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2019 AP Calc AB FRQs     Solutions

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AP Calc Resources by Sequential Topic

0.0 Precalculus Topics

0.1  Properties of Logarithms

0.1.1  Video:  What You Need to Know about Logs  (20:36)

0.2  Vertical Asymptotes

0.2.1 Video:  Vertical Asymptotes of Rational Functions (8:41)

0.3  Horizontal Asymptotes

0.3.1  Video:  Horizontal Aymptotes (4:34)

0.4  Unit Circle Memorization

0.4.1 Video: Memorizing Unit Circle  (6:16)

0.4.2 Video:  Another Memorizing Unit Circle (13:11)

0.5 Special Triangle Trig

0.5.1 Video: 45-45-90 and 30-60-90 Triangles (13:13)

0.6 Prerequisite Test for Calculus

0.6.1  Test (pdf)

0.6.2  Answers (pdf)

1.0 Limits and Continuity

1.1 Understanding Limits (Graphically and Numerically)

1.2 Limits Analytically

1.3 Limits of Exponential Functions (Graphically and Analytically)

1.4 Limits of Trig Functions (Analytical)

1.5 Continuity With Limits (Graphical and Analytical)

1.6 Intermediate Value Theoreom

1.7 Infinite Limits and Limits at Infinity

AP Multiple Choice and FRQ Practice Problems

Test Practice Problems

2.0 Understanding the Derivative

2.1 The Difference Quotient

2.2 Derivatives - Graphical and Numeric Approach

2.3 Finding Derivatives Analytically - Polynomial, Sine, Cosine

2.4 Connections Between f(x) and f'(x)

2.5 Derivatives as the Tangent Line Slope

3.0 Differentiation: Composite, Implicit, and Inverse Functions

3.1 The Chain Rule

3.2 Implicit Differentiation

3.3 Differentiating Inverse Functions

3.4 Differentiating Inverse Trig Functions

3.5 Selecting Procedures for Calculating Derivatives

3.6 Calculating Higher-Order Derivatives

4.0 Contextual Applications of Differentiation

4.1 Interpreting the Meaning of Derivative in Context

4.2 Straight-Line Motion: Position, Velocity, 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 Using Local Linearity

4.7 Using L'Hopital's Rule for Determining Limits of Indeterminate Forms

5.0  Analytical Applications of Differentiation

5.1 Using the Mean Value Theorem

5.2 Extreme Value Theorem, Global and 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 Local Extrema

5.5 Using Candidates Test to Determine Global Extrema

5.6 Determining Concavity of Functions over Their Domain

5.7 Using the Second Derivative Test to Determine Extrema

5.8 Sketching Graphs of Functions and Their Derivatives

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

5.10 Introduction to Optimization Problems

5.11 Solving Optimization Problems

5.12 Exploring Behaviors of Implicit Relations 

6.0  Integration and Accumulation of Change

6.1 Exploring Accumulation of Change

6.2 Approximating Areas with Riemann Sums

6.3 Riemann Sums, Summation Notation, and Definite Integral

6.4 The Fundamental Theorem of Calculus and Accumulation Functions

6.5 Interpreting the Behavior of Accumulation Functions Involving Area

6.6 Applying Properties of Definite Integrals

6.7 The Fundamental Theorem of Calculus and Definite Integrals

6.8 Finding Anti-Derivatives and Indefinite Integrals: Basic Rules and Notation

6.9 Integration Using Substitution

6.10 Integrating Functions Using Long Division

6.11  Skipped (BC Only)

6.12 Skipped (BC Only)

6.13 Skipped (BC Only)

6.14 Selecting Techniques for Antidifferentiation

7.0  Differential Equations

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 Skipped (BC Only)

7.6 Finding General Solutions Using Separation of Variables

7.7 Finding Particular Solutions Using Initial Conditions

7.8 Exponential Models with Differential Equations

8.0  Applications of Integration

8.1 Finding the 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 as Functions of x

8.5 Finding the Area Between Curves as Functions of y

8.6 Finding the Area Between Curves that Intersect at More than 2 Points

8.7 Finding Volumes with Cross Sections

8.8 Finding Volumes with Disk and Washer Method 

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