AP Precalculus Formulae 2025 - 2026

Explore function definitions, domain and range, vertical line test, and methods to evaluate functions. Fundamental for all precalculus topics.

Learn how to find, verify, and interpret inverse functions and their properties, including domain-range swaps and graph reflections.

Covers vertical/horizontal shifts, stretches, compressions, and reflections for all major function types, enabling flexible graphing and modeling.

Includes standard/vertex forms, parabola properties, methods for solving quadratics, and applications in graphing and optimization.

Master polynomial manipulation including factoring, expanding, solving equations, and connection to function behavior.

Investigate polynomial function properties, end behavior, zeros, graphing, and the Fundamental Theorem of Algebra.

Analyze ratios of polynomials, domain restrictions, vertical/horizontal asymptotes, and graphing techniques.

Explore properties, growth/decay models, and behaviors of exponential functions. Compare with linear and polynomial growth.

Covers core log properties, conversion from exponential form, solving log equations, and calculator usage.

Dive into inverse relationships to exponentials, transformation, graphing, and applications to scientific notation and pH.

Methods for solving equations using properties of logs/exponentials, natural log, and e-based equations.

Roots, powers, rationalizing denominators, and graphing radical functions with proper domain.

Converting roots to fractional powers, manipulating exponents in equations and inequalities.

Methods for solving linear and nonlinear systems via graphing, substitution, elimination, and matrix methods.

Solve and graph systems of linear and absolute value inequalities, locate feasible solution regions and vertices.

Tackle quadratic and polynomial inequalities, graph solution sets, and write intervals for valid values.

Rules for matrix operations, determinants, inverses, scalar multiplication, and solving matrix equations.

All core trigonometry concepts: unit circle, ratios, laws of sines/cosines, special angles, and solving triangles.

Properties, graphs, and models for sine, cosine, tangent functions, amplitude, period, phase shift, and translations.

Fundamental identities (Pythagorean, sum/difference, reciprocal, complementary, and more) for all trigonometric proofs and equations.

Parabola, circle, ellipse, and hyperbola formulas—standard forms, properties, axes, centers, eccentricity, and graphing.

Addition, subtraction, multiplication, division, conjugates, absolute value (modulus), and powers of \( i \) for complex numbers.

Graphical representation, arithmetic, modulus (distance), midpoint, and distance formulas for complex numbers on the plane.

Convert between rectangular and polar forms, find modulus/argument of complex numbers, and interpret polar graphs.

Vector properties, magnitude, direction, component form, scalar multiplication, unit vectors, and vector arithmetic in 2D.

Vector properties in 3D, including magnitude, direction, addition, subtraction, scalar multiplication, and linear combinations.

Definitions, notation, explicit and recursive rules for arithmetic and geometric sequences, term formulas, and examples.

Summation notation, arithmetic/geometric formulas, partial and infinite series, convergence, and fraction conversions.

Calculate probabilities, combinations, permutations, independent and conditional probabilities, and utilize rules for calculation.

Discrete and continuous distributions, expected value, variance, standard deviation, and applications to games of chance.

Binomial probability formulas, mean/variance/SD, normal curves, z-scores, the Central Limit Theorem and normal approximation methods.

Variance, standard deviation, outlier detection, confidence intervals, bias, experiment design, and simulations in one-variable data.

Scatter plots and outliers, correlation coefficients, regression equations, interpretation and analysis of data sets.

Graphical and algebraic approaches to limits, one-sided/two-sided, laws, asymptotes, end behavior, and evaluating using limit laws.

Definitions and criteria of continuity, types of discontinuity, interval continuity and graphical analysis.

Learn about average and instantaneous rates of change, derivative definitions via limits, velocity, tangent lines, and secant slopes.