Calculus AB interactive
Read Calculus AB · Course outline and scope · Subject glossary
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Adjustable calculus labs (8)
- Unit 1: Limits and Continuity
Adjustable graph, computed table and explanation in the native lesson.
- Unit 2: Differentiation: Definition and Fundamental Properties
Adjustable graph, computed table and explanation in the native lesson.
- Unit 3: Differentiation: Composite, Implicit, and Inverse Functions
Adjustable graph, computed table and explanation in the native lesson.
- Unit 4: Contextual Applications of Differentiation
Adjustable graph, computed table and explanation in the native lesson.
- Unit 5: Analytical Applications of Differentiation
Adjustable graph, computed table and explanation in the native lesson.
- Unit 6: Integration and Accumulation of Change
Adjustable graph, computed table and explanation in the native lesson.
- Unit 7: Differential Equations
Adjustable graph, computed table and explanation in the native lesson.
- Unit 8: Applications of Integration
Adjustable graph, computed table and explanation in the native lesson.
Topic retrieval workspaces (81)
- Topic 1.1: 1.1 Introducing Calculus: Can Change Occur at an Instant?
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- Topic 1.2: 1.2 Defining Limits and Using Limit Notation
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- Topic 1.3: 1.3 Estimating Limit Values from Graphs
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- Topic 1.4: 1.4 Estimating Limit Values from Tables
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- Topic 1.5: 1.5 Determining Limits Using Algebraic Properties of Limits
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- Topic 1.6: 1.6 Determining Limits Using Algebraic Manipulation
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- Topic 1.7: 1.7 Selecting Procedures for Determining Limits
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- Topic 1.8: 1.8 Determining Limits Using the Squeeze Theorem
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- Topic 1.9: 1.9 Connecting Multiple Representations of Limits
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- Topic 1.10: 1.10 Exploring Types of Discontinuities
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- Topic 1.11: 1.11 Defining Continuity at a Point
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- Topic 1.12: 1.12 Confirming Continuity over an Interval
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- Topic 1.13: 1.13 Removing Discontinuities
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- Topic 1.14: 1.14 Connecting Infinite Limits and Vertical Asymptotes
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- Topic 1.15: 1.15 Connecting Limits at Infinity and Horizontal Asymptotes
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- Topic 1.16: 1.16 Working with the Intermediate Value Theorem (IVT)
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- Topic 2.1: 2.1 Defining Average and Instantaneous Rates of Change at a Point
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- Topic 2.2: 2.2 Defining the Derivative of a Function and Using Derivative Notation
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- Topic 2.3: 2.3 Estimating Derivatives of a Function at a Point
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- Topic 2.4: 2.4 Connecting Differentiability and Continuity: Determining When Derivatives Do and Do Not Exist
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- Topic 2.5: 2.5 Applying the Power Rule
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- Topic 2.6: 2.6 Derivative Rules: Constant, Sum, Difference, and Constant Multiple
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- Topic 2.7: 2.7 Derivatives of cos x, sin x, e^x, and ln x
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- Topic 2.8: 2.8 The Product Rule
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- Topic 2.9: 2.9 The Quotient Rule
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- Topic 2.10: 2.10 Finding the Derivatives of Tangent, Cotangent, Secant, and/or Cosecant Functions
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- Topic 3.1: 3.1 The Chain Rule
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- Topic 3.2: 3.2 Implicit Differentiation
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- Topic 3.3: 3.3 Differentiating Inverse Functions
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- Topic 3.4: 3.4 Differentiating Inverse Trigonometric Functions
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- Topic 3.5: 3.5 Selecting Procedures for Calculating Derivatives
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- Topic 3.6: 3.6 Calculating Higher-Order Derivatives
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- Topic 4.1: 4.1 Interpreting the Meaning of the Derivative in Context
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- Topic 4.2: 4.2 Straight-Line Motion: Connecting Position, Velocity, and Acceleration
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- Topic 4.3: 4.3 Rates of Change in Applied Contexts Other Than Motion
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- Topic 4.4: 4.4 Introduction to Related Rates
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- Topic 4.5: 4.5 Solving Related Rates Problems
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- Topic 4.6: 4.6 Approximating Values of a Function Using Local Linearity and Linearization
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- Topic 4.7: 4.7 Using L’Hospital’s Rule for Determining Limits of Indeterminate Forms
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- Topic 5.1: 5.1 Using the Mean Value Theorem
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- Topic 5.2: 5.2 Extreme Value Theorem, Global Versus Local Extrema, and Critical Points
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- Topic 5.3: 5.3 Determining Intervals on Which a Function Is Increasing or Decreasing
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- Topic 5.4: 5.4 Using the First Derivative Test to Determine Relative (Local) Extrema
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- Topic 5.5: 5.5 Using the Candidates Test to Determine Absolute (Global) Extrema
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- Topic 5.6: 5.6 Determining Concavity of Functions over Their Domains
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- Topic 5.7: 5.7 Using the Second Derivative Test to Determine Extrema
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- Topic 5.8: 5.8 Sketching Graphs of Functions and Their Derivatives
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- Topic 5.9: 5.9 Connecting a Function, Its First Derivative, and Its Second Derivative
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- Topic 5.10: 5.10 Introduction to Optimization Problems
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- Topic 5.11: 5.11 Solving Optimization Problems
