Calculus

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List of Lessons

Version #1

Unit 0

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0.1 Summer Packet

0.2 Calculator Skillz

Unit 1

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1.1 Can Change Occur at an instant

1.2 Defining Limits and Using Limit Notation

1.3 Limit Values from Graphs

1.4 Limit Values from Tables

1.5 Determining Limits Using Algebraic Properties

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

mid-Unit 1 Review

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 Infinite Limits and Vertical Asymptotes

1.15 Limits at Infinity and Horizontal Asymptotes

1.16 Intermediate Value Theorem

End of Unit 1 Review

Unit 2

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2.1 Defining Average and Instantaneous Rate of Change at a Point

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: Constant, Sum, Difference, and Constant Multiple

2.7 Derivatives of cos(x), sin(x), e^x, and ln(x)

2.8 The Product Rule

2.9 The Quotient Rule

2.10 Derivatives of tan(x), cot(x), sec(x), csc(x)

Unit 2 Review

Unit 3

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3.1 The Chain Rule

3.2 Implicit Differentiation

3.3 Differentiating Inverse Functions

3.4 Differentiating Inverse Trigonometric Functions

3.5 Selecting Procedures for Calculating Derivatives

3.6 Calculating Higher-Order Derivatives

Unit 3 Review

Unit 4

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4.1 Interpreting the Meaning of the Derivative in Context

4.2 Straight-Line Motion: Connecting Position, Velocity, and Acceleration

4.3 Rates of Change in Applied Contexts Other Than Motion

4.4 Introduction 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’Hopital’s Rule for Determining Limits of Indeterminate Forms

Unit 4 Review

Unit 5

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5.1 Using the Mean Value Theorem

5.2 Extreme Value Theorem, Global Versus 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 of Functions over Their Domains

5.7 Using the Second Derivative Test to Determine Extrema

mid-Unit 5 Review

5.8 Sketching Graphs of Functions and Their Derivatives

5.9 Connecting a Function, Its First Derivative, and Its Second Derivative

5.10 Introduction to Optimization Problems

5.11 Solving Optimization Problems

5.12 Exploring Behaviors of Implicit Relations

End of Unit 5 Review

Unit 6

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6.1 Exploring Accumulation of Change

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

Mid-Unit 6 Review

6.6 Applying Properties of 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 Substitution

6.10 Integrating Functions Using Long Division and Completing the Square

6.11 Integration by Parts

6.12 Integrating Using Linear Partial Fractions

6.13 Evaluating Improper Integrals

6.14 Selecting Techniques for Antidifferentiation

End of Unit 6 Review

Unit 7

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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 General Solutions Using Separation of Variables

7.7 Particular Solutions using Initial Conditions and Separation of Variables

7.8 Exponential Models with Differential Equations

7.9 Logistic Models with Differential Equations

Unit 7 Review

Unit 8

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8.1 Average Value of a Function on an Interval

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 Area Between Curves Expressed as Functions of y

8.6 Finding the Area Between Curves That Intersect at More Than Two Points

Mid-Unit 8 Review

8.7 Volumes with Cross Sections: Squares and Rectangles

8.8 Volumes with Cross Sections: Triangles and Semicircles

8.9 Volume with Disc Method: Revolving Around the x- or y-Axis

8.10 Volume with Disc Method: Revolving Around Other Axes

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

End of Unit 8 Review

Unit 9

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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 9 Review

Unit 10

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10.1 Defining Convergent and Divergent Infinite Series

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

Mid-Unit 10 Review

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 Representing Functions as a Power Series

End of Unit 10 Review

Version #2

Derivatives

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Unit 0 – Calc Prerequisites

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0.1 Things to Know for Calc

0.2 Summer Packet

0.3 Calculator Skillz

Unit 1 – Limits

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1.1 Limits Graphically

1.2 Limits Analytically

1.3 Asymptotes

1.4 Continuity

Review – Unit 1

Unit 2 – The Derivative

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2.1 Average Rate of Change

2.2 Definition of the Derivative

2.3 Differentiability

Review – Unit 2

Unit 3 – Basic Differentiation

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3.1 Power Rule

3.2 Product & Quotient Rule

3.3 Velocity/Rates of Change

3.4 Chain Rule

3.5 Trig Derivatives

Review – Unit 3

Unit 4 – More Derivatives

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4.1 Exp and Log Derivatives

4.2 Inverse Derivatives

4.3 L’Hopitals Rule

Review – Unit 4

Unit 5 – Curve Sketching

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5.1 Extreme Values

5.2 First Derivative Test

5.3 Second Derivative Test

Review – Unit 5

Unit 6 – Implicit Differentiation

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6.1 Implicit Differentiation

6.2 Related Rates

6.3 Optimization

Review – Unit 6

SEMESTER REVIEW

Integrals

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Unit 7 – Approximation Methods

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7.1 Rectangular Approximation

7.2 Trapezoidal Approximation

Unit 8 – Integration

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8.1 Definite Integral

8.2 First Fundamental Theorem of Calculus

8.3 Antiderivatives

Review – Unit 8

Unit 9 – FTC Part 2

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9.1 The 2nd FTC

9.2 Trig Integrals

9.3 Average Value

9.4 Net Change

Review – Unit 9

Unit 10 – More Integrals

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10.1 Slope Fields

10.2 u Sub Indefinite Integral

10.3 u Sub Definite Integral

10.4 Separation of Variables

Review – Unit 10

Unit 11 – Area and Volume

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11.1 Area Between Curves

11.2 Solids of Revolution (Discs)

11.3 Solids of Revolution (Washers)

11.4 Perpendicular Cross Sections

Review – Unit 11

FRQ

2022 AB

2022 BC

Teacher Resources

2022 FRQ for AP Calculus AB

frq_ab_2022.pdf

File Size:

359 kb

File Type:

pdf

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Question 1

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Question 6