AP Calculus Terms

Absolute value definition, equations, inequalities, and rules

Core algebra vocabulary, properties, and general mathematical concepts

Related rates, optimization, curve sketching, and derivative applications

Area, volume, arc length, surface area of revolution, work, and center of mass

2D measurement formulas for area and perimeter of common shapes

Basic arithmetic operations, exponents, powers, roots, and order of operations

Upper/lower bounds, bounded sets, intervals, and ordering concepts

Circle properties, arcs, sectors, chords, tangent lines, and inscribed angles

Coordinate plane, distance formula, midpoint, analytic geometry, and coordinate systems

Conics review, spheroids, extrema, inflection points, and advanced function analysis

Derivative definition, differentiation rules, and higher-order derivatives

Introduction to differential equations, solution methods, and parametric/polar calculus

Exponential functions, logarithms, growth/decay, and their properties

Interest, annuities, present/future value, and financial formulas

Function notation, domain, range, types of functions, and function operations

Foundational geometry concepts, planes, measurement units, non-Euclidean geometry, and general vocabulary

Translations, reflections, stretches, compressions, and symmetry of graphs

Amplitude, period, phase shift, sinusoids, and graphing trig functions

Inequalities, compound inequalities, absolute value inequalities, interval notation, and complex numbers

Power series, Taylor series, convergence tests, and series expansions

Definite/indefinite integrals, integration methods, and the Fundamental Theorem

Arcsine, arccosine, arctangent, and inverse trig function properties

Limits, one-sided limits, continuity, intermediate value theorem, and theorems

Introduction to limits, continuity, neighborhoods, and indeterminate forms

Slope, linear equations, systems of equations, and graphing lines

Conditional statements, proof methods, logical connectives, and quantifiers

Measurement, scientific notation, rounding, significant digits, and mathematical notation

Partial derivatives, multivariable calculus, and advanced calculus topics

Algebraic properties, number classifications, and equivalence relations

Gaussian integers, modular arithmetic, transcendental numbers, and number-theoretic concepts

Types of numbers: integers, rationals, reals, primes, composites, and number classification systems

Parametric equations, polar coordinates, polar curves, and special curves

Polynomial operations, factoring, synthetic division, and polynomial theorems

Function analysis, advanced algebra connections, and precalculus methods

Quadratic formula, factoring quadratics, discriminant, vertex form, and parabolas

Radicals, radical equations, rational expressions, and rationalizing

Arithmetic and geometric sequences, series, summation notation, and convergence

Sets, set operations, Venn diagrams, and set notation

3D measurement: surface area and volume of prisms, cylinders, cones, spheres, and other solids

Sine, cosine, tangent, unit circle, SOHCAHTOA, law of sines/cosines, and basic trig definitions

Pythagorean, double angle, half angle, sum/difference, and other trig identities

Direct, inverse, and joint variation; proportional relationships

Vectors, dot product, cross product, magnitude, and unit vectors