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AP Calculus BC
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- 1Limits and Continuity
- 2Differentiation: Definition and Fundamental Properties
- 3Differentiation: Composite, Implicit, and Inverse Functions
- 4Contextual Applications of Differentiation
- 5Analytical Applications of Differentiation
- 6Integration and Accumulation of Change
- 7Differential Equations
- 8Applications of Integration
- 9Parametric Equations, Polar Coordinates, and Vector-Valued Functions
- 10Infinite Sequences and Series
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Downloads
- Course & Exam Description 2-up
- Revision Sheet
- Syllabus Checklist 2-up
- Scheme of Work
- Exam Technique 2-up
- Command Words — A3 poster
- Lesson Plans — one page per topic 2-up
- Class Mark Book
1. Limits and Continuity 39 files
Handouts
Presentation slides
Exercise walk-through slides
- 1.1 Introducing Calculus: Can Change Occur at an Instant?
- 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
- 1.7 Selecting Procedures for Determining Limits
- 1.8 Determining Limits Using the Squeeze Theorem
- 1.9 Connecting Multiple Representations of Limits
- 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 Past-paper walk-through
- 1.16 Working with the Intermediate Value Theorem (IVT) Past-paper walk-through
Vocabulary
Topic Quizzes
Exercise sheets
- 1.1 Introducing Calculus: Can Change Occur at an Instant? 2-up
- 1.2 Defining Limits and Using Limit Notation 2-up
- 1.3 Estimating Limit Values from Graphs 2-up
- 1.4 Estimating Limit Values from Tables 2-up
- 1.5 Determining Limits Using Algebraic Properties of Limits 2-up
- 1.6 Determining Limits Using Algebraic Manipulation 2-up
- 1.7 Selecting Procedures for Determining Limits 2-up
- 1.8 Determining Limits Using the Squeeze Theorem 2-up
- 1.9 Connecting Multiple Representations of Limits 2-up
- 1.10 Exploring Types of Discontinuities 2-up
- 1.11 Defining Continuity at a Point 2-up
- 1.12 Confirming Continuity over an Interval 2-up
- 1.13 Removing Discontinuities 2-up
- 1.14 Connecting Infinite Limits and Vertical Asymptotes 2-up
- 1.15 Connecting Limits at Infinity and Horizontal Asymptotes 2-up
- 1.16 Working with the Intermediate Value Theorem (IVT) 2-up
Past Paper Questions
Unit Tests
2. Differentiation: Definition and Fundamental Properties 32 files
Presentation slides
Exercise walk-through slides
- 2.1 Defining Average and Instantaneous Rates of Change at a Point Past-paper walk-through
- 2.2 Defining the Derivative of a Function and Using Derivative Notation
- 2.3 Estimating Derivatives of a Function at a Point Past-paper walk-through
- 2.4 Connecting Differentiability and Continuity: Determining When Derivatives Do and Do Not Exist Past-paper walk-through
- 2.5 Applying the Power Rule
- 2.6 Derivative Rules: Constant, Sum, Difference, and Constant Multiple Past-paper walk-through
- 2.7 Derivatives of cos x, sin x, e^x, and ln x Past-paper walk-through
- 2.8 The Product Rule Past-paper walk-through
- 2.9 The Quotient Rule Past-paper walk-through
- 2.10 Finding the Derivatives of Tangent, Cotangent, Secant, and/or Cosecant Functions
Exercise sheets
- 2.1 Defining Average and Instantaneous Rates of Change at a Point 2-up
- 2.2 Defining the Derivative of a Function and Using Derivative Notation 2-up
- 2.3 Estimating Derivatives of a Function at a Point 2-up
- 2.4 Connecting Differentiability and Continuity: Determining When Derivatives Do and Do Not Exist 2-up
- 2.5 Applying the Power Rule 2-up
- 2.6 Derivative Rules: Constant, Sum, Difference, and Constant Multiple 2-up
- 2.7 Derivatives of cos x, sin x, e^x, and ln x 2-up
- 2.8 The Product Rule 2-up
- 2.9 The Quotient Rule 2-up
- 2.10 Finding the Derivatives of Tangent, Cotangent, Secant, and/or Cosecant Functions 2-up
Past Paper Questions
- 2.1 Defining Average and Instantaneous Rates of Change at a Point 2-upAnswers2-up
- 2.3 Estimating Derivatives of a Function at a Point 2-upAnswers2-up
- 2.4 Connecting Differentiability and Continuity: Determining When Derivatives Do and Do Not Exist 2-upAnswers2-up
- 2.6 Derivative Rules: Constant, Sum, Difference, and Constant Multiple 2-up
- 2.7 Derivatives of cos x, sin x, e^x, and ln x 2-up
- 2.8 The Product Rule 2-upAnswers2-up
- 2.9 The Quotient Rule 2-upAnswers2-up
3. Differentiation: Composite, Implicit, and Inverse Functions 20 files
Presentation slides
Exercise walk-through slides
- 3.1 The Chain Rule Past-paper walk-through
- 3.2 Implicit Differentiation Past-paper walk-through
- 3.3 Differentiating Inverse Functions
- 3.4 Differentiating Inverse Trigonometric Functions
- 3.5 Selecting Procedures for Calculating Derivatives
- 3.6 Calculating Higher-Order Derivatives Past-paper walk-through
Exercise sheets
Past Paper Questions
4. Contextual Applications of Differentiation 25 files
Presentation slides
Exercise walk-through slides
- 4.1 Interpreting the Meaning of the Derivative in Context Past-paper walk-through
- 4.2 Straight-Line Motion: Connecting Position, Velocity, and Acceleration Past-paper walk-through
- 4.3 Rates of Change in Applied Contexts Other Than Motion
- 4.4 Introduction to Related Rates Past-paper walk-through
- 4.5 Solving Related Rates Problems Past-paper walk-through
- 4.6 Approximating Values of a Function Using Local Linearity and Linearization Past-paper walk-through
- 4.7 Using L'Hospital's Rule for Determining Limits of Indeterminate Forms Past-paper walk-through
Topic Quizzes
Exercise sheets
- 4.1 Interpreting the Meaning of the Derivative in Context 2-up
- 4.2 Straight-Line Motion: Connecting Position, Velocity, and Acceleration 2-up
- 4.3 Rates of Change in Applied Contexts Other Than Motion 2-up
- 4.4 Introduction to Related Rates 2-up
- 4.5 Solving Related Rates Problems 2-up
- 4.6 Approximating Values of a Function Using Local Linearity and Linearization 2-up
- 4.7 Using L'Hospital's Rule for Determining Limits of Indeterminate Forms 2-up
Past Paper Questions
- 4.1 Interpreting the Meaning of the Derivative in Context 2-upAnswers2-up
- 4.2 Straight-Line Motion: Connecting Position, Velocity, and Acceleration 2-upAnswers2-up
- 4.4 Introduction to Related Rates 2-upAnswers2-up
- 4.5 Solving Related Rates Problems 2-upAnswers2-up
- 4.6 Approximating Values of a Function Using Local Linearity and Linearization 2-upAnswers2-up
- 4.7 Using L'Hospital's Rule for Determining Limits of Indeterminate Forms 2-upAnswers2-up