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- Topic 5.12: 5.12 Exploring Behaviors of Implicit Relations
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- Topic 6.1: 6.1 Exploring Accumulations of Change
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- Topic 6.2: 6.2 Approximating Areas with Riemann Sums
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- Topic 6.3: 6.3 Riemann Sums, Summation Notation, and Definite Integral Notation
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- Topic 6.4: 6.4 The Fundamental Theorem of Calculus and Accumulation Functions
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- Topic 6.5: 6.5 Interpreting the Behavior of Accumulation Functions Involving Area
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- Topic 6.6: 6.6 Applying Properties of Definite Integrals
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- Topic 6.7: 6.7 The Fundamental Theorem of Calculus and Definite Integrals
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- Topic 6.8: 6.8 Finding Antiderivatives and Indefinite Integrals: Basic Rules and Notation
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- Topic 6.9: 6.9 Integrating Using Substitution
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- Topic 6.10: 6.10 Integrating Functions Using Long Division and Completing the Square
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- Topic 6.14: 6.14 Selecting Techniques for Antidifferentiation
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- Topic 7.1: 7.1 Modeling Situations with Differential Equations
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- Topic 7.2: 7.2 Verifying Solutions for Differential Equations
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- Topic 7.3: 7.3 Sketching Slope Fields
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- Topic 7.4: 7.4 Reasoning Using Slope Fields
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- Topic 7.6: 7.6 Finding General Solutions Using Separation of Variables
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- Topic 7.7: 7.7 Finding Particular Solutions Using Initial Conditions and Separation of Variables
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- Topic 7.8: 7.8 Exponential Models with Differential Equations
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- Topic 8.1: 8.1 Finding the Average Value of a Function on an Interval
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- Topic 8.2: 8.2 Connecting Position, Velocity, and Acceleration of Functions Using Integrals
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- Topic 8.3: 8.3 Using Accumulation Functions and Definite Integrals in Applied Contexts
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- Topic 8.4: 8.4 Finding the Area Between Curves Expressed as Functions of x
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- Topic 8.5: 8.5 Finding the Area Between Curves Expressed as Functions of y
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- Topic 8.6: 8.6 Finding the Area Between Curves That Intersect at More Than Two Points
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- Topic 8.7: 8.7 Volumes with Cross Sections: Squares and Rectangles
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- Topic 8.8: 8.8 Volumes with Cross Sections: Triangles and Semicircles
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- Topic 8.9: 8.9 Volume with Disc Method: Revolving Around the x- or y-Axis
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- Topic 8.10: 8.10 Volume with Disc Method: Revolving Around Other Axes
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- Topic 8.11: 8.11 Volume with Washer Method: Revolving Around the x- or y-Axis
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- Topic 8.12: 8.12 Volume with Washer Method: Revolving Around Other Axes
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Retained source study widgets (186)
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- Interactive 4.4.1 3-D graph for problem 4.4.2
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- Gallery 4.4.1 Graph of example 4.4.2
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- Interactive 4.3.1 Visualizing the Chain Rule
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- Gallery 4.3.1 Just for fun
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- Interactive 4.3.2 The hardest derivative ever (so far)
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- Pop Quiz 4.3.1 Chain Rule Review
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- Interactive 4.1.1 Example Problem 4.1.1
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- Pop Quiz 4.1.1 Product rule and second derivatives
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- Pop Quiz 4.2.1 The Reciprocal and Quotient Rules
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- Interactive 9.3.1 Volume of a cylinder
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- Interactive 9.3.2 Cylindrical shells
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- Interactive 9.2.1 Trigonometric Integrals
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- Pop Quiz 9.2.1 Integrals using Trigonometric Substitution
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- Pop Quiz 9.1.1 U-Substitution
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- Gallery 6.4.1 Estimation accuracy using different methods of Approximation
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- Interactive 6.4.1 The best way to estimate
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- Interactive 6.4.2 Understanding trapezoidal areas
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- Interactive 6.1.1 Maximinima of sin(πx)/πx
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- Pop Quiz 6.1.1 Maximinima
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- Interactive 6.2.1 Aluminum can
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- Pop Quiz 6.2.1 Conceptualizing Optimization
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- Interactive 6.3.1 Example Problem 6.3.2
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- Pop Quiz 6.3.1 Related Rates
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- Interactive 3.3.1 Newton-Raphson Method
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- Pop Quiz 3.3.1 All about Newton and Raphson
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- Gallery 3.3.1 Inconveniences related to Newton-Raphson
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- Gallery 3.1.1 Differentiability
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- Gallery 3.1.2 Making smooth piece-wise functions
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- Pop Quiz 3.1.1 Utilizing the power rule
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- Gallery 3.4.1 Derivative concepts
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- Pop Quiz 3.4.1 Section 4 cumulative
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- Interactive 3.2.1 An alternate definition of e.
