AP Calculus Terms
AP Calculus (AB and BC) covers limits, continuity, differentiation, integration, and (for BC only) infinite series and parametric/polar functions. This page links to every calculus term and formula on Mathwords to help you review for the AP exam. The AP Calculus exam is in May — use this as your study guide.
Key Concepts
A limit is the value that a function approaches as its input gets closer and closer to a specific number. Rather than...
The derivative is a function that gives the instantaneous rate of change (slope) of a curve at any point. It is found...
The Power Rule is a formula for finding the derivative of a function where a variable is raised to a constant exponen...
The Chain Rule is a formula for finding the derivative of a composition of functions. It states that the derivative o...
The product rule is a differentiation formula that tells you how to find the derivative of two functions multiplied t...
The Quotient Rule is a formula used in calculus to find the derivative of a function that is written as one function ...
An integral is a fundamental concept in calculus that represents the accumulation of quantities, such as the area und...
A definite integral is the integral of a function evaluated over a specific interval $[a, b]$, written as $\int_a^b f...
Integration by Parts is a technique for integrating the product of two functions by transforming it into a simpler in...
A Taylor series is an infinite sum of terms expressed as powers of $(x - a)$, where each term involves the derivative...
A Maclaurin series is a power series expansion of a function f(x) centered at x = 0, expressing f(x) as an infinite s...
A Riemann sum is an approximation of the area under a curve (the definite integral) formed by dividing an interval in...
Related rates is a type of calculus problem where you find how fast one quantity is changing by using its relationshi...
The Mean Value Theorem is a fundamental result in calculus stating that for any function that is continuous on a clos...
An improper integral is a definite integral where either the interval of integration is infinite (extending to $\inft...
All AP Calculus Terms Terms (233)
- Absolute Convergence
- Absolute Maximum
- Absolute Minimum
- Acceleration
- Algorithm
- Alternating Series
- Alternating Series Remainder
- Alternating Series Test
- Analytic Methods
- Annulus
- Antiderivative of a Function
- Approximation by Differentials
- ARC
- Arc Length of a Curve
- Area below a Curve
- Area between Curves
- Area of a Parabolic Segment
- Area of an Ellipse
- Area Using Parametric Equations
- Area Using Polar Coordinates
- Asymptote
- Average Value of a Function
- Axis of Rotation
- Boundary Value Problem
- Bounded Function
- Bounded Sequence
- Bounds of Integration
- Calculus
- Cartesian Form
- Cavalieri’s Principle
- Center of Mass Formula
- Centroid
- Chain Rule
- Comparison Test
- Concave
- Concave Down
- Concave Up
- Conditional Convergence
- Constant Term
- Continued Sum
- Continuous Function
- Continuously Differentiable Function
- Converge
- Convergence Tests
- Convergent Sequence
- Convergent Series
- Critical Number
- Critical Point
- Curly d
- Curve
- Curve Sketching
- Cusp
- Cylindrical Shell Method
- Decreasing Function
- Definite Integral
- Definite Integral Rules
- Degenerate
- Del Operator
- Deleted Neighborhood
- Delta (Δ δ)
- Derivative
- Derivative of a Power Series
- Derivative Rules
- Difference Quotient
- Differentiable
- Differential
- Differential Equation
- Differentiation
- Discontinuity
- Discontinuous Function
- Disk
- Disk Method
- Distance from a Point to a Line
- Diverge
- Divergent Sequence
- Divergent Series
- e
- Ellipsoid
- End Behavior
- Essential Discontinuity
- Explicit Differentiation
- Explicit Function
- Exponential Decay
- Exponential Growth
- Exponential Model
- Extreme Value Theorem
- Extreme Values of a Polynomial
- Extremum
- Factorial
- Falling Bodies
- First Derivative
- First Derivative Test
- First Order Differential Equation
- Fixed
- Function Operations
- Fundamental Theorem of Calculus
- GLB
- Golden Spiral
- Graphic Methods
- Harmonic Progression
- Harmonic Series
- Helix
- Higher Derivative
- Hole
- Homogeneous System of Equations
- Hyperbolic Trig
- Identity Function
- Implicit Differentiation
- Implicit Function or Relation
- Improper Integral
- Increasing Function
- Indefinite Integral
- Indeterminate Expression
- Infinite Geometric Series
- Infinite Limit
- Infinite Series
- Infinitesimal
- Infinity
- Inflection Point
- Initial Value Problem
- Instantaneous Acceleration
- Instantaneous Rate of Change
- Instantaneous Velocity
- Integrable Function
- Integral
- Integral Methods
- Integral of a Function
- Integral of a Power Series
- Integral Table
- Integral Test
- Integral Test Remainder
- Integrand
- Integration
- Integration by Parts
- Integration by Substitution
- Intermediate Value Theorem
- Interval of Convergence
- Iterative Process
- Jump Discontinuity
- Least Upper Bound
- Limit
- Limit Comparison Test
- Limit from Above
- Limit from Below
- Limit Test for Divergence
- Local Behavior
- Local Maximum
- Local Minimum
- Logarithmic Differentiation
- Logistic Growth
- Mathematical Model
- Maximize
- Maximum of a Function
- Mean Value Theorem
- Mean Value Theorem for Integrals
- Mesh
- Minimize
- Minimum of a Function
- Mode
- Moment
- Multivariable
- Multivariable Analysis
- n-tuple
- Neighborhood
- Normal
- nth Degree Taylor Polynomial
- nth Derivative
- nth Partial Sum
- Oblate Spheroid
- One-Sided Limit
- Order of a Differential Equation
- Ordinary Differential Equation
- p-series
- Parallel Cross Sections
- Parameter (algebra)
- Parametric Derivative Formulas
- Parametric Equations
- Parametrize
- Partial Fractions
- Partial Sum of a Series
- Partition of an Interval
- Piecewise Continuous Function
- Pinching Theorem
- Polar Derivative Formulas
- Positive Series
- Power Rule
- Power Series
- Power Series Convergence
- Product Rule
- Prolate Spheroid
- Quotient Rule
- Radius of Convergence
- Ratio Test
- Rationalizing Substitutions
- Reciprocal Rule
- Related Rates
- Remainder of a Series
- Riemann Sum
- Root Test
- Scalar
- Secant Line
- Second Derivative
- Second Derivative Test
- Second Order Critical Point
- Second Order Differential Equation
- Separable Differential Equation
- Sequence
- Sequence of Partial Sums
- Series
- Series Rules
- Simple Closed Curve
- Simple Harmonic Motion (SHM)
- Simpson's Rule
- Slope of a Curve
- Solid
- Solid of Revolution
- Solve Analytically
- Solve Graphically
- Speed
- Surface
- Surface Area of a Surface of Revolution
- Surface of Revolution
- Tangent Line
- Taylor Series
- Taylor Series Remainder
- Torus
- Trapezoid Rule
- Trig Substitution
- Uniform
- Velocity
- Volume
- Washer Method
- Work