5. Analytical Applications of Differentiation 39 files
Presentation slides
Exercise walk-through slides
- 5.1 Using the Mean Value Theorem Past-paper walk-through
- 5.2 Extreme Value Theorem, Global Versus Local Extrema, and Critical Points Past-paper walk-through
- 5.3 Determining Intervals on Which a Function Is Increasing or Decreasing Past-paper walk-through
- 5.4 Using the First Derivative Test to Determine Relative (Local) Extrema Past-paper walk-through
- 5.5 Using the Candidates Test to Determine Absolute (Global) Extrema Past-paper walk-through
- 5.6 Determining Concavity of Functions over Their Domains Past-paper walk-through
- 5.7 Using the Second Derivative Test to Determine Extrema Past-paper walk-through
- 5.8 Sketching Graphs of Functions and Their Derivatives
- 5.9 Connecting a Function, Its First Derivative, and Its Second Derivative Past-paper walk-through
- 5.10 Introduction to Optimization Problems Past-paper walk-through
- 5.11 Solving Optimization Problems
- 5.12 Exploring Behaviors of Implicit Relations Past-paper walk-through
Topic Quizzes
Exercise sheets
- 5.1 Using the Mean Value Theorem 2-up
- 5.2 Extreme Value Theorem, Global Versus Local Extrema, and Critical Points 2-up
- 5.3 Determining Intervals on Which a Function Is Increasing or Decreasing 2-up
- 5.4 Using the First Derivative Test to Determine Relative (Local) Extrema 2-up
- 5.5 Using the Candidates Test to Determine Absolute (Global) Extrema 2-up
- 5.6 Determining Concavity of Functions over Their Domains 2-up
- 5.7 Using the Second Derivative Test to Determine Extrema 2-up
- 5.8 Sketching Graphs of Functions and Their Derivatives 2-up
- 5.9 Connecting a Function, Its First Derivative, and Its Second Derivative 2-up
- 5.10 Introduction to Optimization Problems 2-up
- 5.11 Solving Optimization Problems 2-up
- 5.12 Exploring Behaviors of Implicit Relations 2-up
Past Paper Questions
- 5.1 Using the Mean Value Theorem 2-upAnswers2-up
- 5.2 Extreme Value Theorem, Global Versus Local Extrema, and Critical Points 2-upAnswers2-up
- 5.3 Determining Intervals on Which a Function Is Increasing or Decreasing 2-upAnswers2-up
- 5.4 Using the First Derivative Test to Determine Relative (Local) Extrema 2-upAnswers2-up
- 5.5 Using the Candidates Test to Determine Absolute (Global) Extrema 2-upAnswers2-up
- 5.6 Determining Concavity of Functions over Their Domains 2-upAnswers2-up
- 5.7 Using the Second Derivative Test to Determine Extrema 2-upAnswers2-up
- 5.9 Connecting a Function, Its First Derivative, and Its Second Derivative 2-upAnswers2-up
- 5.10 Introduction to Optimization Problems 2-upAnswers2-up
- 5.12 Exploring Behaviors of Implicit Relations 2-upAnswers2-up
6. Integration and Accumulation of Change 44 files
Presentation slides
Exercise walk-through slides
- 6.1 Exploring Accumulations of Change Past-paper walk-through
- 6.2 Approximating Areas with Riemann Sums Past-paper walk-through
- 6.3 Riemann Sums, Summation Notation, and Definite Integral Notation Past-paper walk-through
- 6.4 The Fundamental Theorem of Calculus and Accumulation Functions Past-paper walk-through
- 6.5 Interpreting the Behavior of Accumulation Functions Involving Area Past-paper walk-through
- 6.6 Applying Properties of Definite Integrals Past-paper walk-through
- 6.7 The Fundamental Theorem of Calculus and Definite Integrals Past-paper walk-through
- 6.8 Finding Antiderivatives and Indefinite Integrals: Basic Rules and Notation Past-paper walk-through
- 6.9 Integrating Using Substitution
- 6.10 Integrating Functions Using Long Division and Completing the Square
- 6.11 Integrating Using Integration by Parts Past-paper walk-through
- 6.12 Integrating Using Linear Partial Fractions Past-paper walk-through
- 6.13 Evaluating Improper Integrals Past-paper walk-through
- 6.14 Selecting Techniques for Antidifferentiation
Vocabulary
Topic Quizzes
Exercise sheets
- 6.1 Exploring Accumulations of Change 2-up
- 6.2 Approximating Areas with Riemann Sums 2-up
- 6.3 Riemann Sums, Summation Notation, and Definite Integral Notation 2-up
- 6.4 The Fundamental Theorem of Calculus and Accumulation Functions 2-up
- 6.5 Interpreting the Behavior of Accumulation Functions Involving Area 2-up
- 6.6 Applying Properties of Definite Integrals 2-up
- 6.7 The Fundamental Theorem of Calculus and Definite Integrals 2-up
- 6.8 Finding Antiderivatives and Indefinite Integrals: Basic Rules and Notation 2-up
- 6.9 Integrating Using Substitution 2-up
- 6.10 Integrating Functions Using Long Division and Completing the Square 2-up
- 6.11 Integrating Using Integration by Parts 2-up
- 6.12 Integrating Using Linear Partial Fractions 2-up
- 6.13 Evaluating Improper Integrals 2-up
- 6.14 Selecting Techniques for Antidifferentiation 2-up
Past Paper Questions
- 6.1 Exploring Accumulations of Change 2-upAnswers2-up
- 6.2 Approximating Areas with Riemann Sums 2-upAnswers2-up
- 6.3 Riemann Sums, Summation Notation, and Definite Integral Notation 2-up
- 6.4 The Fundamental Theorem of Calculus and Accumulation Functions 2-upAnswers2-up
- 6.5 Interpreting the Behavior of Accumulation Functions Involving Area 2-upAnswers2-up
- 6.6 Applying Properties of Definite Integrals 2-upAnswers2-up
- 6.7 The Fundamental Theorem of Calculus and Definite Integrals 2-upAnswers2-up
- 6.8 Finding Antiderivatives and Indefinite Integrals: Basic Rules and Notation 2-up
- 6.11 Integrating Using Integration by Parts 2-upAnswers2-up
- 6.12 Integrating Using Linear Partial Fractions 2-upAnswers2-up
- 6.13 Evaluating Improper Integrals 2-upAnswers2-up
7. Differential Equations 29 files
Handouts
Presentation slides
Exercise walk-through slides
- 7.1 Modeling Situations with Differential Equations
- 7.2 Verifying Solutions for Differential Equations Past-paper walk-through
- 7.3 Sketching Slope Fields Past-paper walk-through
- 7.4 Reasoning Using Slope Fields Past-paper walk-through
- 7.5 Approximating Solutions Using Euler's Method Past-paper walk-through
- 7.6 Finding General Solutions Using Separation of Variables Past-paper walk-through
- 7.7 Finding Particular Solutions Using Initial Conditions and Separation of Variables Past-paper walk-through
- 7.8 Exponential Models with Differential Equations
- 7.9 Logistic Models with Differential Equations
Vocabulary
Topic Quizzes
Exercise sheets
- 7.1 Modeling Situations with Differential Equations 2-up
- 7.2 Verifying Solutions for Differential Equations 2-up
- 7.3 Sketching Slope Fields 2-up
