Basic Trope: A character makes pathetic grades but is of relatively intelligent regarding non-academic pursuits.
Straight: Alice regularly makes terrible grades in her classes, but comes up with clever and intricate plans outside of the classroom.
Exaggerated: Alice is a perpetual F student, but solves practical quantum physics problems in her spare time.
Downplayed: Alice gets below-average (C/D) but not terrible grades, even though she's of around just over average intelligence and maybe even could get a C+ or even B- if she really tried.
Alice has the potential to be a good or even great student, but she's too shy/modest to apply herself in the classroom.
Alice either finds school boring or a waste of her time, or both. She'd rather apply her talents elsewhere.
Alice may be smart,but she's illiterate.
Alice doesn't know the jargon or the "code words" of the educational institution or the teacher enough to fit in, and trying to read just what she'd already taught herself to this would lead to the Centipede's Dilemma. This one happens to musicians in Real Life - self-taught singers and drummers, especially, can run into huge problems trying to re-learn how to do things "right," because when one teaches oneself to sing or to play a rhythmic percussion instrument, it may have been learned far differently than how one is "supposed" to learn (e.g. a singer learning by karaoke and singing along to music and miming other singers over adolescence or older, as opposed to taking singing classes from youth and being instructed on everything from proper technique to proper terminology, or a drummer who understands time signatures but cannot discuss them and the theory behind them in depth), and trying to connect the two while actually performing = Centipede's Dilemma.
A variant of this, also Truth in Television is called the specialization of intelligence: there are plenty of people who do and use things without knowing every bit of theory or jargon or even completely how they work, and therefore, if quizzed or otherwise forced to explain their knowledge of them, would fail miserably. As a couple of examples, unless you're an expert computer hardware builder and software engineer for all platforms, you're a definite example yourself if you're reading this (and which is why if your screen becomes unreadable, you'll be looking for computer repair or googling "why does my screen not work" on another device), and it also applies to 85% or so of vehicle drivers who are not even capable of basic car repairs (which are why roadside assistance services and mechanics as a profession exist) This is that there are so many things in the world to learn and know that trying to do it all is impossible, and therefore some people learn some things (e.g. being fiction writers) and others learn others (e.g. how to fix said writer's laptop when its screen looks like a Call Back to the days of scrambled TV). This even applies to the human body itself - which is why the medical profession exists - and to human interaction in some instances - which is why the legal and law enforcement professions exist.
Alice is not native to the culture or location, and cannot understand the local language, despite being incredibly smart and capable if someone only thought to engage her in her own language or help her learn the local language.
Alice is not good with languages and therefore can't learn the local language, but that does not make her any less smart or capable - it only means she needs a translator or dual-language communications.
Alice lives in a setting where standards of education are very poor and there are no opportunities, and is not expected to go anywhere. For example, no one expects girls in her country to be capable of learning anything beyond the eighth grade, and there are no work opportunities for women other than Housewife, so she gives up trying, because it's pointless.
Alice lives in a setting where standards of education are too high or are too reliant on standardized testing or one discipline. So although, for example, she is a bookworm and incredibly talented writer, she is also an example of Writers Cannot Do Math, and her school district or college will not pass anyone with less than a B in at least two high-level algebra and calculus courses. There is no way to waive the requirements even if it could be proven that Alice's career path will have no need for higher-level math (e.g. law or the humanities/liberal arts), so she drops out of school, despite, having been granted the waiver or allowed to substitute an easier math class, she could have gone on to law school or to a master's or doctorate in something related to literature or art.
Alice could easily be a A+ student, but at her last school she got bullied for being "too nerdy" so she gives up trying.
Zig Zagged: Alice gets bad grades in school, but they start going up suddenly. This turns out to be because she built an android to go to school for her. Then the android malfunctions and becomes Book Dumb itself, so it builds another one to go to school for it. The same thing happens until Alice droids take over the world.
Averted: Alice is a well-rounded student and an intelligent person.
Enforced: "Those idiots in the audience need a character that is intelligent despite poor academic performance to sympathize with!"
Lampshaded: "You know, if you worked half as hard on your schoolwork as you did on your scheming, you'd be headed to Harvard!"
Invoked: "I'm not going to study today. Not when there's too much to do."
Defied: Alice decides to buckle down and study for an important test.
Discussed: "Mr. and Mrs. Troper, if your daughter showed the same enthusiasm for school as she did for making mischief, she'd have a much brighter future".
Conversed: "So, wait. If these protagonists are so clever, why do they always get such horrible grades? You'd think they'd at least be able to pull off a B average".
Implied: While Alice's book dumbness is never explicitly lampshaded, in the background of her house you can sometimes see test scores of F-, and on the other side of the room a periodic table of elements Alice has owned since she was six.
Deconstructed: Alice's poor academic performance comes back to bite her, as while she is an effective Schemer, any potential colleges/employers won't be able to look past her bad grades.
However, Alice decides to make her own path, and becomes decidedly successful in a different field.
A professor gets her working at an academic institution despite her grades, due to a few strings pulled.
Played For Drama: Alice's bad grades lead to her dropping out of high school and having to live on the streets. She becomes a alcoholic to cope with the pain, and during this lonely period she writes captivating, compelling, intelligent passages in her diary. After she tragically dies of liver failure before her 18th birthday, only then do the teachers who expelled her discover that she actually may of been the smartest girl in school when they read her diary entries.