♾️ 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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