AP Calculus AB/BC

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Q&A Student Study Session

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For many students in AP Calculus, the multiple-choice section is easier than the free-response section. You'll be asked more straightforward skills-based questions, problems typically don't build off of each other, 

 you have the power to guess. Still, 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!

Understanding the format of the exam is key to dividing your studying and pacing yourself when doing practice questions.

The multiple-choice section makes up 50% of your score, and you have an hour and 45 minutes to answer 45 questions. This section has 2 parts:

And here's how often each unit shows up on the test:

For free AP multiple choice practice, try:

If you want more AP-style multiple choice practice, consider buying a prep book. They usually sell for under $20 and have upwards of 3 full-length practice tests. Check out this list of the best prep books [coming soon] for Fiveable's top picks!

If you know the format, use these strategies, and practice until you're confident, you'll rock the multiple choice section of the exam. Good luck! 🎉

AP Calculus AB/BC Multiple Choice Help (MCQ)

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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 🎉

 you'll be tested over is key to getting a 5. First, let's look at the format of the exam, which is the same for both AP Calculus AB and BC.

The free-response section makes up the other 50% of your score, and you have an hour and 30 minutes to answer 6 questions. This section has 2 parts:

Now, let's look at the content of the tests:

You can use this information to guide your studying. For example, since unit 6 makes up a large portion of the test, you might want to focus on integration over a smaller unit like differential equations 🤔.

2. Memorize derivative and integral rules ✅

You won’t get an equation sheet on the test, so you need to know your rules to get a 5. Keep practicing the product, quotient, and chain rules. Also remember to go over those trickier derivatives and integrals for trig functions, logarithms, a^x, and inverse functions 📈

You must know how to solve derivatives and integrals, but the College Board also wants to know if you can apply that knowledge to real-world problems. At least 2 questions on the free-response section use a real-world scenario 🌏

Take some time to review units 4, 5, and 8 to make sure you understand related rates, motion, and optimization problems. Use these Fiveable resources to help you study:

Last but not least, the best way to set yourself up for a 5 is to take practice tests! This will help you understand exactly how the College Board asks problems. As you practice, take note of what you get wrong and review the concepts you struggled with.

 to find questions by unit, topic, and type (calculator or non-calculator). You can also check out some of these FRQ review streams to see walkthroughs of recent prompts:

For the multiple-choice section, use these free, full-length

 from the College Board. If you're willing to spend some money, prep books will often have AP-style practice tests. Check out this list of the best prep books [TK] if you're considering buying one!

To sum it up: practice. If you're struggling to understand concepts on your own, don't be afraid to ask questions! AP Calculus can be difficult, but as long as you keep working at it, you'll be on your way to a 5.

How to Get a 5 in AP Calculus AB/BC

AP Calculus will probably be more difficult than the other math classes you've taken. At the same time, it's totally doable! Concepts build on each other pretty quickly, so make sure to keep up with the work and ask questions if you're confused. It's a new way of thinking, but as long as you have a solid foundation in algebra, you'll make it through.

On the test, you'll have 1 hour and 45 minutes to answer 45 multiple choice questions, then 1 hour and 30 minutes to answer 6 free-response questions. You will 

 be able to use a graphing calculator on 4 of the FRQs, but don't worry! If you have to work with numbers on a non-calculator question, the calculations will be relatively simple. Check out

 to get an idea of what questions you might be asked.

Here are the score distributions from 2019:

In comparison to other AP classes, AP Calculus AB has a middle-of-the-road pass rate and an above-average 5 rates. AP Calculus BC has a high pass rate 

 5 rates. This data seems to suggest that AP Calculus isn't too difficult, but it's important to consider that students who are taking an AP math class are more likely to be math-inclined. So, how do students feel?

We surveyed 41 students about the difficulty of AP Calculus.

 They ranked each class on a scale of 1 to 5, where 1 was "extremely easy" and 5 was "extremely difficult." Here are the results:

In that survey from earlier, we asked for advice for students going into AP Calculus. There were three common tips that people seemed to agree on.

First, don't just memorize formulas. Try to understand the reasoning behind each concept. There's a large focus on graphing and real-world applications, so make sure to figure out the meaning behind formulas and rules.

Second, brush up on your algebra skills. Oftentimes, students will understand the calculus part of a question, but they'll make mistakes because of small algebraic errors.

Third, practice FRQs! Try to answer questions in the time limit. When you finish, look at the answer key and compare your work. Remember that every time you correct a mistake, you learn something.

Lastly, listen to some words of wisdom from the Fiveable community:

"It's a different kind of math. Don't feel bad if you don't like it, but give it a shot because you really might!"

"Don’t give up! Especially for the first few months. It's hard to get adjusted, but you’ll get the hang of it. And if you don’t understand one topic, it's okay! Some topics will be better than others."

"Remember that it's an entirely new way of thinking, so it's normal to struggle at first. Stick with it and you'll have a lot of fun!"

All in all, AP Calculus is definitely worth taking. It's extremely useful for most STEM fields, like physics, chemistry, and biology. Even if you aren't going into STEM, calculus is a new type of math that you just might like if you try.

If you start to find it difficult, don't get discouraged! You'll come out of the class knowing more than you did before, and Fiveable has 

Is AP Calculus AB/BC Hard? Is AP Calculus AB/BC Worth Taking?

By now, you've probably covered basic differentiation of a function y in terms of a single variable x. This is called 

 on the other hand, is differentiating a variable 

. We're not just taking the derivative of 

 anymore, we're taking the derivative of whole equations like 

Need a quick review on taking and finding derivatives, make sure you watch this 🎥 

video introducing and explaining derivatives

So how do you do implicit differentiation? 

