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What Memes Are Perfect for AP Calculus AB/BC?

5 min readโ€ขoctober 1, 2021

Catherine Liu

Catherine Liu


AP Calculus AB/BCย โ™พ๏ธ

279ย resources
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Keeping up with the fast and challenging curriculum of AP Calculus can be hard to handle sometimes. 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.

Meme #1

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-aLgv0UXjizmk.png?alt=media&token=990aab2c-4d8f-4a43-83ca-72e7e1cd1642

Image Courtesy of Nerdy Jokes Tumblr

Your calculator can only be in two different modes: degrees or radians. This joke is referencing the fact that if youโ€™re not in degree mode, youโ€™re in radian mode. RAD is the abbreviation for radian mode.
In AP Calculus class, knowing what mode to have your calculator in is crucial for calculating trigonometric values. Something most students donโ€™t know is that the mode of your calculator only matters when using trigonometric functions such as sine, cosine, tangent, secant, cosecant, or cotangent. With every other calculation, youโ€™ll get the same answer regardless of which mode youโ€™re in. Hereโ€™s a simple breakdown of when you should be using each mode:
Degrees:
  • When you're using degrees as a unit.
  • If the question is sin(48ยฐ), then your calculator needs to be in degrees.
  • If your input (which is 48 degrees in the above example) is in degrees, then your output needs to be in degrees.
Radians:
  • When youโ€™re using radians as a unit.
  • If the question is sin(3๐…/4), then your calculator needs to be in radians. Keep in mind that a number doesnโ€™t need to have a pi symbol to be in radians
  • If your input (which is 3๐…/4 in the above example) is in radians, then your output needs to be in radians.
For more calculator tips, check out "What Calculator Functions Will Save Your Life?"

Meme #2

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-0TuQTYJcRvix.png?alt=media&token=f1d53c75-a9c6-4c63-bf76-7a1eb595dd6b

Image Courtesy of Architecture & Civil Engineering Facebook

One of the most important things to know about calculus is the relationship between derivatives and integrals. To put it simply, an integral is an โ€œoppositeโ€ derivative. This joke is a classic example of the concept. If you derive the milk, you get cheese because that is the next step of the process. If you integrate milk, you get a cow because that is the previous step in the process. In this situation, the process is cow โ†’ milk โ†’ cheese.
For some more help with understanding derivatives, check out this set of guides! What about integrals? Check out this set!

Meme #3 and #4

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-JZ1UgUl8cVQU.png?alt=media&token=682d4670-9cf2-4aa0-bc1c-0ca69c3251a0
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-4BzOCIMxTnhH.png?alt=media&token=f9bb2515-f6e0-46a2-a7c0-d2cf5f063d22

Images Courtesy of Erica S Pinterest and 9GAG.com

When learning about derivatives, youโ€™ll most likely have to memorize the derivatives or certain functions like natural logs and trig functions. One of the easiest derivatives to remember is that the derivative of e^x is e^x.
In the first meme, it shows how the natural log function was changed into a 1/x and x^2 function was changed into a 2x. The e^x function was unchanged because its derivative is the same as the function. In the end, it is revealed that the book is a derivative.
Similarly, in the second meme, the man is unchanged despite deriving multiple times. Thus, the only explanation is that he is e^x.
Hereโ€™s a chart to help you remember your derivatives:
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-6Qn1qK1JTZU2.png?alt=media&token=03a8c802-031a-4330-8857-4130088a97af

Image Courtesy of Magoosh AP Calc Prep

Meme #5

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-LVn7TF4iMpRA.png?alt=media&token=ad014fe1-e57f-49c8-b621-c8d3773e7d2f

Image Courtesy of Bowman Dickson

While this meme isnโ€™t actually calculus-related, I have found that many students still make this mistake from time to time. When I was taking calculus, my teacher couldnโ€™t stand when his students did this. It is crucial to remember that addition and subtraction cannot be treated the same way as multiplication and division when it comes to exponents.
As seen in the meme, most students think that (x^2 +3)^2 equals x^4 + 9 However, the answer is actually x^4 + 6x + 9 because you have to FOIL (first, outer, inner, last). It is important to recognize that (x^2 +3)^2 is the same as (x^2 + 3)(x^2 + 3) not x^4 + 9.

