Praise be to Allah.
The Ramadaan fast is one of the pillars on which Islam is based. Al-Bukhaari (8) and Muslim (16) narrated that Ibn 'Umar (may Allaah be pleased with him) said: The Messenger of Allaah (peace and blessings of Allaah be upon him) said: “Islam is built on five (pillars): the testimony that there is no god except Allaah and that Muhammad is the Messenger of Allaah; establishing regular prayer; paying zakaah; fasting Ramadaan, and performing Pilgrimage to the House (the Ka’bah).”
Whoever does not fast has abandoned one of the pillars of Islam and has committed a grave major sin. In fact, some of the salaf were of the view that such a one is a kaafir and an apostate – Allaah forbid.
Al-Dhahabi (may Allaah have mercy on him) said in al-Kabaa'ir (p. 64):
The believers are unanimously agreed that whoever forsakes the Ramadaan fast when he is not sick and has no other excuse for that is worse than an adulterer or one who is addicted to alcohol. They doubt whether he is a Muslim and they think of him as a heretic and deviant. End quote.
As for breaking the fast because of exams, Shaykh Ibn Baaz (may Allaah have mercy on him) was asked about that and he replied:
It is not permissible for an adult of sound mind to break the fast during Ramadaan because of exams, because that is not one of the excuses permitted in Islam. Rather he has to fast and do his studying at night if it is hard for him to do it during the day. Those who are in charge of exams should be kind to the students and arrange the exams at a time other than Ramadaan, so as to serve two purposes: the purpose of fasting and that of giving students time to prepare for the exams. It is narrated in a saheeh report that the Messenger of Allaah (peace and blessings of Allaah be upon him) said: "O Allaah, whoever is appointed over any of my ummah’s affairs and treats them kindly, treat him kindly, and whoever is appointed over any of my ummah’s affairs and treats them harshly, treat him harshly." Narrated by Muslim in his Saheeh.
So my advise to those who are in charge of exams is to be kind to the students and not organize the exams in Ramadaan, rather to do them before or after that. We ask Allaah to guide us all. End quote.
Fataawa al-Shaykh Ibn Baaz, 4/223.
The Standing Committee was asked: I am going to be tested in Ramadaan for a period of 6 and a half consecutive hours, with a 45 minute break. I did the same test last year, but I could not concentrate because of fasting. Is it permissible for me to break the fast on the day of the test?
They replied: It is not permissible to break the fast for the reason you mentioned, rather that is haraam, because it is not included among the excuses for which it is permissible to break the Ramadaan fast. End quote.
Fataawa al-Lajnah al-Daa'imah, 10/240.
With regard to whether it is obligatory to make up the fasts, it depends.
If you broke the fast because you thought that it was permissible to do so because of the exams, then you have to make it up, because you are excused for this mistaken thinking, and you did not deliberately commit a haraam action.
But if you broke your fast and you knew that it was haraam to do so, then you have to repent and regret this sin, and resolve not to commit this grave sin again.
As for making it up, if you broke the fast during the day after having started to fast, then you have to make it up, but if you did not fast at all, then you do not have to make it up, and it is sufficient to repent to Allaah sincerely. And you have to do a lot of righteous deeds such as observing voluntary fasts etc; that will make up for the shortfall in fulfilling the obligatory duty.
Shaykh Ibn 'Uthaymeen (may Allaah have mercy on him) was asked about the ruling on breaking the fast during the day in Ramadaan for no legitimate reason.
Breaking the fast during the day in Ramadaan for no legitimate reason is one of the worst of major sins, because of which a person may be regarded as a faasiq (disobedient, rebellious) who has to repent to Allaah and make up the day when he broke the fast. I.e., if he fasted then during the day he broke his fast with no excuse, he has committed a sin, and he has to make up that day because when he started that fast, it became binding on him to complete it, so he has to make it up, like a vow. But if he did not fast at all, deliberately and with no excuse, then the correct view is that he does not have to make it up, because that will not benefit him at all, as it will never be accepted from him. The basic principle with regard to acts of worship that are connected to specific times is that if a person delays them beyond that specific time with no excuse, they will not be accepted from him, because the Prophet said: "Whoever does a deed that is not in accordance with this matter of ours, will have it rejected." And because it is a transgression of the sacred limits of Allaah, may He be glorified and exalted, and transgressing the sacred limits of Allaah is zulm (wrongdoing), and no deeds are accepted from the zaalim (wrongdoer). Allaah says (interpretation of the meaning):
“And whoever transgresses the limits ordained by Allaah, then such are the Zaalimoon (wrongdoers)”
If he does this act of worship early – i.e., before the time for it begins – it will not be accepted from him, and similarly if he does it after that, it will not be accepted from him, unless he has an excuse. End quote.
Majmoo' Fataawa al-Shaykh Ibn 'Uthaymeen, 19; question no. 45.
You have to repent to Allah for delaying making up the fasts all these years. The one who owes days from Ramadaan has to make them up before the next Ramadaan begins. If he delays that, he is committing a haraam action, but does he have to offer the expiation of feeding one poor person for each day because of this delay? There is a dispute among the scholars concerning that, but the most correct view is that he does not have to do so, but if he does that in order to be on the safe side, that is good.
See the answer to question no. 26865.
To sum up:
You have to make up the fasts if you thought that it was permissible to break the fast because of the exams, or if you broke the fast during the day, but you do not have to offer expiation as well as make up the fasts.
We ask Allah to accept your repentance.
And Allah knows best.