- 7.4 Reasoning Using Slope Fields 2-up
- 7.5 Approximating Solutions Using Euler's Method 2-up
- 7.6 Finding General Solutions Using Separation of Variables 2-up
- 7.7 Finding Particular Solutions Using Initial Conditions and Separation of Variables 2-up
- 7.8 Exponential Models with Differential Equations 2-up
- 7.9 Logistic Models with Differential Equations 2-up
Past Paper Questions
- 7.2 Verifying Solutions for Differential Equations 2-upAnswers2-up
- 7.3 Sketching Slope Fields 2-upAnswers2-up
- 7.4 Reasoning Using Slope Fields 2-upAnswers2-up
- 7.5 Approximating Solutions Using Euler's Method 2-upAnswers2-up
- 7.6 Finding General Solutions Using Separation of Variables 2-upAnswers2-up
- 7.7 Finding Particular Solutions Using Initial Conditions and Separation of Variables 2-upAnswers2-up
Unit Tests
8. Applications of Integration 40 files
Handouts
Presentation slides
Exercise walk-through slides
- 8.1 Finding the Average Value of a Function on an Interval Past-paper walk-through
- 8.2 Connecting Position, Velocity, and Acceleration of Functions Using Integrals Past-paper walk-through
- 8.3 Using Accumulation Functions and Definite Integrals in Applied Contexts Past-paper walk-through
- 8.4 Finding the Area Between Curves Expressed as Functions of x Past-paper walk-through
- 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: Squares and Rectangles Past-paper walk-through
- 8.8 Volumes with Cross Sections: Triangles and Semicircles
- 8.9 Volume with Disc Method: Revolving Around the x- or y-Axis Past-paper walk-through
- 8.10 Volume with Disc Method: Revolving Around Other Axes
- 8.11 Volume with Washer Method: Revolving Around the x- or y-Axis Past-paper walk-through
- 8.12 Volume with Washer Method: Revolving Around Other Axes Past-paper walk-through
- 8.13 The Arc Length of a Smooth, Planar Curve and Distance Traveled Past-paper walk-through
Vocabulary
Topic Quizzes
Exercise sheets
- 8.1 Finding the Average Value of a Function on an Interval 2-up
- 8.2 Connecting Position, Velocity, and Acceleration of Functions Using Integrals 2-up
- 8.3 Using Accumulation Functions and Definite Integrals in Applied Contexts 2-up
- 8.4 Finding the Area Between Curves Expressed as Functions of x 2-up
- 8.5 Finding the Area Between Curves Expressed as Functions of y 2-up
- 8.6 Finding the Area Between Curves That Intersect at More Than Two Points 2-up
- 8.7 Volumes with Cross Sections: Squares and Rectangles 2-up
- 8.8 Volumes with Cross Sections: Triangles and Semicircles 2-up
- 8.9 Volume with Disc Method: Revolving Around the x- or y-Axis 2-up
- 8.10 Volume with Disc Method: Revolving Around Other Axes 2-up
- 8.11 Volume with Washer Method: Revolving Around the x- or y-Axis 2-up
- 8.12 Volume with Washer Method: Revolving Around Other Axes 2-up
- 8.13 The Arc Length of a Smooth, Planar Curve and Distance Traveled 2-up
Past Paper Questions
- 8.1 Finding the Average Value of a Function on an Interval 2-upAnswers2-up
- 8.2 Connecting Position, Velocity, and Acceleration of Functions Using Integrals 2-upAnswers2-up
- 8.3 Using Accumulation Functions and Definite Integrals in Applied Contexts 2-upAnswers2-up
- 8.4 Finding the Area Between Curves Expressed as Functions of x 2-upAnswers2-up
- 8.7 Volumes with Cross Sections: Squares and Rectangles 2-upAnswers2-up
- 8.9 Volume with Disc Method: Revolving Around the x- or y-Axis 2-upAnswers2-up
- 8.11 Volume with Washer Method: Revolving Around the x- or y-Axis 2-up
- 8.12 Volume with Washer Method: Revolving Around Other Axes 2-up
- 8.13 The Arc Length of a Smooth, Planar Curve and Distance Traveled 2-upAnswers2-up
Unit Tests
9. Parametric Equations, Polar Coordinates, and Vector-Valued Functions 31 files
Presentation slides
Exercise walk-through slides
- 9.1 Defining and Differentiating Parametric Equations Past-paper walk-through
- 9.2 Second Derivatives of Parametric Equations
- 9.3 Finding Arc Lengths of Curves Given by Parametric Equations Past-paper walk-through
- 9.4 Defining and Differentiating Vector-Valued Functions Past-paper walk-through
- 9.5 Integrating Vector-Valued Functions Past-paper walk-through
- 9.6 Solving Motion Problems Using Parametric and Vector-Valued Functions Past-paper walk-through
- 9.7 Defining Polar Coordinates and Differentiating in Polar Form Past-paper walk-through
- 9.8 Find the Area of a Polar Region or the Area Bounded by a Single Polar Curve Past-paper walk-through
- 9.9 Finding the Area of the Region Bounded by Two Polar Curves Past-paper walk-through
Exercise sheets
- 9.1 Defining and Differentiating Parametric Equations 2-up
- 9.2 Second Derivatives of Parametric Equations 2-up
- 9.3 Finding Arc Lengths of Curves Given by Parametric Equations 2-up
- 9.4 Defining and Differentiating Vector-Valued Functions 2-up
- 9.5 Integrating Vector-Valued Functions 2-up
- 9.6 Solving Motion Problems Using Parametric and Vector-Valued Functions 2-up
- 9.7 Defining Polar Coordinates and Differentiating in Polar Form 2-up
- 9.8 Find the Area of a Polar Region or the Area Bounded by a Single Polar Curve 2-up
- 9.9 Finding the Area of the Region Bounded by Two Polar Curves 2-up
Past Paper Questions
- 9.1 Defining and Differentiating Parametric Equations 2-upAnswers2-up
- 9.3 Finding Arc Lengths of Curves Given by Parametric Equations 2-upAnswers2-up
- 9.4 Defining and Differentiating Vector-Valued Functions 2-upAnswers2-up
- 9.5 Integrating Vector-Valued Functions 2-upAnswers2-up
- 9.6 Solving Motion Problems Using Parametric and Vector-Valued Functions 2-upAnswers2-up
- 9.7 Defining Polar Coordinates and Differentiating in Polar Form 2-upAnswers2-up
- 9.8 Find the Area of a Polar Region or the Area Bounded by a Single Polar Curve 2-upAnswers2-up
- 9.9 Finding the Area of the Region Bounded by Two Polar Curves 2-upAnswers2-up
10. Infinite Sequences and Series 47 files
Handouts
Presentation slides
Exercise walk-through slides
- 10.1 Defining Convergent and Divergent Infinite Series
- 10.2 Working with Geometric Series Past-paper walk-through
- 10.3 The nth Term Test for Divergence
- 10.4 Integral Test for Convergence Past-paper walk-through
- 10.5 Harmonic Series and p-Series
- 10.6 Comparison Tests for Convergence Past-paper walk-through
- 10.7 Alternating Series Test for Convergence Past-paper walk-through
- 10.8 Ratio Test for Convergence Past-paper walk-through
- 10.9 Determining Absolute or Conditional Convergence Past-paper walk-through
