AP Precalculus Formula 2025 - 2026

1. Function Concepts & Domain / Range
Explore function definitions, domain and range, vertical line test, and methods to evaluate functions. Fundamental for all precalculus topics.
2. Inverse Functions
Learn how to find, verify, and interpret inverse functions and their properties, including domain-range swaps and graph reflections.
3. Function Transformations
Covers vertical/horizontal shifts, stretches, compressions, and reflections for all major function types, enabling flexible graphing and modeling.
4. Quadratic Functions
Includes standard/vertex forms, parabola properties, methods for solving quadratics, and applications in graphing and optimization.
5. Polynomial Expressions & Equations
Master polynomial manipulation including factoring, expanding, solving equations, and connection to function behavior.
6. Polynomial Functions
Investigate polynomial function properties, end behavior, zeros, graphing, and the Fundamental Theorem of Algebra.
7. Rational Functions
Analyze ratios of polynomials, domain restrictions, vertical/horizontal asymptotes, and graphing techniques.
8. Exponential Functions
Explore properties, growth/decay models, and behaviors of exponential functions. Compare with linear and polynomial growth.
9. Logarithms
Covers core log properties, conversion from exponential form, solving log equations, and calculator usage.
10. Logarithmic Functions
Dive into inverse relationships to exponentials, transformation, graphing, and applications to scientific notation and pH.
11. Exponential & Logarithmic Equations
Methods for solving equations using properties of logs/exponentials, natural log, and e-based equations.
12. Radical Expressions & Functions
Roots, powers, rationalizing denominators, and graphing radical functions with proper domain.
13. Rational Exponents
Converting roots to fractional powers, manipulating exponents in equations and inequalities.
14. Systems of Equations
Methods for solving linear and nonlinear systems via graphing, substitution, elimination, and matrix methods.
15. Systems of Inequalities
Solve and graph systems of linear and absolute value inequalities, locate feasible solution regions and vertices.
16. Nonlinear Inequalities
Tackle quadratic and polynomial inequalities, graph solution sets, and write intervals for valid values.
17. Matrices
Rules for matrix operations, determinants, inverses, scalar multiplication, and solving matrix equations.
18. Trigonometry
All core trigonometry concepts: unit circle, ratios, laws of sines/cosines, special angles, and solving triangles.
19. Trigonometric Functions
Properties, graphs, and models for sine, cosine, tangent functions, amplitude, period, phase shift, and translations.
20. Trigonometric Identities
Fundamental identities (Pythagorean, sum/difference, reciprocal, complementary, and more) for all trigonometric proofs and equations.
21. Conic Sections
Parabola, circle, ellipse, and hyperbola formulas—standard forms, properties, axes, centers, eccentricity, and graphing.
22. Complex Numbers
Addition, subtraction, multiplication, division, conjugates, absolute value (modulus), and powers of \( i \) for complex numbers.
23. Complex Plane
Graphical representation, arithmetic, modulus (distance), midpoint, and distance formulas for complex numbers on the plane.
24. Polar Form
Convert between rectangular and polar forms, find modulus/argument of complex numbers, and interpret polar graphs.
25. Two-Dimensional Vectors
Vector properties, magnitude, direction, component form, scalar multiplication, unit vectors, and vector arithmetic in 2D.
26. Three-Dimensional Vectors
Vector properties in 3D, including magnitude, direction, addition, subtraction, scalar multiplication, and linear combinations.
27. Sequences
Definitions, notation, explicit and recursive rules for arithmetic and geometric sequences, term formulas, and examples.
28. Series
Summation notation, arithmetic/geometric formulas, partial and infinite series, convergence, and fraction conversions.
29. Probability
Calculate probabilities, combinations, permutations, independent and conditional probabilities, and utilize rules for calculation.
30. Probability Distributions
Discrete and continuous distributions, expected value, variance, standard deviation, and applications to games of chance.
31. Binomial & Normal Distributions
Binomial probability formulas, mean/variance/SD, normal curves, z-scores, the Central Limit Theorem and normal approximation methods.
32. Single-Variable Statistics
Variance, standard deviation, outlier detection, confidence intervals, bias, experiment design, and simulations in one-variable data.
33. Bivariate Statistics
Scatter plots and outliers, correlation coefficients, regression equations, interpretation and analysis of data sets.
34. Limits
Graphical and algebraic approaches to limits, one-sided/two-sided, laws, asymptotes, end behavior, and evaluating using limit laws.
35. Continuity
Definitions and criteria of continuity, types of discontinuity, interval continuity and graphical analysis.
36. Introduction to Derivatives
Learn about average and instantaneous rates of change, derivative definitions via limits, velocity, tangent lines, and secant slopes.