We can even simplify further to solve for 

...And there you have it!

Implicit differentiation is useful in solving differential equations, where you'll need to solve for 

. Some applications include optimization, e.g. finding the rate of change of volume with respect to the rate of change of time. 

For more examples and help watch this video about 

implicit differentiation and derivatives.

What is implicit differentiation and how do I do it?

U-sub, also known as integration by substitution, is one of the key components of integrals. Need a refresher on integration, check out this 🎥 

Chances are, you've come across an integral like the one below and been completely lost on where to start. 

Fear not! In this article, we'll go over what U-Sub is and how and when you should use it! For the sake of learning the concept first, all of the examples we're going to be using will be indefinite integrals.

Before using u-sub, you want to be able to write your integral as 

If we look at the function above, there are a couple things that we should take note of

g(x) - the 'x' of 'f(x)', in the example at the top of this article, this would be 

U-substitution is all about making taking the integral of a function easier. To do this, we need to substitute a part of the function with '

' so we can be left with something easier to work with. 

 of g(x) changes as well. G'(x) becomes the derivative of '

This example is perfect because we can clearly see what the derivative of g(x) is but it doesn't always work out so easily. To ensure that you're correctly finding g'(x), simply take the derivative of g(x). 

In the case of the example, this would play out something like this

Now that we have 'u' and 'du', we can substitute them into our original integral. 


Next, all we have to do is take the integral in terms of 'u', which basically just means taking the integral but instead of 'x' as you would usually put, 'u' would take its place. 


Our last step is to substitute back in g(x) for 'u'. 


While this example worked out pretty well, as mentioned before, the majority of the integrals you're going to be taking won't. This means that it might take a little bit of extra work getting the integral into this type of format


Say, we have the another integral like the one below


It looks very similar to the one that we just worked with! The only problem, is that pesky '12x'. So, how do we go about solving this? 

We're going to go through the same steps that we did last time. 

We see that everything matches up except g'(x). 12x is simply 2x multiplied by 6 right? So, if we use the rule of constants we can pull that 6 up front and be left with the 2x we need. 

Now, we can take the integral as usual, but make sure not to forget about the 6 we took out! 


And that's it! Now you know how to use u-sub like a pro! If you need some extra help and practice with this concept check out these awesome links too! 


What is U-Sub and How Do I Use It?

AP Calculus AB/BC Exams

AP Calculus AB/BC Exam Prep | Reviews +  Free Practice | Fiveable

Free Review 2020

Free Response Questions (FRQ)

Unit 1: Limits & Continuity

Unit 2: Differentiation: Definition & Fundamental Properties

Unit 3: Differentiation: Composite, Implicit & Inverse Functions

Unit 4: Contextual Applications of the Differentiation

Unit 5: Analytical Applications of Differentiation

Unit 6: Integration and Accumulation of Change

Unit 7: Differential Equations

Unit 8: Applications of Integration

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

AP Calculus Exam Prep 2020-21

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Free Review 2020﻿

Free Response Questions (FRQ)﻿

Unit 1: Limits & Continuity﻿

Unit 2: Differentiation: Definition & Fundamental Properties﻿

Unit 3: Differentiation: Composite, Implicit & Inverse Functions﻿

Unit 4: Contextual Applications of the Differentiation﻿

Unit 5: Analytical Applications of Differentiation﻿

Unit 6: Integration and Accumulation of Change﻿

Unit 7: Differential Equations﻿

Unit 8: Applications of Integration﻿

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

Unit 10: Infinite Sequences and Series (BC Only)﻿

Multiple Choice Questions (MCQ)﻿

Blogs﻿

creators

Jenni MacLean﻿

Jerry Kosoff﻿

Jamil Siddiqui﻿

Meghan Dwyer﻿

Suzanne Ferrell-Locke﻿

Jennifer Durost﻿

Bob Amar﻿

Amy Dunn-Ruiz﻿

Mark Howell﻿

Bryan Passwater﻿

Daniel Romero﻿

Peter Cao﻿

Jed Quiaoit﻿

Sander Owens﻿

Brandon Wu﻿

Catherine Liu﻿

Jillian Holbrook﻿

Jacob Jeffries﻿

Sumi Vora﻿

Anusha Tekumulla﻿

John Le﻿

Nick Molnar﻿

Leen Amro﻿

Jack Iorio﻿

Austin Monroe﻿

Student Student﻿

pooja mathur﻿

Free Review 2020

Free Response Questions (FRQ)

Unit 1: Limits & Continuity

Unit 2: Differentiation: Definition & Fundamental Properties

Unit 3: Differentiation: Composite, Implicit & Inverse Functions

Unit 4: Contextual Applications of the Differentiation

Unit 5: Analytical Applications of Differentiation

Unit 6: Integration and Accumulation of Change

Unit 7: Differential Equations

Unit 8: Applications of Integration

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

Unit 10: Infinite Sequences and Series (BC Only)

Multiple Choice Questions (MCQ)

Blogs

Jenni MacLean

Jerry Kosoff

Jamil Siddiqui

Meghan Dwyer

Suzanne Ferrell-Locke

Jennifer Durost

Bob Amar

Amy Dunn-Ruiz

Mark Howell

Bryan Passwater

Daniel Romero

Peter Cao

Jed Quiaoit

Sander Owens

Brandon Wu

Catherine Liu

Jillian Holbrook

Jacob Jeffries

Sumi Vora

Anusha Tekumulla

John Le

Nick Molnar

Leen Amro

Jack Iorio

Austin Monroe

Student Student

pooja mathur