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- Pop Quiz 3.2.1 Special derivatives
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- Interactive 7.2.1 Example Problem 7.2.1
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- Interactive 7.2.2 Example 7.2.2
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- Pop Quiz 7.2.1 Midpoint Method
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- Interactive 7.1.1 Example Problem 7.1.1
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- Interactive 7.1.2 Example Problem 7.1.2
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- Pop Quiz 7.1.1 Corner point estimation of areas under curves
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- Interactive 7.3.1 Example Problem 7.3.1
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- Pop Quiz 7.3.1 Trapezoidal Approximation
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- Interactive 10.1.1 Example 10.1.1 visualized
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- Interactive 10.1.2 Example 10.1.2
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- Pop Quiz 10.1.1 Volume through cylindrical shells
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- Interactive 10.3.1 3-D Parabloid
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- Interactive 10.2.1 A familiar shape
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- Interactive 10.2.2 Example 10.2.1
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- Interactive 10.2.3 A Hint for Example 10.2.2
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- Pop Quiz 10.2.1 Method of discs
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- Pop Quiz 8.3.1 Inverse Trig functions
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- Interactive 8.1.1 Example Problem 8.1.1
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- Interactive 8.2.1 Integrals at Infinity
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- Pop Quiz 8.2.1 Finite areas at infinity
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- Gallery 1.1.1 The Special Right Triangles
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- Gallery 1.1.2 The Unit Circle
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- Gallery 1.1.3 The six trigonometric functions and their definitions
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- Gallery 1.1.2 Graphs of trigonometric functions
Gallery steps and all-frame reading. Retained source context; follow its local scope and review notes.
- Pop Quiz 1.1.1 The Unit Circle
Source quiz · reviewed and unfinished items labeled in context. Retained source context; follow its local scope and review notes.
- Interactive 1.3.1 Understanding range
Figure and selectable notes. Retained source context; follow its local scope and review notes.
- Interactive 1.3.2 Testing our Prediction from Example Problem 1.3.4
Figure and selectable notes. Retained source context; follow its local scope and review notes.
- Show your work for Problem 2
Written-work workspace. Retained source context; follow its local scope and review notes.
- Show your work for Problem 1
Written-work workspace. Retained source context; follow its local scope and review notes.
- Show your work for Problem 3
Written-work workspace. Retained source context; follow its local scope and review notes.
- Show your work for Problem 4
Written-work workspace. Retained source context; follow its local scope and review notes.
- Show your work for Problem 5
Written-work workspace. Retained source context; follow its local scope and review notes.
- Show your work for Problem 6
Written-work workspace. Retained source context; follow its local scope and review notes.
- Show your work for Problem 7
Written-work workspace. Retained source context; follow its local scope and review notes.
- Show your work for Problem 8
Written-work workspace. Retained source context; follow its local scope and review notes.
- Show your work for Problem 9
Written-work workspace. Retained source context; follow its local scope and review notes.
- Show your work for Problem 10
Written-work workspace. Retained source context; follow its local scope and review notes.
- Gallery 1.2.1 Examples of reflection at work.
Gallery steps and all-frame reading. Retained source context; follow its local scope and review notes.
- Gallery 1.2.2. Graphs from Example Problems 1.2.2 and 1.2.3
Gallery steps and all-frame reading. Retained source context; follow its local scope and review notes.
- Gallery 1.2.3. Stretching and Compression
Gallery steps and all-frame reading. Retained source context; follow its local scope and review notes.
- Pop Quiz 1.2.1 Transforms Review
Source quiz · reviewed and unfinished items labeled in context. Retained source context; follow its local scope and review notes.
