AP Calculus

AP Calculus AB Exam

The intention of this collection of notes is to serve as a reference for studying for the AP Calc AB Exam. If you are not here because I sent you a link, I am amazed and sorry for you. There might be something useful here but this is a WIP reorganization of materials from College Board and other sources of AP calc reference material(as well as my own opinions inserted randomly).

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  • As soon as college board changes anything from the 2024 exam, this guide will become out of date. Until then, have fun!

Content

Knowledge is power. What do you need to know?

So you want to pass the AP calc exam? Sick bro. College Board Defines 8 Units that you should be aware of.

1. Limits and Continuity
2. Differentiation - Definition and Fundamental Properties
3. Differentiation - Composite Implicit and Inverse Functions
4. Contextual Applications of Differentiation
5. Analytical Applications of Differentiation
6. Integration and Accumulation of Change
7. Differential Equations
8. Applications of Integration

Which if you look at it really boils down to:

1. Fundamental Calculus Definitions(Limits)
2. Doing Things With Derivatives
3. Doing Things With Integrals
4. Differential Equations

Where do you gain this knowledge?

• Khan Academy
• MIT Calc Course
• Some Guy Named Paul
• 3Blue1Brown Youtube Videos
  • O0o0ooo pictures(Don’t worry about the Taylor series)
• AP classroom? I think college board has more resources online but I don’t have an AP classroom account and I don’t want one so idk.
• Openstax

Practice Materials

• Random Practice Tests Online
• Old FRQs
• Kahn Academy Unit and Course Challenge Tests

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Exam Shit

You are going into battle against college board. You should know your enemy.

Here’s the Content Breakdown:

Unit	Exam Weight
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%

Beyond the scope of knowing calculus you need to consider how college board crafts an exam and defines content in a narrower scope that mathematical correctness. In terms of exam logistics there are two sections:

Section 1 - Multiple Choice

Part A(No Calculator)

• 30 Questions | 60 Minutes | $\approx 2$ Minutes Per Question
• 33.3% of the Exam Score

Part B(Calculator)

• 15 Questions | 45 Minutes | $\approx 3$ Minutes Per Question
• 16.7% of the Exam Score

Section 2 - Free Response Questions

Part A(Calculator)

• 2 Questions | 30 Minutes | $\approx 15$ Minutes Per Question
• 16.7% of the Exam Score

Part B(No Calculator)

• 4 Questions | 60 Minutes | $\approx 15$ Minutes Per Question
• 33.3% of the Exam Score

This means that the FRQ questions are very important because each individual question makes up a far higher percent of your grade and they should be harder to solve because the right answer is not an option to select from. AP Score Calculators estimate that if you get 100% on the multiple choice and a 0% on the FRQ, you could get a score of 3 on the exam, but you don’t want to rely on that. You have a much better chance to get a much better score by doing decently well on the FRQ and doing even ok on the multiple choice.

A few notes about the FRQ section. You need to show your work(process and reasoning), otherwise you will not get credit and you need to have the correct answer otherwise there is no partial credit. You need to clearly cross out any work that is incorrect so it is not graded. There is a big ass document that outlines what they expect from an FRQ question and how they will not give you credit.

It’s also important to consider that there are 4 ways in which college board thinks you can use math:

1. “Implementing Mathematical Processes: Determine expressions and values using mathematical procedures and rules.”

Can you solve equations using formulas and theories correctly?

2. ”Connecting Representations: Translate mathematical information from a single representation or across multiple representations”

Can you take a problem or concept in X and translate what it would look like or mean in Y?

3. ”Justification: Justify reasoning and solutions”

Idk why this one is described in 5 words because it’s kinda important and kinda tricky. Can you practice the skills of defending your conclusion through mathematical reasoning and logic and citing theories and definitions.

4. ”Communication and Notation: Use correct notation, language, and mathematical conventions to communicate results or solutions.”

Can you accurately and coherently report the results of something in a way that someone else who knows calc could understand?

If you can understand what category and given question might fall under, you will give you self an advantage in knowing what skills you are expected to demonstrate.