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All Key Terms
AP Calculus AB/BC
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AP Calculus AB/BC
Key Terms
1106 essential vocabulary terms and definitions to know for your AP Calculus AB/BC exam
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AP Calculus AB/BC
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Unit 1 – Limits and Continuity
1.1 Introducing Calculus
1.10 Exploring Types of Discontinuities
1.11 Defining Continuity at a Point
1.12 Confirming Continuity over an Interval
1.13 Removing Discontinuities
1.14 Connecting Infinite Limits and Vertical Asymptotes
1.15 Connecting Limits at Infinity and Horizontal Asymptotes
1.16 Working with the Intermediate Value Theorem (IVT Calc)
1.2 Defining Limits and Using Limit Notation
1.3 Estimating Limit Values from Graphs
1.4 Estimating Limit Values from Tables
1.5 Determining Limits Using Algebraic Properties of Limits
1.6 Determining Limits Using Algebraic Manipulation
1.8 Determining Limits Using the Squeeze Theorem
Unit 2 – Fundamentals of Differentiation
2.1 Defining Average and Instantaneous Rates of Change at a Point
2.10 Finding the Derivatives of Tangent, Cotangent, Secant, and/or Cosecant Functions
2.2 Defining the Derivative of a Function and Using Derivative Notation
2.3 Estimating Derivatives of a Function at a Point
2.4 Connecting Differentiability and Continuity
2.5 Applying the Power Rule
2.6 Derivative Rules
2.7 Derivatives of cos x, sinx, e^x, and ln x
2.8 The Product Rule
2.9 The Quotient Rule
Unit 3 – Composite, Implicit, and Inverse Functions
3.1 The Chain Rule
3.2 Implicit Differentiation
3.3 Differentiating Inverse Functions
3.4 Differentiating Inverse Trigonometric Functions
3.6 Calculating Higher-Order Derivatives
Unit 4 – Contextual Applications of Differentiation
4.1 Interpreting the Meaning of the Derivative in Context
4.2 Straight-Line Motion
4.3 Rates of Change in Applied Contexts other than Motion
4.4 Intro to Related Rates
4.5 Solving Related Rates Problems
4.6 Approximating Values of a Function Using Local Linearity and Linearization
4.7 Using L'Hopitals Rule for Determining Limits in Indeterminate Forms
Unit 5 – Analytical Applications of Differentiation
5.10 Introduction to Optimization Problems
5.1 Using the Mean Value Theorem
5.11 Solving Optimization Problems
5.12 Exploring Behaviors of Implicit Relations
5.2 Extreme Value Theorem, Global vs Local Extrema, and Critical Points
5.3 Determining Intervals on Which a Function is Increasing or Decreasing
5.4 Using the First Derivative Test to Determine Relative (Local) Extrema
5.5 Using the Candidates Test to Determine Absolute (Global) Extrema
5.6 Determining Concavity
5.7 Using the Second Derivative Test to Determine Extrema
5.8 Sketching Graphs of Functions and Their Derivatives
5.9 Connecting a Function, Its First Derivative, and its Second Derivative
Unit 6 – Integration and Accumulation of Change
6.1 Unit 6
6.10 Integrating Functions Using Long Division and Completing the Square
6.11 Integrating Using Integration by Parts
6.12 Using Linear Partial Fractions
6.13 Evaluation Improper Integrals
6.2 Approximating Areas with Riemann Sums
6.3 Riemann Sums, Summation Notation, and Definite Integral Notation
6.4 The Fundamental Theorem of Calculus and Accumulation Functions
6.5 Interpreting the Behavior of Accumulation Functions Involving Area
6.6 Applying Properties of 3 Definite Integrals
6.7 The Fundamental Theorem of Calculus and Definite Integrals
6.8 Finding Antiderivatives and Indefinite Integrals: Basic Rules and Notation
