# ♾️ 2023 AP Calculus AB and BC Study Plan

Welcome to this plethora of resources that cover everything you need to know for AP Calc AB and BC! This toolkit is **constantly being updated** with more resources! AP Calculus AB and BC are college-level calculus courses meant to substitute for two semesters of college calculus. You will learn differential and integral calculus by engaging with real-world problems.

## The AP Calculus AB Exam

A breakdown of the AB exam by percentage.

Unit | Exam Weighting (MCQ) |
---|---|

Unit 1: Limits and Continuity | 10%–12% |

Unit 2: Differentiation: Definition and Fundamental Properties | 10%–12% |

Unit 3: Differentiation: Composite, Implicit, and Inverse Functions | 9%–13% |

Unit 4: Contextual Applications of Differentiation | 10%–15% |

Unit 5: Analytical Applications of Differentiation | 15%–18% |

Unit 6: Integration and Accumulation of Change | 17%–20% |

Unit 7: Differential Equations | 6%–12% |

Unit 8: Applications of Integration | 10%–15% |

## The AP Calculus BC Exam

The AP Calc BC exam covers all the units that the AB exam does with two additional units at the end. Here’s a breakdown of the BC exam content by percentage.

Unit | Exam Weighting (MCQ) |
---|---|

Unit 1: Limits and Continuity | 4%–7% |

Unit 2: Differentiation: Definition and Fundamental Properties | 4%–7% |

Unit 3: Differentiation: Composite, Implicit, and Inverse Functions | 4%–7% |

Unit 4: Contextual Applications of Differentiation | 6%–9% |

Unit 5: Analytical Applications of Differentiation | 8%–11% |

Unit 6: Integration and Accumulation of Change | 17%–20% |

Unit 7: Differential Equations | 6%–9% |

Unit 8: Applications of Integration | 6%–9% |

Unit 9: Parametric Equations, Polar Coordinates, and Vector-Valued Functions | 11%–12% |

Unit 10: Infinite Sequences and Series | 17%–18% |

## Mathematical Practices for AB

By taking AP Calc AB, you’ll gain a variety of skills that will help you think and problem-solve like a mathematician.

Skill | Description |
---|---|

1. Implementing Mathematical Processes | Determine expressions and values using mathematical processes. |

2. Connecting Representations | Translate mathematical information from a single representation. |

3. Justification | Justify reasoning and solutions. |

4. Communication and Notation | Use correct notation, language, and mathematical conventions. |

## Mathematical Practices for BC

By taking AP Calc BC, you’ll build on the mathematical practices you developed in Calc AB to increase your ability to think and problem-solve like a mathematician. Differences between the skillsets are bolded.

Skill | Description | Exam Weighting (MCQ) | Exam Weighting (FRQ) |
---|---|---|---|

1. Implementing Mathematical Processes | Determine expressions and values using mathematical procedures and rules. |
53%–66% | 37%–59% |

2. Connecting Representations | Translate mathematical information from a single representation or across multiple representations. |
18%–28% | 9%–16% |

3. Justification | Justify reasoning and solutions. | 11%–18% | 37%–59% |

4. Communication and Notation | Use correct notation, language, and mathematical conventions to communicate results or solutions. |
Only assessed in the free-response section. | 9%–20% |

## Study Guides for Every Unit

### 👑 **Unit 1: Limits & Continuity**

- 1.0 Unit 1 Overview
- 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
- 1.10 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
- 1.16 Working with the Intermediate Value Theorem (IVT)
- 1.17 Multiple Choice Questions
- 1.18 MC Answers and Review

### 🤓 **Unit 2: Differentiation: Definition & Fundamental Properties**

- 2.0 Unit 2 Overview
- 2.1 Defining Average and Instantaneous Rates 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: Determining When Derivatives Do and Do Not Exist
- 2.5 Applying the Power Rule
- 2.6 Derivative Rules: Constant, Sum, Difference, and Constant Multiple
- 2.7 Derivatives of cos x, sinx, e^x, and ln x
- 2.8 The Product Rule
- 2.9 The Quotient Rule
- 2.10 Finding the Derivatives of Tangent, Cotangent, Secant, and/or Cosecant Functions
- 2.11 Multiple Choice Questions
- 2.12 MC Answers and Review

