Concept Taxonomy
The following taxonomy organizes the 307 AP Pre-Calculus concepts into 12 categories for visualization and navigation in the learning graph.
Categories
1. Foundation Concepts (FOUND)
Core mathematical building blocks including the real number system, coordinate plane, variables, expressions, and basic notation systems that all other concepts build upon.
2. Function Fundamentals (FUNC)
Essential function concepts including definition, notation, evaluation, domain, range, behavior, symmetry, and the vertical line test.
3. Rates of Change (RATE)
Concepts related to how quantities change together, including average rate of change, slope, secant lines, concavity, and increasing/decreasing rates.
4. Linear and Quadratic (LNQD)
Linear functions (slope-intercept, point-slope, standard form, regression) and quadratic functions (vertex form, factored form, quadratic formula, complex numbers).
5. Polynomial Functions (POLY)
Higher-degree polynomial concepts including degree, zeros, multiplicity, end behavior, graphing, extrema, factoring, division, and the Fundamental Theorem of Algebra.
6. Rational Functions (RATL)
Rational function concepts including asymptotes (vertical, horizontal, slant), holes, zeros, domain restrictions, end behavior, and graphing.
7. Transformations and Modeling (TMOD)
Function transformations (translations, stretches, reflections) and data modeling concepts (regression, model selection, validation, residual analysis, competing models).
8. Sequences and Exponential (SEQX)
Arithmetic and geometric sequences, exponential functions (growth, decay, natural base e, compound interest), and related modeling applications.
9. Logarithmic Functions (LOGR)
Logarithms (common, natural), properties of logarithms, logarithmic equations, graphs, modeling, semi-log plots, and data linearization.
10. Trigonometric Functions (TRIG)
Unit circle, sine, cosine, tangent, reciprocal functions, trig evaluation, trig graphs, sinusoidal functions, identities, and inverse trig functions.
11. Polar and Parametric (POLR)
Polar coordinates, polar function graphs (roses, limaçons, cardioids), parametric equations, parametric motion, and projectile motion.
12. Vectors and Matrices (VECM)
Vectors (magnitude, direction, operations, dot product), matrices (operations, determinant, inverse, linear transformations), and AP exam preparation strategies.