6.9 Integrating Using 1 Substitution
Unit 7 – Differential Equations
7.1 Modeling Situations with Differential Equations
7.2 Verifying Solutions for Differential Equations
7.3 Sketching Slope Fields
7.4 Reasoning Using Slope Fields
7.5 Approximating Solutions Using Euler’s Method
7.6 Finding General Solutions Using Separation of Variables
7.7 Finding Particular Solutions Using Initial Conditions and Separation of Variables
7.8 Exponential Models with Differential Equations
7.9 Logistic Models with Differential Equations
Unit 8 – Applications of Integration
8.1 Finding the Average Value of a Function on an Interval
8.10 Volume with Disc Method
8.11 Volume with Washer Method
8.12 Volume with Washer Method
8.13 The Arc Length of a Smooth, Planar Curve and Distance Traveled
8.2 Connecting Position, Velocity, and Acceleration of Functions Using Integrals
8.3 Using Accumulation Functions and Definite Integrals in Applied Contexts
8.4 Finding the Area Between Curves Expressed as Functions of x
8.5 Finding the Area Between Curves Expressed as Functions of y
8.6 Finding the Area Between Curves That Intersect at More Than Two Points
8.7 Volumes with Cross Sections
8.8 Volumes with Cross Sections
8.9 Volume with Disc Method
Unit 9 – Parametric Equations, Polar Coordinates, and Vector–Valued Functions (BC Only)
9.1 Defining and Differentiating Parametric Equations
9.2 Second Derivatives of Parametric Equations
9.3 Finding Arc Lengths of Curves Given by Parametric Equations
9.4 Defining and Differentiating Vector-Valued Functions
9.5 Integrating Vector-Valued Functions
9.6 Solving Motion Problems Using Parametric and Vector-Valued Functions
9.7 Defining Polar Coordinates and Differentiating in Polar Form
9.8 Find the Area of a Polar Region or the Area Bounded by a Single Polar Curve
9.9 Finding the Area of the Region Bounded by Two Polar Curves
Unit 10 – Infinite Sequences and Series (BC Only)
10.1 Defining Convergent and Divergent Infinite Series
10.10 Alternating Series Error Bound
10.11 Finding Taylor Polynomial Approximations of Functions
10.12 Lagrange Error Bound
10.13 Radius and Interval of Convergence of Power Series
10.14 Finding Taylor or Maclaurin Series for a Function
10.15 MC Answers and Review
10.2 Working with Geometric Series
10.3 The nth Term Test for Divergence
10.4 Integral Test for Convergence
10.5 Harmonic Series and p-Series
10.6 Comparison Tests for Convergence
10.7 Alternating Series Test for Convergence
10.8 Ratio Test for Convergence
10.9 Determining Absolute or Conditional Convergence
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\sin(t)
E^{sin(x)}
F'(x)
F(x) = 2x - 1
X = k
(-csc(x)cot(x))
(-csc^2(x))
(1, 1)
(2x + 1)
(2x - 1)^4
(6x+3)/(x-2)
(cot(x))'
(sec^2(x))
(x^2-4)/(x-2)
(x→2)
[a,b]
\frac{1}{1+x}
\frac{d}{dx}
|x|
ΔY/ΔX
θ
θ (theta)
θ^2
π (pi)
π/2
π/4
π/6
∆x
∑(n=1 to ∞) ((-1)^n/n))
∑(n=1 to ∞) (1/n^3)
∑(𝑛=1 to ∞)
∑|a_n|
√(4-y^2)
√(x)
√x
∫x^2 * cos(x) dx
0 ≤ x ≤ 1
0 ≤ y ≤ 1
1 ≤ x ≤ 4
1 ≤ y ≤ e
1/x
2^x
2e^(2x)
2e^x
2x
2x^2 + 1
2x³
3x
4x^3 + x
5x^3 - 2x^2 + 4x - 1
A
A(t)
A(x)
Absolute Error
Absolute Extrema
Absolute Maximum
Absolute Maximums
Absolute minimum
Absolute Minimum Value
Absolute Value
Absolute Value Expressions
Absolute Value Function
Absolute Value Functions
Absolutely Convergent
Accelerating
Acceleration
Acceleration Function
Acceleration Vector
Acceleration vector-valued function
Accumulation Function
Accumulation Functions
Accumulation of Change
Accumulation of Distance
Accuracy of an Approximation
Actual Function Value
Air Resistance
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