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AP Calculus AB
Curriculum Map
Chapter
1) Prerequisites for Calculus
Section
1.1 Lines
Anchor
Skills
AB.1.1.1 1.1.1 Find Coordinate Increments Between Two Points
1.1.2 Given Two Points on a Line, Find the Slope and Graph the Line
1.1.3 Given a Point, Write the Equations for the Horizontal/Vertical Line Through the Point
1.1.4 Given a Point and a Slope, Write the Point-Slope Equation for a Line
1.1.5 Given a Slope and Y-Intercept, Write the Slope-Intercept Equation for a Line
1.1.6 Given Two Points, Write the General Linear Equation of a Line
1.1.7 Write the Equation of a Line Parallel/Perpendicular to a Given Line
1.1.8 Given a Table of Values, Determine the Slope of a Line
1.2 Functions and Graphs
AB.1.1.1 1.2.1 Find the Domain and Range of a Function
AB.1.1.2 1.2.2 Use a Graphing Calculator to Graph a Function
AB.1.2.1 1.2.3 Determine whether a Given Function is Even, Odd, or Neither
AB.5.1.1 1.2.4 Graph a Piecewise-Defined Function
1.2.5 Use the Vertical Line Test to Determine Whether a Graph Represents a Function
1.2.6 Given a Graph, Write a Piecewise-Defined Equation
1.2.7 Simplify/Evaluate the Composition of Two Functions
1.2.8 Memorize Characteristics of Common Functions (Squaring, Cubing, Identity, etc.)
1.3 Exponential Functions
AB.1.1.3 1.3.1 Graph an Exponential Function
AB.1.2.1 1.3.2 Find the Domain and Range of an Exponential Function
AB.5.1.2 1.3.3 Use a Graphing Calculator to Find the Zeros of an Exponential Function
1.3.4 Match the Graph of an Exponential Function With Its Equation
1.5 Functions and Logarithms
AB.1.1.3 1.5.1 Determine if a Graph Represents a One-to-One Function
AB.1.2.1 1.5.2 Given an Equation, Determine if a Function has an Inverse (and Find It)
1.5.3 Use a Graphing Calculator to Find the Domain and Range of a Logarithmic Function
1.6 Trigonometric Functions
AB.1.2.1 1.6.1 Find Trigonometric Function Values for General Angles
AB.1.3.1 1.6.2 Determine the Period, Amplitude, Domain, and Range of a Trigonometric Function
1.6.3 Evaluate Expressions Involving Inverse Trigonometric Functions
2) Limits and Continuity
2.1 Rates of Change and Limits
AB.2.1.1 2.1.1 Evaluate a Limit Using Substitution
AB.2.1.2 2.1.2 Determine a Limit Graphically and Support It Algebraically
AB.2.1.3 2.1.3 Given an Equation or Graph, Determine if a Limit Fails to Exists
2.1.4 Given a Piecewise-Defined Graph, Find Sided and General Limits
2.1.5 Find a Limit Given a Table of Values
2.2 Limits Involving Infinity
AB.2.1.1 2.2.1 Given an Equation, Find Limits as the Variable Value Approaches Infinity
AB.2.1.2 2.2.2 Given an Equation, Identify where Horizontal and Vertical Asymptotes Occur
AB.2.2.1 2.2.3 Find a Power Function End Behavior Model
AB.2.2.2
2.3 Continuity
AB.2.3.1 2.3.1 Given an Equation, Find and Classify All Points of Discontinuity
AB.2.3.2 2.3.2 Given a Piecewise-Defined Graph, Find and Classify All Points of Discontinuity
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AP Calculus AB
Curriculum Map
AB.2.3.3 2.3.3 Find the Formula for a Continuous Extended Function
2.3.4 Identify Intervals on Which a Zero Exists Using the Intermediate Value Theorem
2.4 Rates of Change and Tangent Lines
AB.2.2.3 2.4.1 Find the Average Rate of Change for a Function Over a Given Interval
2.4.2 Use the Difference Quotient to Find the Slope of a Curve at a Given Point
2.4.3 Find the Equation of a Line Tangent to a Curve at a Given Point
2.4.4 Find the Equation of a Line Normal to a Curve at a Given Point
3) Derivatives
3.1 Derivative of a Function
AB.3.1.1 3.1.1 Use the Difference Quotient to Find the Derivative of a Function at a Given Point
AB.3.1.2 3.1.2 Use the Difference Quotient to Find a Derivative Rule
AB.3.1.3 3.1.3 Match the Graph of a Function with a Graph of Its Derivative
AB.3.2.2 3.1.4 Given a Function or Function Value, Find Equations for the Tangent/Normal Lines
AB.3.2.3 3.1.5 Memorize Common Derivatives
AB.3.2.4 3.1.6 Define Derivative Using Various Terms (Slope of Curve, Inst. Rate of Change, etc.)