- 10.10 Alternating Series Error Bound Past-paper walk-through
- 10.11 Finding Taylor Polynomial Approximations of Functions Past-paper walk-through
- 10.12 Lagrange Error Bound Past-paper walk-through
- 10.13 Radius and Interval of Convergence of Power Series Past-paper walk-through
- 10.14 Finding Taylor or Maclaurin Series for a Function Past-paper walk-through
- 10.15 Representing Functions as Power Series Past-paper walk-through
Vocabulary
Topic Quizzes
Exercise sheets
- 10.1 Defining Convergent and Divergent Infinite Series 2-up
- 10.2 Working with Geometric Series 2-up
- 10.3 The nth Term Test for Divergence 2-up
- 10.4 Integral Test for Convergence 2-up
- 10.5 Harmonic Series and p-Series 2-up
- 10.6 Comparison Tests for Convergence 2-up
- 10.7 Alternating Series Test for Convergence 2-up
- 10.8 Ratio Test for Convergence 2-up
- 10.9 Determining Absolute or Conditional Convergence 2-up
- 10.10 Alternating Series Error Bound 2-up
- 10.11 Finding Taylor Polynomial Approximations of Functions 2-up
- 10.12 Lagrange Error Bound 2-up
- 10.13 Radius and Interval of Convergence of Power Series 2-up
- 10.14 Finding Taylor or Maclaurin Series for a Function 2-up
- 10.15 Representing Functions as Power Series 2-up
Past Paper Questions
- 10.2 Working with Geometric Series 2-upAnswers2-up
- 10.4 Integral Test for Convergence 2-upAnswers2-up
- 10.6 Comparison Tests for Convergence 2-upAnswers2-up
- 10.7 Alternating Series Test for Convergence 2-upAnswers2-up
- 10.8 Ratio Test for Convergence 2-upAnswers2-up
- 10.9 Determining Absolute or Conditional Convergence 2-upAnswers2-up
- 10.10 Alternating Series Error Bound 2-upAnswers2-up
- 10.11 Finding Taylor Polynomial Approximations of Functions 2-upAnswers2-up
- 10.12 Lagrange Error Bound 2-upAnswers2-up
- 10.13 Radius and Interval of Convergence of Power Series 2-upAnswers2-up
- 10.14 Finding Taylor or Maclaurin Series for a Function 2-upAnswers2-up
- 10.15 Representing Functions as Power Series 2-upAnswers2-up
Unit Tests
- AP Calculus BC — Question index 2-up
- 1.15 Connecting Limits at Infinity and Horizontal Asymptotes 2-upAnswers2-up
- 1.16 Working with the Intermediate Value Theorem (IVT) 2-upAnswers2-up
- 2.1 Defining Average and Instantaneous Rates of Change at a Point 2-upAnswers2-up
- 2.3 Estimating Derivatives of a Function at a Point 2-upAnswers2-up
- 2.4 Connecting Differentiability and Continuity: Determining When Derivatives Do and Do Not Exist 2-upAnswers2-up
- 2.6 Derivative Rules: Constant, Sum, Difference, and Constant Multiple 2-up
- 2.7 Derivatives of cos x, sin x, e^x, and ln x 2-up
- 2.8 The Product Rule 2-upAnswers2-up
- 2.9 The Quotient Rule 2-upAnswers2-up
- 3.1 The Chain Rule 2-upAnswers2-up
- 3.2 Implicit Differentiation 2-upAnswers2-up
- 3.6 Calculating Higher-Order Derivatives 2-upAnswers2-up
- 4.1 Interpreting the Meaning of the Derivative in Context 2-upAnswers2-up
- 4.2 Straight-Line Motion: Connecting Position, Velocity, and Acceleration 2-upAnswers2-up
- 4.4 Introduction to Related Rates 2-upAnswers2-up
- 4.5 Solving Related Rates Problems 2-upAnswers2-up
- 4.6 Approximating Values of a Function Using Local Linearity and Linearization 2-upAnswers2-up
- 4.7 Using L'Hospital's Rule for Determining Limits of Indeterminate Forms 2-upAnswers2-up
- 5.1 Using the Mean Value Theorem 2-upAnswers2-up
- 5.2 Extreme Value Theorem, Global Versus Local Extrema, and Critical Points 2-upAnswers2-up
- 5.3 Determining Intervals on Which a Function Is Increasing or Decreasing 2-upAnswers2-up
- 5.4 Using the First Derivative Test to Determine Relative (Local) Extrema 2-upAnswers2-up
- 5.5 Using the Candidates Test to Determine Absolute (Global) Extrema 2-upAnswers2-up
- 5.6 Determining Concavity of Functions over Their Domains 2-upAnswers2-up
- 5.7 Using the Second Derivative Test to Determine Extrema 2-upAnswers2-up
- 5.9 Connecting a Function, Its First Derivative, and Its Second Derivative 2-upAnswers2-up
- 5.10 Introduction to Optimization Problems 2-upAnswers2-up
- 5.12 Exploring Behaviors of Implicit Relations 2-upAnswers2-up
- 6.1 Exploring Accumulations of Change 2-upAnswers2-up
- 6.2 Approximating Areas with Riemann Sums 2-upAnswers2-up
- 6.3 Riemann Sums, Summation Notation, and Definite Integral Notation 2-up
- 6.4 The Fundamental Theorem of Calculus and Accumulation Functions 2-upAnswers2-up
- 6.5 Interpreting the Behavior of Accumulation Functions Involving Area 2-upAnswers2-up
- 6.6 Applying Properties of Definite Integrals 2-upAnswers2-up
- 6.7 The Fundamental Theorem of Calculus and Definite Integrals 2-upAnswers2-up
- 6.8 Finding Antiderivatives and Indefinite Integrals: Basic Rules and Notation 2-up
- 6.11 Integrating Using Integration by Parts 2-upAnswers2-up
- 6.12 Integrating Using Linear Partial Fractions 2-upAnswers2-up
- 6.13 Evaluating Improper Integrals 2-upAnswers2-up
- 7.2 Verifying Solutions for Differential Equations 2-upAnswers2-up
- 7.3 Sketching Slope Fields 2-upAnswers2-up
- 7.4 Reasoning Using Slope Fields 2-upAnswers2-up
- 7.5 Approximating Solutions Using Euler's Method 2-upAnswers2-up
- 7.6 Finding General Solutions Using Separation of Variables 2-upAnswers2-up
- 7.7 Finding Particular Solutions Using Initial Conditions and Separation of Variables 2-upAnswers2-up
- 8.1 Finding the Average Value of a Function on an Interval 2-upAnswers2-up
- 8.2 Connecting Position, Velocity, and Acceleration of Functions Using Integrals 2-upAnswers2-up
- 8.3 Using Accumulation Functions and Definite Integrals in Applied Contexts 2-upAnswers2-up
- 8.4 Finding the Area Between Curves Expressed as Functions of x 2-upAnswers2-up
- 8.7 Volumes with Cross Sections: Squares and Rectangles 2-upAnswers2-up
- 8.9 Volume with Disc Method: Revolving Around the x- or y-Axis 2-upAnswers2-up
- 8.11 Volume with Washer Method: Revolving Around the x- or y-Axis 2-up
- 8.12 Volume with Washer Method: Revolving Around Other Axes 2-up
- 8.13 The Arc Length of a Smooth, Planar Curve and Distance Traveled 2-upAnswers2-up
- 9.1 Defining and Differentiating Parametric Equations 2-upAnswers2-up
- 9.3 Finding Arc Lengths of Curves Given by Parametric Equations 2-upAnswers2-up
- 9.4 Defining and Differentiating Vector-Valued Functions 2-upAnswers2-up
- 9.5 Integrating Vector-Valued Functions 2-upAnswers2-up
- 9.6 Solving Motion Problems Using Parametric and Vector-Valued Functions 2-upAnswers2-up
- 9.7 Defining Polar Coordinates and Differentiating in Polar Form 2-upAnswers2-up
