Taxonomy Distribution Report

Overview

• Total Concepts: 307
• Number of Taxonomies: 12
• Average Concepts per Taxonomy: 25.6

Distribution Summary

Category	TaxonomyID	Count	Percentage	Status
TRIG	TRIG	71	23.1%	✅
FUNC	FUNC	30	9.8%	✅
VECM	VECM	29	9.4%	✅
POLY	POLY	27	8.8%	✅
SEQX	SEQX	27	8.8%	✅
POLR	POLR	25	8.1%	✅
LNQD	LNQD	22	7.2%	✅
TMOD	TMOD	22	7.2%	✅
LOGR	LOGR	20	6.5%	✅
RATL	RATL	12	3.9%	✅
Foundation Concepts - Prerequisites	FOUND	11	3.6%	✅
RATE	RATE	11	3.6%	✅

Visual Distribution

TRIG                      ███████████  71 ( 23.1%)
FUNC                      ████  30 (  9.8%)
VECM                      ████  29 (  9.4%)
POLY                      ████  27 (  8.8%)
SEQX                      ████  27 (  8.8%)
POLR                      ████  25 (  8.1%)
LNQD                      ███  22 (  7.2%)
TMOD                      ███  22 (  7.2%)
LOGR                      ███  20 (  6.5%)
RATL                      █  12 (  3.9%)
Foundation Concepts - Pre █  11 (  3.6%)
RATE                      █  11 (  3.6%)

Balance Analysis

✅ No Over-Represented Categories

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

Category Details

TRIG (TRIG)

Count: 71 concepts (23.1%)

Concepts:

• 1. Angle Definition
• 1. Degree Measure
• 1. Radian Measure
• 1. Degree-Radian Conversion
• 1. Arc Length
• 1. Sector Area
• 1. Standard Position
• 1. Terminal Side
• 1. Reference Angle
• 1. Coterminal Angles
• 1. Unit Circle Definition
• 1. Unit Circle Coordinates
• 1. Special Angles
• 1. Quadrantal Angles
• 1. Signs by Quadrant
• ...and 56 more

FUNC (FUNC)

Count: 30 concepts (9.8%)

Concepts:

• 1. Function Definition
• 1. Function Notation
• 1. Domain
• 1. Range
• 1. Vertical Line Test
• 1. Function Evaluation
• 1. Piecewise Functions
• 1. Domain Restrictions
• 1. Graphing Functions
• 1. Intercepts
• 1. X-Intercept
• 1. Y-Intercept
• 1. Increasing Functions
• 1. Decreasing Functions
• 1. Constant Functions
• ...and 15 more

VECM (VECM)

Count: 29 concepts (9.4%)

Concepts:

• 1. Vector Definition
• 1. Vector Notation
• 1. Magnitude of a Vector
• 1. Direction of a Vector
• 1. Component Form
• 1. Unit Vectors
• 1. Vector Addition
• 1. Vector Subtraction
• 1. Scalar Multiplication
• 1. Dot Product
• 1. Vector Applications
• 1. Matrix Definition
• 1. Matrix Dimensions
• 1. Matrix Addition
• 1. Matrix Subtraction
• ...and 14 more

POLY (POLY)

Count: 27 concepts (8.8%)

Concepts:

• 1. Polynomial Definition
• 1. Degree of a Polynomial
• 1. Leading Coefficient
• 1. Monomial
• 1. Binomial
• 1. Trinomial
• 1. Polynomial Addition
• 1. Polynomial Multiplication
• 1. Factoring Polynomials
• 1. Factor Theorem
• 1. Remainder Theorem
• 1. Synthetic Division
• 1. Long Division of Polynomials
• 1. Zeros of Polynomials
• 1. Multiplicity of Zeros
• ...and 12 more

SEQX (SEQX)

Count: 27 concepts (8.8%)

Concepts:

• 1. Sequence Definition
• 1. Arithmetic Sequence
• 1. Common Difference
• 1. Arithmetic Sequence Formula
• 1. Geometric Sequence
• 1. Common Ratio
• 1. Geometric Sequence Formula
• 1. Recursive Formulas
• 1. Explicit Formulas
• 1. Sequence Convergence
• 1. Sequence Divergence
• 1. Exponential Function Def
• 1. Base of Exponential
• 1. Growth Factor
• 1. Decay Factor
• ...and 12 more