AB.3.3.1 3.1.7 Find the Average Rate of Change and Compare to the Instantaneous Rate of Change
AB.3.6.1 3.1.8 Approximate the Derivative Given a Table of Values
3.2 Differentiability
AB.3.1.4 3.2.1 Compare Right and Left Hand Derivatives to Determine if a Derivative Exists at a Point
AB.3.2.1 3.2.2 Given a Graph, Determine Where a Function is Continuous and Differentiable
3.2.3 Identify Places Where a Function Fails to be Differentiable (ex. Corner, Cusp, etc.)
3.3 Rules for Differentiation
AB.3.2.1 3.3.1 Find the Derivative of a Polynomial Using the Power and Constant Multiple Rules
AB.3.2.2 3.3.2 Find the Horizontal Tangents to a Given Curve
AB.5.1.3 3.3.3 Find a Derivative Using the Product Rule
3.3.4 Find a Derivative Using the Quotient Rule
3.3.5 Given a Function/Derivative Value, Use the Product/Quotient Rule to Simplify
3.3.6 Find the Derivative of Expressions Involving Negative Exponents
3.3.7 Find the Equation of a Tangent/Normal Line
3.3.8 Find Higher Order Derivatives
3.3.9 Use a Graphing Calculator to Find a Derivative Value
3.4 Velocity and Other Rates of Change
AB.3.5.5 3.4.1 Given a Position Equation, Find a Velocity and Acceleration Equation and Evaluate
3.4.2 Given a Position Equation, Find the Displacement and Average Velocity on an Interval
3.4.3 Analyze a Velocity Graph to Find Characteristics of Position, Velocity, and Acceleration
3.4.4 Analyze a Position Graph to Find Characteristics of Position, Velocity, and Acceleration
3.5 Derivatives of Trigonometric Functions
AB.3.6.1 3.5.1 Use Derivative Rules to Find the Derivative of a Trigonometric Function
3.5.2 Find the Equation of a Line Tangent/Normal to a Trigonometric Function
3.6 Chain Rule
AB.3.6.2 3.6.1 Use the Chain Rule to Find the Derivative of an Equation
3.6.2 Use Multiple Derivative Rules to Find the Derivative of an Equation
3.6.3 Find the Derivative of a Composition of Functions and Evaluate
3.6.4 Find the Equation of a Line Tangent to a Curve Using the Chain Rule
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AP Calculus AB
Curriculum Map
3.7 Implicit Differentiation
AB.3.5.4 3.7.1 Find the Implicit Derivative of a Function
AB.3.6.2 3.7.2 Find the Slope of a Curve at a Point Using Implicit Differentiation
AB.3.5.4 3.7.3 Determine Where the Slope of a Curve is Undefined
3.7.4 Find the Equation of a Line Tangent/Normal to a Curve Using Implicit Differentiation
3.7.5 Use Implicit Differentiation to Find the Derivative of an Inverse
4) Applications of Derivatives
4.6 Related Rates
AB.3.5.3 4.6.1 Use Implicit Differentiation to Solve Problems Involving Related Rates
4.1 Extreme Values of Functions
AB.2.3.3 4.1.1 Given a Graph, Find Where Extreme Values Occur
AB.3.5.2 4.1.2 Given a Graph, Determine What the Extreme Values Are
4.1.3 Given an Equation, Find the Critical Points, the Extreme Values and Where They Occur
4.1.4 Given an Absolute Value Equation, Find Extreme Values and Where They Occur
4.1.5 Given a Piecewise Function Equation, Find Extreme Values and Where They Occur
4.2 Mean Value Theorem
AB.3.3.3 4.2.1 Find the Average Rate Of Change of a Function
4.2.2 Given an Equation, Determine if the Function Satisfies the Hypothesis of the MVT
4.2.3 Given an Equation and an Interval, Find the Value at Which the MVT is Satisfied
4.2.4 Use the MVT to Solve Real-World Problems
4.2.5 Given an Equation, Determine Where the Function is Increasing/Decreasing
4.3 Connecting f' and f'' with the Graph of f