Meme #6

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-lFLTAkcbDvVn.png?alt=media&token=03984b30-6d2d-4394-ae73-fcc586f67310

Image Courtesy of Zazzle.com

When deriving the position function, the first derivative is velocity and the second derivative is acceleration. The 3rd derivative, which is shown in the meme as d3x/dt3, is known as a jerk. Thus, the meme says โ€œDonโ€™t be a jerkโ€.

Meme #7

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-5SYic28Gt5zV.png?alt=media&token=e7ea086b-6acb-466b-b9ea-b20fd283b0d0

Image Courtesy of @iam.miss.physics Instagram

This meme shows how the original function, f(x), can change drastically after being derived once or twice. In the meme, the first picture of the hair represents the original function. As you can see, the hair gets shorter and shorter similar to how a functionโ€™s graph changes when it is derived.

Meme #8 and #9

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-Rd4r4xl7XWvL.png?alt=media&token=8a313e1c-071c-4537-b572-6f48d2b0603e
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-x6gxheqxJfTm.png?alt=media&token=b7f7c358-63f8-4dc5-8e44-06019a8033ba

Images Courtesy of Spiked Math Comics

Both of these memes reference the same concept of calculus. When youโ€™re integrating any function, you must have a โ€œ+ Cโ€ on the end. As mentioned previously, integration is essentially a reverse derivative. Take a look at this example to better understand this: 15x^2 + 8
If f(x) = 5x^3 +8x + 7 and fโ€™(x) = 15x^2 + 8, then โˆซ fโ€™(x)dx should equal f(x). However, โˆซ 15x^2 + 8 dx actually equals 5x^3 +8x. The problem here is that constant from the original function (7) isnโ€™t represented.
Thus, it is important to add โ€œ+ Cโ€ at the end of the function when you integrate so the constant is represented. This โ€œ+ Cโ€ is an arbitrary constant that can be anything you want, as seen in the first meme.

Meme #10

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-rpVjI02PRWGV.png?alt=media&token=4a918bba-e565-4e17-a20d-65989a5ef756

Image Courtesy of @math.hero Instagram

When youโ€™re first learning about derivatives in AP Calculus class, youโ€™ll likely learn to take a derivative using a limit rather than using derivative rules. To take a derivative using a limit, you must use the difference quotient. The formula for the difference quotient is shown in the speech bubble of the meme. Thus, the difference quotient can be thought of as a derivativeโ€™s โ€œfull nameโ€.

Closing Thoughts

Hopefully, these memes will help you better grasp the complex concepts of AP Calculus. If you are ever confused, consider talking to your teacher or chatting with us here at Fiveable.
Good Luck with your AP Calculus studying!

Browse Study Guides By Unit
๐Ÿ‘‘Unit 1 โ€“ Limits & Continuity
๐Ÿค“Unit 2 โ€“ Fundamentals of Differentiation
๐Ÿค™๐ŸฝUnit 3 โ€“ Composite, Implicit, & Inverse Functions
๐Ÿ‘€Unit 4 โ€“ Contextual Applications of Differentiation
โœจUnit 5 โ€“ Analytical Applications of Differentiation
๐Ÿ”ฅUnit 6 โ€“ Integration & Accumulation of Change
๐Ÿ’ŽUnit 7 โ€“ Differential Equations
๐ŸถUnit 8 โ€“ Applications of Integration
๐Ÿฆ–Unit 9 โ€“ Parametric Equations, Polar Coordinates, & Vector-Valued Functions (BC Only)
โ™พUnit 10 โ€“ Infinite Sequences & Series (BC Only)
๐ŸงMultiple Choice Questions (MCQ)
โœ๏ธFree Response Questions (FRQ)
๐Ÿ“†Big Reviews: Finals & Exam Prep

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