POLR (POLR)

Count: 25 concepts (8.1%)

Concepts:

• 1. Polar Coordinate System
• 1. Polar Point Plotting
• 1. Rectangular to Polar
• 1. Polar to Rectangular
• 1. Multiple Polar Represent
• 1. Polar Function Definition
• 1. Polar Graphs
• 1. Circles in Polar Form
• 1. Cardioids
• 1. Limaçons
• 1. Rose Curves
• 1. Petal Count of Roses
• 1. Symmetry of Polar Graphs
• 1. Polar Rate of Change
• 1. Polar Graph Intersections
• ...and 10 more

LNQD (LNQD)

Count: 22 concepts (7.2%)

Concepts:

• 1. Linear Function Definition
• 1. Slope-Intercept Form
• 1. Point-Slope Form
• 1. Standard Form of a Line
• 1. Parallel Lines
• 1. Perpendicular Lines
• 1. Linear Regression
• 1. Residuals
• 1. Correlation
• 1. Quadratic Function Definition
• 1. Standard Form of Quadratic
• 1. Vertex Form
• 1. Factored Form
• 1. Vertex
• 1. Axis of Symmetry
• ...and 7 more

TMOD (TMOD)

Count: 22 concepts (7.2%)

Concepts:

• 1. Parent Functions
• 1. Vertical Translation
• 1. Horizontal Translation
• 1. Vertical Stretch
• 1. Vertical Compression
• 1. Horizontal Stretch
• 1. Horizontal Compression
• 1. Reflection Over X-Axis
• 1. Reflection Over Y-Axis
• 1. Combined Transformations
• 1. Transformation Order
• 1. Writing Transformed Eqns
• 1. Function Model Selection
• 1. Data Analysis for Models
• 1. Regression Models
• ...and 7 more

LOGR (LOGR)

Count: 20 concepts (6.5%)

Concepts:

• 1. Logarithm Definition
• 1. Common Logarithm
• 1. Natural Logarithm
• 1. Logarithmic Form
• 1. Exponential-Log Conversion
• 1. Properties of Logarithms
• 1. Product Rule for Logs
• 1. Quotient Rule for Logs
• 1. Power Rule for Logs
• 1. Change of Base Formula
• 1. Logarithmic Equations
• 1. Logarithmic Graphs
• 1. Logarithmic Transformations
• 1. Logarithmic Modeling
• 1. Logarithmic Scale
• ...and 5 more

RATL (RATL)

Count: 12 concepts (3.9%)

Concepts:

• 1. Rational Function Definition
• 1. Rational Expressions
• 1. Simplifying Rational Expr
• 1. Vertical Asymptotes
• 1. Horizontal Asymptotes
• 1. Slant Asymptotes
• 1. Holes in Graphs
• 1. Rational Function Zeros
• 1. Rational Function Domain
• 1. End Behavior of Rationals
• 1. Rational Function Graphs
• 1. Rational Inequalities

Foundation Concepts - Prerequisites (FOUND)

Count: 11 concepts (3.6%)

Concepts:

• 1. Real Number System
• 1. Number Line
• 1. Order of Operations
• 1. Variables and Expressions
• 1. Coordinate Plane
• 1. Ordered Pairs
• 1. Input and Output
• 1. Independent Variable
• 1. Dependent Variable
• 1. Interval Notation
• 1. Set-Builder Notation

RATE (RATE)

Count: 11 concepts (3.6%)

Concepts:

• 1. Change in Tandem
• 1. Average Rate of Change
• 1. Slope
• 1. Slope Formula
• 1. Rate of Change Units
• 1. Secant Line
• 1. Linear Rate of Change
• 1. Nonlinear Rate of Change
• 1. Concavity from Rates
• 1. Increasing Rate of Change
• 1. Decreasing Rate of Change

Recommendations

• ✅ Good balance: Categories are reasonably distributed (spread: 19.5%)
• ✅ 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