Free NBPTS AYA Math Exam Prep

Polynomials and factoring, complex numbers, rational expressions, sequences and series, exponential and logarithmic functions, and structural reasoning about number systems.

Congruence and similarity, transformations, coordinate proof, circles, area and volume of solids, vectors, and matrix algebra.

Function families (linear, quadratic, polynomial, rational, exponential, logarithmic, trigonometric, piecewise), composition, inverses, domain/range, transformations, and asymptotic behavior.

Unit circle, identities (Pythagorean, double-angle, sum/difference), Law of Sines and Cosines, sinusoidal modeling, and polar representations.

Descriptive statistics, normal and binomial distributions, correlation, confidence intervals, hypothesis testing (z-test and t-test, p-values, Type I/II errors), and probability rules.

Limits, derivative rules, average versus instantaneous rate of change, Riemann sums, and the Fundamental Theorem of Calculus at a level appropriate for secondary teaching.

Combinatorics, graph theory, mathematical induction, logic, and set theory.

Five Core Propositions, the eight Common Core Standards for Mathematical Practice, formative assessment, error analysis, productive struggle, and equity-centered task design.