- 9.8 Find the Area of a Polar Region or the Area Bounded by a Single Polar Curve 2-upAnswers2-up
- 9.9 Finding the Area of the Region Bounded by Two Polar Curves 2-upAnswers2-up
- 10.2 Working with Geometric Series 2-upAnswers2-up
- 10.4 Integral Test for Convergence 2-upAnswers2-up
- 10.6 Comparison Tests for Convergence 2-upAnswers2-up
- 10.7 Alternating Series Test for Convergence 2-upAnswers2-up
- 10.8 Ratio Test for Convergence 2-upAnswers2-up
- 10.9 Determining Absolute or Conditional Convergence 2-upAnswers2-up
- 10.10 Alternating Series Error Bound 2-upAnswers2-up
- 10.11 Finding Taylor Polynomial Approximations of Functions 2-upAnswers2-up
- 10.12 Lagrange Error Bound 2-upAnswers2-up
- 10.13 Radius and Interval of Convergence of Power Series 2-upAnswers2-up
- 10.14 Finding Taylor or Maclaurin Series for a Function 2-upAnswers2-up
- 10.15 Representing Functions as Power Series 2-upAnswers2-up
Topic quizzes
- 1. Limits and Continuity 2-up
- 2. Differentiation: Definition and Fundamental Properties 2-up
- 3. Differentiation: Composite, Implicit, and Inverse Functions 2-up
- 4. Contextual Applications of Differentiation 2-up
- 5. Analytical Applications of Differentiation 2-up
- 6. Integration and Accumulation of Change 2-up
- 7. Differential Equations 2-up
- 8. Applications of Integration 2-up
- 9. Parametric Equations, Polar Coordinates, and Vector-Valued Functions 2-up
- 10. Infinite Sequences and Series 2-up
Unit tests
- 1. Limits and Continuity 2-upAnswers2-up
- 2. Differentiation: Definition and Fundamental Properties 2-upAnswers2-up
- 3. Differentiation: Composite, Implicit, and Inverse Functions 2-upAnswers2-up
- 4. Contextual Applications of Differentiation 2-upAnswers2-up
- 5. Analytical Applications of Differentiation 2-upAnswers2-up
- 6. Integration and Accumulation of Change 2-upAnswers2-up
- 7. Differential Equations 2-upAnswers2-up
- 8. Applications of Integration 2-upAnswers2-up
- 9. Parametric Equations, Polar Coordinates, and Vector-Valued Functions 2-upAnswers2-up
- 10. Infinite Sequences and Series 2-upAnswers2-up
Mock papers
Course companion
Glossary
Topic handouts
- 1. Limits and Continuity 2-up
- 2. Differentiation: Definition and Fundamental Properties 2-up
- 3. Differentiation: Composite, Implicit, and Inverse Functions 2-up
- 4. Contextual Applications of Differentiation 2-up
- 5. Analytical Applications of Differentiation 2-up
- 6. Integration and Accumulation of Change 2-up
- 7. Differential Equations 2-up
- 8. Applications of Integration 2-up
- 9. Parametric Equations, Polar Coordinates, and Vector-Valued Functions 2-up
- 10. Infinite Sequences and Series 2-up
- 1.1 Introducing Calculus: Can Change Occur at an Instant? 2-up
- 1.2 Defining Limits and Using Limit Notation 2-up
- 1.3 Estimating Limit Values from Graphs 2-up
- 1.4 Estimating Limit Values from Tables 2-up
- 1.5 Determining Limits Using Algebraic Properties of Limits 2-up
- 1.6 Determining Limits Using Algebraic Manipulation 2-up
- 1.7 Selecting Procedures for Determining Limits 2-up
- 1.8 Determining Limits Using the Squeeze Theorem 2-up
- 1.9 Connecting Multiple Representations of Limits 2-up
- 1.10 Exploring Types of Discontinuities 2-up
- 1.11 Defining Continuity at a Point 2-up
- 1.12 Confirming Continuity over an Interval 2-up
- 1.13 Removing Discontinuities 2-up
- 1.14 Connecting Infinite Limits and Vertical Asymptotes 2-up
- 1.15 Connecting Limits at Infinity and Horizontal Asymptotes 2-up
- 1.16 Working with the Intermediate Value Theorem (IVT) 2-up
- 2.1 Defining Average and Instantaneous Rates of Change at a Point 2-up
- 2.2 Defining the Derivative of a Function and Using Derivative Notation 2-up
- 2.3 Estimating Derivatives of a Function at a Point 2-up
- 2.4 Connecting Differentiability and Continuity: Determining When Derivatives Do and Do Not Exist 2-up
- 2.5 Applying the Power Rule 2-up
- 2.6 Derivative Rules: Constant, Sum, Difference, and Constant Multiple 2-up
- 2.7 Derivatives of cos x, sin x, e^x, and ln x 2-up
- 2.8 The Product Rule 2-up
- 2.9 The Quotient Rule 2-up
- 2.10 Finding the Derivatives of Tangent, Cotangent, Secant, and/or Cosecant Functions 2-up
- 3.1 The Chain Rule 2-up
- 3.2 Implicit Differentiation 2-up
- 3.3 Differentiating Inverse Functions 2-up
- 3.4 Differentiating Inverse Trigonometric Functions 2-up
- 3.5 Selecting Procedures for Calculating Derivatives 2-up
- 3.6 Calculating Higher-Order Derivatives 2-up
- 4.1 Interpreting the Meaning of the Derivative in Context 2-up
- 4.2 Straight-Line Motion: Connecting Position, Velocity, and Acceleration 2-up
- 4.3 Rates of Change in Applied Contexts Other Than Motion 2-up
- 4.4 Introduction to Related Rates 2-up
- 4.5 Solving Related Rates Problems 2-up
- 4.6 Approximating Values of a Function Using Local Linearity and Linearization 2-up
- 4.7 Using L'Hospital's Rule for Determining Limits of Indeterminate Forms 2-up
- 5.1 Using the Mean Value Theorem 2-up
- 5.2 Extreme Value Theorem, Global Versus Local Extrema, and Critical Points 2-up
- 5.3 Determining Intervals on Which a Function Is Increasing or Decreasing 2-up
- 5.4 Using the First Derivative Test to Determine Relative (Local) Extrema 2-up
- 5.5 Using the Candidates Test to Determine Absolute (Global) Extrema 2-up
- 5.6 Determining Concavity of Functions over Their Domains 2-up
- 5.7 Using the Second Derivative Test to Determine Extrema 2-up
- 5.8 Sketching Graphs of Functions and Their Derivatives 2-up
- 5.9 Connecting a Function, Its First Derivative, and Its Second Derivative 2-up
- 5.10 Introduction to Optimization Problems 2-up
- 5.11 Solving Optimization Problems 2-up
- 5.12 Exploring Behaviors of Implicit Relations 2-up
- 6.1 Exploring Accumulations of Change 2-up
- 6.2 Approximating Areas with Riemann Sums 2-up
- 6.3 Riemann Sums, Summation Notation, and Definite Integral Notation 2-up
- 6.4 The Fundamental Theorem of Calculus and Accumulation Functions 2-up
- 6.5 Interpreting the Behavior of Accumulation Functions Involving Area 2-up
- 6.6 Applying Properties of Definite Integrals 2-up
- 6.7 The Fundamental Theorem of Calculus and Definite Integrals 2-up
- 6.8 Finding Antiderivatives and Indefinite Integrals: Basic Rules and Notation 2-up
- 6.9 Integrating Using Substitution 2-up
- 6.10 Integrating Functions Using Long Division and Completing the Square 2-up
- 6.11 Integrating Using Integration by Parts 2-up
- 6.12 Integrating Using Linear Partial Fractions 2-up
- 6.13 Evaluating Improper Integrals 2-up
