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I'm a student and I recently asked myself if cheating in a test is an Averah. I've always believed it obviously is, but after thinking it through I can't think of a specific Averah that would include cheating on a test or homework. It may be dishonest with the teacher, but it doesn't seem like lying.
Even if it wouldn't be an Averah I still wouldn't do it. But what Averah encompasses cheating on a test?
R. Moshe Feinstein has a responsum about cheating. He was asked by someone who had heard that in yeshivot they allow the students to steal the answers for the Regents.
R. Moshe answered that it is absolutely forbidden. Not only is it geneivat da'at (deception), it is also geneivat mamon (outright monetary theft) because when someone applies for a job they present their diploma which indicates that they are learned in the subjects taught in school, so if you cheated on the test then you are actually less qualified for the job.
הנה בדבר שאלתו על מה ששמע שבישיבות מתירין להתלמידים לגנוב את התשובות להשאלות במבחני הסיום שעושה המדינה (רידזענס) כדי להונות ולקבל את התעודות שגמרו בטוב הנה דבר זה אסור לא רק מדינא דמלכותא אלא מדין התורה ואין זה רק גניבת דעת שג"כ אסור כדאמר שמואל בחולין דף צ"ד ע"א שאסור לגנוב דעת הבריות ואפילו דעתו של עכו"ם וכ"ש הכא שהוא גניבת דעת לכולי עלמא אף לישראל אלא דהוא גם גניבת דבר ממש דהא כשירצה לפרנסתו במשך הזמן להשכיר עצמו אצל אחד לעבוד בעסקיו ורוצים ברוב הפעמים במי שגמר היטב למודיו דחול והוא יראה לו התעודה איך שגמר בטוב ועל סמך זה קבלוהו שזהו גניבת ממון ממש ואין לו (לטעות) [לטעון] ולומר שאף אם קבלוהו לעבוד אצלו אדעתא דהכי הוא כמקפיד על דבר שאינו צריך שרשאי לשקר חדא דאף אם הוא אמת שאין להקפיד הוא ודאי קפידא ובטלה קבלתו וגם שאסור לשקר בכל אופן אף שאינו נוגע לשום דבר דאינו מהתלת מילי דרשאי לשנות (בב"מ דף כ"ג ע"ב) וגם אם ידע שהוא משקר לא היה סומך עליו בכלום ויגרום שיחשוד לאחר כשיחסר איזה דבר דאותו לא יחשוד מחמת שלמד בישיבה ומחזיק לת"ח ואיש נאמן ויסלק להאחר ממשרתו אף שהאמת שהאחר לא לקח ואם היה יודע שזה שלמד בישיבה שיקר לו לא היה בטוח לסלק את האחר ועוד דכאן שמקפידין אינשי ודאי שייך להקפיד דיש ודאי דברים דמי שהוא בקי בלמודי חול הוא יותר יודע בעניני עסקי פרנסה ממשא ומתן וממילא ודאי אסור אף למחשבתו שירויח עי"ז בלמוד התורה שגם בשביל למוד התורה אסור לגנוב ואם חשקה נפשו בתורה אין לו לדאוג שמא לא ידע כל כך ולא יהיה לו סימן טוב עלייהו אבל האמת שאין בזה ענין בטול תורה דמאחר שהולך ללמוד למודי חול הוא רק עצלות בעלמא כשלומד באופן שלא לידע כי הזמן הוא עכ"פ מבטל ואדרבה מתרגל שלא לידע מה שלומד ומתרגל לעצלות
אבל ברור שעצם הדבר ששמע מע"כ הוא שקר משונאי הישיבות ומאלו שרוצים להחריב הישיבות ולהעליל עלילות ברשע כי אדרבה ידוע שבני הישיבה הם מאלו שאף בלמודי חול עדיפי מתלמידים שלומדים בבתי ספר שלהם ואל יחוש להשמועות של שקר אף שהיה נכתב זה בעתון מפורסם לשונא תורה ויראי ה' ויכול מע"כ לומר בפה מלא שהוא שקר וכזב משונאי תורה ודת ישראל
It is a sin, and it's basically a form of theft.