- Gallery 2.1.1 Discontinuities
Gallery steps and all-frame reading. Retained source context; follow its local scope and review notes.
- Pop Quiz 2.1.1 Limits and Laws
Source quiz · reviewed and unfinished items labeled in context. Retained source context; follow its local scope and review notes.
- Interactive 2.1.1 Visualizing the Squeeze Theorem
Figure and selectable notes. Retained source context; follow its local scope and review notes.
- Interactive 2.4.1 Secant lines and tangent lines.
Figure and selectable notes. Retained source context; follow its local scope and review notes.
- Gallery 2.4.1 How to make lines tangent.
Gallery steps and all-frame reading. Retained source context; follow its local scope and review notes.
- Pop Quiz 2.4.1 Conceptual Review of Limits
Source quiz · reviewed and unfinished items labeled in context. Retained source context; follow its local scope and review notes.
- Show your work for Problem 2
Written-work workspace. Retained source context; follow its local scope and review notes.
- Show your work for Problem 1
Written-work workspace. Retained source context; follow its local scope and review notes.
- Show your work for Problem 3
Written-work workspace. Retained source context; follow its local scope and review notes.
- Show your work for Problem 4
Written-work workspace. Retained source context; follow its local scope and review notes.
- Show your work for Problem 6
Written-work workspace. Retained source context; follow its local scope and review notes.
- Show your work for Problem 5
Written-work workspace. Retained source context; follow its local scope and review notes.
- Show your work for Problem 7
Written-work workspace. Retained source context; follow its local scope and review notes.
- Show your work for Problem 8
Written-work workspace. Retained source context; follow its local scope and review notes.
- Show your work for Problem 9
Written-work workspace. Retained source context; follow its local scope and review notes.
- Show your work for Problem 10
Written-work workspace. Retained source context; follow its local scope and review notes.
- Gallery 2.2.1 Epsilon Delta Limits
Gallery steps and all-frame reading. Retained source context; follow its local scope and review notes.
- Pop Quiz 2.2.1 Calculating limits
Source quiz · reviewed and unfinished items labeled in context. Retained source context; follow its local scope and review notes.
- Gallery 2.3.1 Special Limits
Gallery steps and all-frame reading. Retained source context; follow its local scope and review notes.
- Pop Quiz 2.3.1 Evaluating polynomial limits
Source quiz · reviewed and unfinished items labeled in context. Retained source context; follow its local scope and review notes.
- Interactive 5.4.1 Sample Problem 5.4.1
Figure and selectable notes. Retained source context; follow its local scope and review notes.
- Show your work for Problem 1
Written-work workspace. Retained source context; follow its local scope and review notes.
- Show your work for Problem 2
Written-work workspace. Retained source context; follow its local scope and review notes.
- Show your work for Problem 4
Written-work workspace. Retained source context; follow its local scope and review notes.
- Show your work for Problem 3
Written-work workspace. Retained source context; follow its local scope and review notes.
- Show your work for Problem 6
Written-work workspace. Retained source context; follow its local scope and review notes.
- Show your work for Problem 5
Written-work workspace. Retained source context; follow its local scope and review notes.
- Show your work for Problem 8
Written-work workspace. Retained source context; follow its local scope and review notes.
- Show your work for Problem 7
Written-work workspace. Retained source context; follow its local scope and review notes.
- Show your work for Problem 10
Written-work workspace. Retained source context; follow its local scope and review notes.
- Show your work for Problem 9
Written-work workspace. Retained source context; follow its local scope and review notes.
- Interactive 5.2.1 Inverse and normal functions.
Figure and selectable notes. Retained source context; follow its local scope and review notes.
- Pop Quiz 5.2.1 Inverse Functions
Source quiz · reviewed and unfinished items labeled in context. Retained source context; follow its local scope and review notes.
- Pop Quiz 5.3.1 A visit to L’Hospital
Source quiz · reviewed and unfinished items labeled in context. Retained source context; follow its local scope and review notes.
- Gallery 5.1.1 Example Problem 5.1.1
Gallery steps and all-frame reading. Retained source context; follow its local scope and review notes.
- Pop Quiz 5.1.1 Logs and Exponents
Source quiz · reviewed and unfinished items labeled in context. Retained source context; follow its local scope and review notes.
- This is a Gallery
Gallery steps and all-frame reading. Retained source context; follow its local scope and review notes.
- This is an Interactive Image
Figure and selectable notes. Retained source context; follow its local scope and review notes.
- This is a Quiz
Source quiz · reviewed and unfinished items labeled in context. Retained source context; follow its local scope and review notes.
- This is a Sketchpad
Written-work workspace. Retained source context; follow its local scope and review notes.