- 6.14 Selecting Techniques for Antidifferentiation 2-up
- 7.1 Modeling Situations with Differential Equations 2-up
- 7.2 Verifying Solutions for Differential Equations 2-up
- 7.3 Sketching Slope Fields 2-up
- 7.4 Reasoning Using Slope Fields 2-up
- 7.5 Approximating Solutions Using Euler's Method 2-up
- 7.6 Finding General Solutions Using Separation of Variables 2-up
- 7.7 Finding Particular Solutions Using Initial Conditions and Separation of Variables 2-up
- 7.8 Exponential Models with Differential Equations 2-up
- 7.9 Logistic Models with Differential Equations 2-up
- 8.1 Finding the Average Value of a Function on an Interval 2-up
- 8.2 Connecting Position, Velocity, and Acceleration of Functions Using Integrals 2-up
- 8.3 Using Accumulation Functions and Definite Integrals in Applied Contexts 2-up
- 8.4 Finding the Area Between Curves Expressed as Functions of x 2-up
- 8.5 Finding the Area Between Curves Expressed as Functions of y 2-up
- 8.6 Finding the Area Between Curves That Intersect at More Than Two Points 2-up
- 8.7 Volumes with Cross Sections: Squares and Rectangles 2-up
- 8.8 Volumes with Cross Sections: Triangles and Semicircles 2-up
- 8.9 Volume with Disc Method: Revolving Around the x- or y-Axis 2-up
- 8.10 Volume with Disc Method: Revolving Around Other Axes 2-up
- 8.11 Volume with Washer Method: Revolving Around the x- or y-Axis 2-up
- 8.12 Volume with Washer Method: Revolving Around Other Axes 2-up
- 8.13 The Arc Length of a Smooth, Planar Curve and Distance Traveled 2-up
- 9.1 Defining and Differentiating Parametric Equations 2-up
- 9.2 Second Derivatives of Parametric Equations 2-up
- 9.3 Finding Arc Lengths of Curves Given by Parametric Equations 2-up
- 9.4 Defining and Differentiating Vector-Valued Functions 2-up
- 9.5 Integrating Vector-Valued Functions 2-up
- 9.6 Solving Motion Problems Using Parametric and Vector-Valued Functions 2-up
- 9.7 Defining Polar Coordinates and Differentiating in Polar Form 2-up
- 9.8 Find the Area of a Polar Region or the Area Bounded by a Single Polar Curve 2-up
- 9.9 Finding the Area of the Region Bounded by Two Polar Curves 2-up
- 10.1 Defining Convergent and Divergent Infinite Series 2-up
- 10.2 Working with Geometric Series 2-up
- 10.3 The nth Term Test for Divergence 2-up
- 10.4 Integral Test for Convergence 2-up
- 10.5 Harmonic Series and p-Series 2-up
- 10.6 Comparison Tests for Convergence 2-up
- 10.7 Alternating Series Test for Convergence 2-up
- 10.8 Ratio Test for Convergence 2-up
- 10.9 Determining Absolute or Conditional Convergence 2-up
- 10.10 Alternating Series Error Bound 2-up
- 10.11 Finding Taylor Polynomial Approximations of Functions 2-up
- 10.12 Lagrange Error Bound 2-up
- 10.13 Radius and Interval of Convergence of Power Series 2-up
- 10.14 Finding Taylor or Maclaurin Series for a Function 2-up
- 10.15 Representing Functions as Power Series 2-up
Lesson slides
- 1. Limits and Continuity
- 2. Differentiation: Definition and Fundamental Properties
- 3. Differentiation: Composite, Implicit, and Inverse Functions
- 4. Contextual Applications of Differentiation
- 5. Analytical Applications of Differentiation
- 6. Integration and Accumulation of Change
- 7. Differential Equations
- 8. Applications of Integration
- 9. Parametric Equations, Polar Coordinates, and Vector-Valued Functions
- 10. Infinite Sequences and Series
Lesson slides
- 1.1 Introducing Calculus: Can Change Occur at an Instant?
- 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
- 1.7 Selecting Procedures for Determining Limits
- 1.8 Determining Limits Using the Squeeze Theorem
- 1.9 Connecting Multiple Representations of Limits
- 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 Past-paper walk-through
- 1.16 Working with the Intermediate Value Theorem (IVT) Past-paper walk-through
- 2.1 Defining Average and Instantaneous Rates of Change at a Point Past-paper walk-through
- 2.2 Defining the Derivative of a Function and Using Derivative Notation
- 2.3 Estimating Derivatives of a Function at a Point Past-paper walk-through
- 2.4 Connecting Differentiability and Continuity: Determining When Derivatives Do and Do Not Exist Past-paper walk-through
- 2.5 Applying the Power Rule
- 2.6 Derivative Rules: Constant, Sum, Difference, and Constant Multiple Past-paper walk-through
- 2.7 Derivatives of cos x, sin x, e^x, and ln x Past-paper walk-through
- 2.8 The Product Rule Past-paper walk-through
- 2.9 The Quotient Rule Past-paper walk-through
- 2.10 Finding the Derivatives of Tangent, Cotangent, Secant, and/or Cosecant Functions
- 3.1 The Chain Rule Past-paper walk-through
- 3.2 Implicit Differentiation Past-paper walk-through
- 3.3 Differentiating Inverse Functions
- 3.4 Differentiating Inverse Trigonometric Functions
- 3.5 Selecting Procedures for Calculating Derivatives
- 3.6 Calculating Higher-Order Derivatives Past-paper walk-through
- 4.1 Interpreting the Meaning of the Derivative in Context Past-paper walk-through
- 4.2 Straight-Line Motion: Connecting Position, Velocity, and Acceleration Past-paper walk-through
- 4.3 Rates of Change in Applied Contexts Other Than Motion
- 4.4 Introduction to Related Rates Past-paper walk-through
- 4.5 Solving Related Rates Problems Past-paper walk-through
- 4.6 Approximating Values of a Function Using Local Linearity and Linearization Past-paper walk-through
- 4.7 Using L'Hospital's Rule for Determining Limits of Indeterminate Forms Past-paper walk-through
- 5.1 Using the Mean Value Theorem Past-paper walk-through
- 5.2 Extreme Value Theorem, Global Versus Local Extrema, and Critical Points Past-paper walk-through
- 5.3 Determining Intervals on Which a Function Is Increasing or Decreasing Past-paper walk-through
- 5.4 Using the First Derivative Test to Determine Relative (Local) Extrema Past-paper walk-through
- 5.5 Using the Candidates Test to Determine Absolute (Global) Extrema Past-paper walk-through
- 5.6 Determining Concavity of Functions over Their Domains Past-paper walk-through
- 5.7 Using the Second Derivative Test to Determine Extrema Past-paper walk-through
- 5.8 Sketching Graphs of Functions and Their Derivatives
- 5.9 Connecting a Function, Its First Derivative, and Its Second Derivative Past-paper walk-through
- 5.10 Introduction to Optimization Problems Past-paper walk-through
- 5.11 Solving Optimization Problems
- 5.12 Exploring Behaviors of Implicit Relations Past-paper walk-through
- 6.1 Exploring Accumulations of Change Past-paper walk-through