### 🤙🏽 **Unit 3: Differentiation: Composite, Implicit & Inverse Functions**

- 3.0 Unit 3 Overview
- 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
- 3.7 Multiple Choice Questions
- 3.8 MC Answers and Review

### 👀 **Unit 4: Contextual Applications of the Differentiation**

- 4.0 Unit 4 Overview
- 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 Intro 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'Hopitals Rule for Determining Limits in Indeterminate Forms
- 4.8 Multiple Choice Questions
- 4.9 MC Answers and Review

### ✨ **Unit 5: Analytical Applications of Differentiation**

- 5.0 Unit 5 Overview
- 5.1 Using the Mean Value Theorem
- 5.2 Extreme Value Theorem, Global vs 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
- 5.6 Determining Concavity
- 5.7 Using the Second Derivative Test to Determine Extrema
- 5.8 Sketching Graphs of Functions and Their Derivatives
- 5.10 Introduction to Optimization Problems
- 5.11 Solving Optimization Problems
- 5.12 Multiple Choice Questions
- 5.13 MC Answers and Review

### 🔥 **Unit 6: Integration and Accumulation of Change**

- 6.0 Unit 6 Overview
- 6.1 Integration and Accumulation of Change
- 6.11 Integrating Using Integration by Parts (
**BC ONLY**) - 6.12 Using Linear Partial Fractions (
**BC ONLY**) - 6.13 Multiple Choice Questions
- 6.14 MC Answers and Review

**💎 Unit 7: Differential Equations**

- 7.0 Unit 7 Overview
- 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 (
**BC ONLY**) - 7.6 Finding General Solutions Using Separation of Variables
- 7.7 Finding Particular Solutions Using Initial Conditions and Separation of Variables
- 7.9 Logistic Models with Differential Equations (
**BC ONLY**) - 7.10 Multiple Choice Questions
- 7.11 MC Answers and Review

**🐶 Unit 8: Applications of Integration**

- 8.0 Unit 8 Overview
- 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 Expressed as Functions of x
- 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
- 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
- 8.14 Multiple Choice Questions
- 8.15 MC Answers and Review

**🦖 Unit 9: Parametric Equations, Polar Coordinates & Vector Valued Functions (BC Only)**

- 9.0 Unit 9 Overview
- 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
- 9.10 Multiple Choice Questions
- 9.11 MC Answers and Review

### ♾️ **Unit 10: Infinite Sequences and Series (BC Only)**

- 10.0 Unit 10 Overview
- 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
- 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 Power Series
- 10.16 Multiple-Choice Questions
- 10.17 MC Answers and Review

## AP Calc MCQ & Writing

**❓****Calculus Multiple Choice Questions**: A complete breakdown of the exam format and logistical details- 🤯
**AP Calculus AB/BC Multiple Choice Help (MCQ)****:**Doing well on the multiple-choice requires good test-taking strategies and lots of practice. Here are our tips and tricks to help you do your best in May! **✍️****Calculus Free Response Questions****:**The second component of the AP Exam includes 6 Free Response Questions (FRQs). Not to worry, though, we’ll detail what you can expect in each part and how to maximize your score.

## Quicklinks

- ✨
**How to Get a 5 in AP Calculus AB/BC****:**To get a 5 in AP Calculus, you need to know how the College Board asks questions. The test is difficult, but if you know the content and do enough practice, you'll set yourself up for a 5. Here are some tips and tricks to make sure you do your best on test day 🎉 - 🧮
**Calculator Functions That'll Save Your Life****:**On the AP Calculus Exam, you will be required to use a graphing calculator on both the Multiple Choice and Free Response Sections. Here are some tips to use your calculator to its full potential on the AP Calculus Exam - 🤔
**Is AP Calculus AB/BC Hard? Is AP Calculus AB/BC Worth Taking?****:**A breakdown of the two most asked questions about AP Calculus, including tips and advice from previous AP Calculus students. - 😂
**Perfect Memes for AP Calculus AB/BC****:**Looking at calculus memes can help you understand complex topics in a more enjoyable way. These ten memes have humorous and educational aspects that will help you better understand AP Calculus.

We have over 250 **replays, slide decks, and study guides** to help you earn that 5 in AP Calc!

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