Dbl Prime
• 1. Graph from Derivative
• 1. Derivative from Graph
• 1. Connecting Three Graphs
• 1. Domain Analysis
• 1. Intercept Analysis
• 1. Symmetry Analysis
• 1. Asymptote Analysis
• 1. Increasing Decreasing
• 1. Local Extrema Analysis
• 1. Concavity Analysis
• 1. Inflection Analysis

Riemann Sums (RIEM)

Count: 12 concepts (3.2%)

Concepts:

• 1. Riemann Sum
• 1. Left Riemann Sum
• 1. Right Riemann Sum
• 1. Midpoint Riemann Sum
• 1. Trapezoidal Rule
• 1. Summation Notation
• 1. Sigma Notation
• 1. Index of Summation
• 1. Limit of Riemann Sum
• 1. Definite Integral
• 1. Definite Integral Notat
• 1. Limits of Integration

Integration Techniques (TECH)

Count: 11 concepts (2.9%)

Concepts:

• 1. u-Substitution
• 1. Substitution Method
• 1. Choosing u
• 1. du Calculation
• 1. Back Substitution
• 1. Definite Substitution
• 1. Changing Bounds
• 1. Long Division Method
• 1. Completing Square
• 1. Partial Fractions
• 1. Integration Strategy

Recommendations

• ✅ Excellent balance: Categories are evenly distributed (spread: 7.4%)
• ✅ MISC category minimal: Good categorization specificity

Educational Use Recommendations

• Use taxonomy categories for color-coding in graph visualizations
• Design curriculum modules based on taxonomy groupings
• Create filtered views for focused learning paths
• Use categories for assessment organization
• Enable navigation by topic area in interactive tools

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Report generated by learning-graph-reports/taxonomy_distribution.py