- 6.2 Approximating Areas with Riemann Sums Past-paper walk-through
- 6.3 Riemann Sums, Summation Notation, and Definite Integral Notation Past-paper walk-through
- 6.4 The Fundamental Theorem of Calculus and Accumulation Functions Past-paper walk-through
- 6.5 Interpreting the Behavior of Accumulation Functions Involving Area Past-paper walk-through
- 6.6 Applying Properties of Definite Integrals Past-paper walk-through
- 6.7 The Fundamental Theorem of Calculus and Definite Integrals Past-paper walk-through
- 6.8 Finding Antiderivatives and Indefinite Integrals: Basic Rules and Notation Past-paper walk-through
- 6.9 Integrating Using Substitution
- 6.10 Integrating Functions Using Long Division and Completing the Square
- 6.11 Integrating Using Integration by Parts Past-paper walk-through
- 6.12 Integrating Using Linear Partial Fractions Past-paper walk-through
- 6.13 Evaluating Improper Integrals Past-paper walk-through
- 6.14 Selecting Techniques for Antidifferentiation
- 7.1 Modeling Situations with Differential Equations
- 7.2 Verifying Solutions for Differential Equations Past-paper walk-through
- 7.3 Sketching Slope Fields Past-paper walk-through
- 7.4 Reasoning Using Slope Fields Past-paper walk-through
- 7.5 Approximating Solutions Using Euler's Method Past-paper walk-through
- 7.6 Finding General Solutions Using Separation of Variables Past-paper walk-through
- 7.7 Finding Particular Solutions Using Initial Conditions and Separation of Variables Past-paper walk-through
- 7.8 Exponential Models with Differential Equations
- 7.9 Logistic Models with Differential Equations
- 8.1 Finding the Average Value of a Function on an Interval Past-paper walk-through
- 8.2 Connecting Position, Velocity, and Acceleration of Functions Using Integrals Past-paper walk-through
- 8.3 Using Accumulation Functions and Definite Integrals in Applied Contexts Past-paper walk-through
- 8.4 Finding the Area Between Curves Expressed as Functions of x Past-paper walk-through
- 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: Squares and Rectangles Past-paper walk-through
- 8.8 Volumes with Cross Sections: Triangles and Semicircles
- 8.9 Volume with Disc Method: Revolving Around the x- or y-Axis Past-paper walk-through
- 8.10 Volume with Disc Method: Revolving Around Other Axes
- 8.11 Volume with Washer Method: Revolving Around the x- or y-Axis Past-paper walk-through
- 8.12 Volume with Washer Method: Revolving Around Other Axes Past-paper walk-through
- 8.13 The Arc Length of a Smooth, Planar Curve and Distance Traveled Past-paper walk-through
- 9.1 Defining and Differentiating Parametric Equations Past-paper walk-through
- 9.2 Second Derivatives of Parametric Equations
- 9.3 Finding Arc Lengths of Curves Given by Parametric Equations Past-paper walk-through
- 9.4 Defining and Differentiating Vector-Valued Functions Past-paper walk-through
- 9.5 Integrating Vector-Valued Functions Past-paper walk-through
- 9.6 Solving Motion Problems Using Parametric and Vector-Valued Functions Past-paper walk-through
- 9.7 Defining Polar Coordinates and Differentiating in Polar Form Past-paper walk-through
- 9.8 Find the Area of a Polar Region or the Area Bounded by a Single Polar Curve Past-paper walk-through
- 9.9 Finding the Area of the Region Bounded by Two Polar Curves Past-paper walk-through
- 10.1 Defining Convergent and Divergent Infinite Series
- 10.2 Working with Geometric Series Past-paper walk-through
- 10.3 The nth Term Test for Divergence
- 10.4 Integral Test for Convergence Past-paper walk-through
- 10.5 Harmonic Series and p-Series
- 10.6 Comparison Tests for Convergence Past-paper walk-through
- 10.7 Alternating Series Test for Convergence Past-paper walk-through
- 10.8 Ratio Test for Convergence Past-paper walk-through
- 10.9 Determining Absolute or Conditional Convergence Past-paper walk-through
- 10.10 Alternating Series Error Bound Past-paper walk-through
- 10.11 Finding Taylor Polynomial Approximations of Functions Past-paper walk-through
- 10.12 Lagrange Error Bound Past-paper walk-through
- 10.13 Radius and Interval of Convergence of Power Series Past-paper walk-through
- 10.14 Finding Taylor or Maclaurin Series for a Function Past-paper walk-through
- 10.15 Representing Functions as Power Series Past-paper walk-through
Vocabulary lists
- 1. Limits and Continuity 2-up
- 2. Differentiation: Definition and Fundamental Properties 2-up
- 3. Differentiation: Composite, Implicit, and Inverse Functions
- 4. Contextual Applications of Differentiation
- 5. Analytical Applications of Differentiation
- 6. Integration and Accumulation of Change 2-up
- 7. Differential Equations
- 8. Applications of Integration
- 9. Parametric Equations, Polar Coordinates, and Vector-Valued Functions
- 10. Infinite Sequences and Series 2-up
Flashcards
Weekly vocab tests
- Week 1 · Topic 1 · Limits and Continuity 2-upAnswer key
- Week 2 · Topic 1 · Limits and Continuity 2-upAnswer key
- Week 3 · Topics 1–2 · Limits and Continuity, Differentiation: Definition and Fundamental Properties 2-upAnswer key
- Week 4 · Topics 2–4 · Differentiation: Definition and Fundamental Properties, Differentiation: Composite, Implicit, and Inverse Functions, Contextual Applications of Differentiation 2-upAnswer key
- Week 5 · Topics 4–6 · Contextual Applications of Differentiation, Analytical Applications of Differentiation, Integration and Accumulation of Change 2-upAnswer key
- Week 6 · Topics 6–8 · Integration and Accumulation of Change, Differential Equations, Applications of Integration 2-upAnswer key
- Week 7 · Topics 8–10 · Applications of Integration, Parametric Equations, Polar Coordinates, and Vector-Valued Functions, Infinite Sequences and Series 2-upAnswer key
Weekly homework
- Week 1 2-up
- Week 2 2-up
- Week 4 2-up
- Week 5 2-up
- Week 8 2-up
- Week 10
- Week 12 2-up
- Week 15
- Week 17 2-up
- Week 18
- Week 19 2-up
- Week 21
- Week 22 2-up
- Week 24
- Week 26 2-up
- Week 27
Exercise sheets
- Complete pack — exercise sheets + past papers 2-up
- 1 Limits and Continuity — Part 1 2-upAnswer key
- 1 Limits and Continuity — Part 2 2-upAnswer key
- 2 Differentiation: Definition and Fundamental Properties — Part 1 2-upAnswer key
- 2 Differentiation: Definition and Fundamental Properties — Part 2 2-upAnswer key
- 3 Differentiation: Composite, Implicit, and Inverse Functions — Part 1 2-upAnswer key
- 3 Differentiation: Composite, Implicit, and Inverse Functions — Part 2 2-upAnswer key