AB.3.3.1 4.3.1 Given an Equation, Use the First Derivative Test to Determine Local Extreme Values
AB.3.3.2 4.3.2 Given an Equation, Use the Concavity Test to Find Where Function is Concave Up/Down
AB.3.3.4 4.3.3 Given an Equation, Find the Points of Inflection
AB.3.4.1 4.3.4 Given a Graph of f, Determine Where f' and f'' will be Positive/Negative/Zero
AB.3.4.2 4.3.5 Given a Graph of f', Find the Critical Values and Where f is Increasing/Decreasing
AB.3.4.3
AB.3.5.1
5) The Definite Integral
4.4 Modeling and Optimizing
AB.3.5.2 4.4.1 Use Critical Points, First Derivative Test, etc. To Maximize/Minimize Real-World Problems
5.1 Estimating with Finite Sums
AB.4.1.1 5.1.1 Approximate the Area Under a Curve Using Rectangles (LRAM, RRAM, MRAM)
AB.4.2.1 5.1.2 Find and LRAM/RRAM/MRAM Given a Table of Values
5.2 Definite Integrals
AB.4.1.2 5.2.1 Evaluate Definite Integrals Using Area Under the Curve
AB.4.4.1 5.2.2 Evaluate Definite Integrals On a Calculator
AB.5.1.4 5.2.3 Evaluate Definite Integrals with Variable Limits of Integration
5.2.4 Memorize Common Antiderivatives
5.3 Definite Integrals and Antiderivatives
AB.4.1.2 5.3.1 Given an Integral Value, Use Integral Rules to Find Related Integral Values
AB.4.1.3 5.3.2 Determine if the Mean Value Theorem Applies to a Given Function
5.3.3 Find the Average Value of a Function
5.3.4 Find Definite Integrals Using Antiderivatives
5.4 Fundamental Theorem of Calculus
AB.4.3.1 5.4.1 Use the FTC (I) to Find the Derivative of an Integral with a Variable Limit
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AP Calculus AB
Curriculum Map
AB.4.3.2 5.4.2 Construct an Integral Function to Represent a Given Differential Equation
5.4.3 Use the FTC (II) to Evaluate Definite Integrals
5.4.4 Find the Area Under a Curve Using the FTC (II)
5.5 Trapezoidal Rule
AB.4.2.1 5.5.1 Given an Integral, Use the Trapezoidal Rule to Approximate an Area
5.5.2 Given a Table of Values, Use the Trapezoidal Rule to Approximate an Area
6) Differential Equations and Math Modeling 6.2 Antidifferentiation by Substitution
AB.4.4.2 6.2.1 Verify that The Integral of f(u)du Does Not Equal the Integral of f(u)dx
6.2.2 Use U-Substitution to Simplify an Indefinite Integral
6.2.3 Use U-Substitution to Evaluate Definite Integrals
7) Applications of Definite Integrals
7.1 Integral as Net Change
AB.4.1.2 7.1.1 Given a Velocity Equation, Determine Direction and Total Distance Traveled
AB.4.5.3 7.1.2 Given a Graph of Velocity, Determine Direction and Total Distance Traveled
AB.4.6.1 7.1.3 Given a Table of Times and Rates, Find Total Values
7.2 Areas in the Plane
AB.4.5.1 7.2.1 Given a Graph, Find the Area Between Two Curves (in Terms of X or Y)
7.2.2 Given an Equation, Find the Area Between Two Curves (in Terms of X or Y)
7.3 Volumes
AB.4.5.2 7.3.1 Find the Volume of a Figure with a Known Cross-Sectional Area
7.3.2 Find Volumes Using the Disk and Washer Methods (in Terms of X or Y)
7.3.3 Find Volumes Using the Cylindrical Shell Method (in Terms of X or Y)
6) Differential Equations and Math Modeling 6.1 Slope Fields and Euler's Method
(Revisited)
AB.3.5.6 6.1.1 Find a General Solution to a Differential Equation
AB.4.6.1 6.1.2 Solve Initial Value Problems
AB.4.6.2 6.1.3 Match a Slope Field to Its Equation
6.1.4 Given an Equation, Construct a Slope Field
6-4 Exponential Growth and Decay
AB.4.6.2 6.4.1 Use Separation of Variables to Solve Initial Value Problems
6.4.2 Model Problems Involving Exponential Growth and Decay
6.4.3 Find the Half-Life in an Exponential Decay Problem