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
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