- 4 Contextual Applications of Differentiation — Part 1 2-upAnswer key
- 4 Contextual Applications of Differentiation — Part 2 2-upAnswer key
- 5 Analytical Applications of Differentiation — Part 1 2-upAnswer key
- 5 Analytical Applications of Differentiation — Part 2 2-upAnswer key
- 6 Integration and Accumulation of Change — Part 1 2-upAnswer key
- 6 Integration and Accumulation of Change — Part 2 2-upAnswer key
- 7 Differential Equations — Part 1 2-upAnswer key
- 7 Differential Equations — Part 2 2-upAnswer key
- 8 Applications of Integration — Part 1 2-upAnswer key
- 8 Applications of Integration — Part 2 2-upAnswer key
- 9 Parametric Equations, Polar Coordinates, and Vector-Valued Functions — Part 1 2-upAnswer key
- 9 Parametric Equations, Polar Coordinates, and Vector-Valued Functions — Part 2 2-upAnswer key
- 10 Infinite Sequences and Series — Part 1 2-upAnswer key
- 10 Infinite Sequences and Series — Part 2 2-upAnswer key
Past papers
- 1.15 Connecting Limits at Infinity and Horizontal Asymptotes Answers2-up
- 1.16 Working with the Intermediate Value Theorem (IVT) Answers2-up
- 2.1 Defining Average and Instantaneous Rates of Change at a Point Answers2-up
- 2.3 Estimating Derivatives of a Function at a Point Answers2-up
- 2.4 Connecting Differentiability and Continuity: Determining When Derivatives Do and Do Not Exist Answers
- 2.6 Derivative Rules: Constant, Sum, Difference, and Constant Multiple
- 2.7 Derivatives of cos x, sin x, e^x, and ln x
- 2.8 The Product Rule Answers2-up
- 2.9 The Quotient Rule Answers
- 3.1 The Chain Rule Answers2-up
- 3.2 Implicit Differentiation Answers2-up
- 3.6 Calculating Higher-Order Derivatives Answers2-up
- 4.1 Interpreting the Meaning of the Derivative in Context Answers
- 4.2 Straight-Line Motion: Connecting Position, Velocity, and Acceleration Answers
- 4.4 Introduction to Related Rates Answers
- 4.5 Solving Related Rates Problems Answers
- 4.6 Approximating Values of a Function Using Local Linearity and Linearization Answers
- 4.7 Using L'Hospital's Rule for Determining Limits of Indeterminate Forms Answers
- 5.1 Using the Mean Value Theorem Answers
- 5.2 Extreme Value Theorem, Global Versus Local Extrema, and Critical Points Answers2-up
- 5.3 Determining Intervals on Which a Function Is Increasing or Decreasing Answers2-up
- 5.4 Using the First Derivative Test to Determine Relative (Local) Extrema Answers2-up
- 5.5 Using the Candidates Test to Determine Absolute (Global) Extrema Answers2-up
- 5.6 Determining Concavity of Functions over Their Domains Answers
- 5.7 Using the Second Derivative Test to Determine Extrema Answers
- 5.9 Connecting a Function, Its First Derivative, and Its Second Derivative Answers
- 5.10 Introduction to Optimization Problems Answers2-up
- 5.12 Exploring Behaviors of Implicit Relations Answers
- 6.1 Exploring Accumulations of Change Answers2-up
- 6.2 Approximating Areas with Riemann Sums Answers2-up
- 6.3 Riemann Sums, Summation Notation, and Definite Integral Notation
- 6.4 The Fundamental Theorem of Calculus and Accumulation Functions Answers2-up
- 6.5 Interpreting the Behavior of Accumulation Functions Involving Area Answers
- 6.6 Applying Properties of Definite Integrals Answers2-up
- 6.7 The Fundamental Theorem of Calculus and Definite Integrals Answers2-up
- 6.8 Finding Antiderivatives and Indefinite Integrals: Basic Rules and Notation
- 6.11 Integrating Using Integration by Parts Answers2-up
- 6.12 Integrating Using Linear Partial Fractions Answers2-up
- 6.13 Evaluating Improper Integrals Answers
- 7.2 Verifying Solutions for Differential Equations Answers
- 7.3 Sketching Slope Fields Answers
- 7.4 Reasoning Using Slope Fields Answers2-up
- 7.5 Approximating Solutions Using Euler's Method Answers2-up
- 7.6 Finding General Solutions Using Separation of Variables Answers
- 7.7 Finding Particular Solutions Using Initial Conditions and Separation of Variables Answers2-up
- 8.1 Finding the Average Value of a Function on an Interval Answers2-up
- 8.2 Connecting Position, Velocity, and Acceleration of Functions Using Integrals Answers
- 8.3 Using Accumulation Functions and Definite Integrals in Applied Contexts Answers2-up
- 8.4 Finding the Area Between Curves Expressed as Functions of x Answers2-up
- 8.7 Volumes with Cross Sections: Squares and Rectangles Answers2-up
- 8.9 Volume with Disc Method: Revolving Around the x- or y-Axis Answers2-up
- 8.11 Volume with Washer Method: Revolving Around the x- or y-Axis
- 8.12 Volume with Washer Method: Revolving Around Other Axes
- 8.13 The Arc Length of a Smooth, Planar Curve and Distance Traveled Answers2-up
- 9.1 Defining and Differentiating Parametric Equations Answers
- 9.3 Finding Arc Lengths of Curves Given by Parametric Equations Answers
- 9.4 Defining and Differentiating Vector-Valued Functions Answers
- 9.5 Integrating Vector-Valued Functions Answers
- 9.6 Solving Motion Problems Using Parametric and Vector-Valued Functions Answers
- 9.7 Defining Polar Coordinates and Differentiating in Polar Form Answers
- 9.8 Find the Area of a Polar Region or the Area Bounded by a Single Polar Curve Answers
- 9.9 Finding the Area of the Region Bounded by Two Polar Curves Answers
- 10.2 Working with Geometric Series Answers2-up
- 10.4 Integral Test for Convergence Answers
- 10.6 Comparison Tests for Convergence Answers2-up
- 10.7 Alternating Series Test for Convergence Answers
- 10.8 Ratio Test for Convergence Answers2-up
- 10.9 Determining Absolute or Conditional Convergence Answers
- 10.10 Alternating Series Error Bound Answers
- 10.11 Finding Taylor Polynomial Approximations of Functions Answers2-up
- 10.12 Lagrange Error Bound Answers2-up
- 10.13 Radius and Interval of Convergence of Power Series Answers2-up
- 10.14 Finding Taylor or Maclaurin Series for a Function Answers2-up
- 10.15 Representing Functions as Power Series Answers
Tips
Sort the released questions by topic, and start with series. Working papers in order spreads the hardest material thinly across months; grouping it makes the choice-of-test pattern obvious.
Name the test and check its conditions in writing. The rubric awards the justification separately from the conclusion, so "converges by the ratio test since lim = 1/2 < 1" scores where a bare "converges" does not.
Keep AB material in rotation — it is a large share of the paper and of the AB subscore, and it is the part most often neglected once series begins.