After doing some research, I found out the Guemara brings the concept of Gneivas Da'as, which is the theft of intellect. This site explains very well this concept.
I remember Rav Aviner was asked a very similar question. He answers at the bottom of this page.
To quote him
Question: I heard that it is permissible to cheat, since it isn't "Genevat Da'at" (deception), as the teachers know that cheating occurs, and it would be "a decree that the community cannot live up to [and which therefore is not binding]." Furthermore, in our institution, there's serious competition among the students to be accepted into a particular program, for which math, English, and Talmud are the main subjects, and the students are accepted based on their relative ranking of grades. Since there's rampant cheating in all of the subjects, I am asking if I too may cheat, since it is likely that otherwise I'll be harmed.
Answer: G-d forbid that it is permissible to cheat on tests and the like! It is "Genevat Da'at" (Rambam, Hilchot Deot 2:6), which is a Torah prohibition according to most authorities (Smag, Negative Mitzvah #155), and is included in the prohibition of "Do not steal." This is because "mind-stealing" (i.e. deception) is considered stealing, as it says [when Lavan accused Ya'akov], "You stole my mind" (Bereshit 31:26), and "Avshalom stole the mind of the people of Israel" (Shmuel 2 15:6).
Furthermore, it is possible that one is also violating "Stay far from a matter of lying," which is a much broader prohibition than "Do not lie," as it also includes indirect lying, various strategies, and even indirectly causing a misunderstanding by one's silence -- as we see from all the examples in the Talmud (Shevuot 30-31).
In addition, even without any verse, it is clear that cheating shows a lack of integrity. For a person to study Torah, he must first have integrity -- an ethical character trait that is both elementary and general. Only on its foundation can one build the holiness of Torah. The claim that "teachers know students cheat" does not make it permissible, just as the police's knowledge that there are thieves does not validate theft. In fact, it is the opposite -- the police force uses this knowledge to prevent theft. Similarly, a teacher's knowledge of cheating does not signify approval, but rather the opposite. The proof is that if a teacher discovers a student cheating, he will punish him.
The claim that the prohibition of cheating is "not a decree the community can live up to" also does not apply, because this is not a new decree, but an old decree of the Creator who commanded us to have integrity. Thank G-d, many students do not cheat. As for the concern that you will be at a disadvantage if you do not cheat, this is also not grounds for permission. Many times people of integrity suffer the consequences of their honesty, but "It is better for me to be called a fool all my life than to become evil in front of G-d even for a moment" (Mishnah, Eduyot 5:6). Other people's stealing does not permit you to steal. In the end, the truth will win out and people of truth will be the leaders of the world.
I would like to add to the excellent answer by Gabe12, that even if no specific ruling can be found that cheating on a test is avelut, it does not really matter. It still goes against the principle of Kedoshim tihiyu (And you shall be Holy). Just because something does not seem expressely prohibited does not mean that it is permitted.
The commentary by Rabbi Rosenzweig on torahweb makes a wellrounded point about how this very narrow way of defining averahs is essentially itself an averah.
While Rashi and the Rambam mostly focus on the need to be scrupulous in resisting sin and temptation generally and specifically as it relates to the issue of arayot, the Ramban projects the obligation to cultivate kedushah as a fundamental approach to halachic life. He formulates kedoshim tihiyu as the requirement to strive to internalize halachic values, insuring their application beyond the obligatory norm. He seems to extend this analysis to argue that kedushah relates to the cultivation of a religious personality ("aval ha-perishut hi…she-baaleha nikraim perushim"). Indeed, the Ramban strongly condemns individuals who abuse and exploit the halachic system by scrupulously observing the letter of halachic law, ever the while trampling on its fundamental values and contravening its most sacred principles. Kidoshim tihiyu, as understood by the Ramban, demands that we not only punctiliously observe halachic law but that we embrace a broad halachic worldview.
