Sometimes during the exam the student is asked to quote a verse from the Qur’an, and because he has forgotten a letter or a word, he deliberately substitutes another word for the word that he has forgotten, because he wants to pass the exam and is afraid of failing. Although he knows that what he has written is a distortion, his aim is not really to distort the Qur’an; rather it is because he is afraid of failing, so he put that word in the place of the word that he had forgotten of the Qur’an.

Is this regarded as distorting the Qur’an which would mean that the student has gone out of Islam?

Praise
be to Allah.

In the answer to question no.
158204 we stated that if a person makes a mistake
in reciting a soorah, or forgets something of it, whilst he is praying, then
he should try to correct the mistake and remember what he forgot. If he is
not able to do that, then he may skip that verse and move on to the next
one, or he may stop reciting that soorah and start reciting a different
one. 

But if he adds to the Qur’an
something that is not part of it deliberately – whether that is during the
prayer or otherwise, then this is emphatically forbidden and the scholars
have stated that whoever omits a letter of the Qur’an or substitutes a
different letter or adds a letter has committed an act of kufr. 

Al-Qaadi ‘Iyaad (may Allah have
mercy on him) said: 

The Muslims are unanimously that
the Qur’an which is recited in all corners of the earth, and is written in
the Mushaf between the two covers by the hands of the Muslims, from the
beginning of Soorat al-Faatihah to the end of Soorat an-Naas is indeed the
word of Allah and His Revelation that He sent down to His Prophet Muhammad
(blessings and peace of Allah be upon him); that everything in it is truth;
and that anyone who deliberately omits a letter of it, or substitutes one
letter for another, or adds to it a letter that is not included in the
Mushaf on which there is consensus, and there is consensus that it is not
part of the Qur’an, has committed an act of kufr.

End quote from ash-Shifa,
2/304-305; see also at-Taqreer wa’t-Tahbeer by Ibn Ameer al-Haaj,
2/215 

It says in al-Mawsoo‘ah al-Fiqhiyyah,
35/214: The Qur’an is the word of Allah, the miracle that was sent down to
the Messenger of Allah (blessings and peace of Allah be upon him), and was
transmitted by means of tawaatur (i.e., it was narrated from so many people
by so many people that it is inconceivable that they could all have agreed
upon a lie). It is haram to deliberately make mistakes in it, whether that
changes the meaning or not, because its words and phrases are tawqeefi
(i.e., to be accepted and recited as they were revealed, and they cannot be
altered) and it was transmitted to us by means of tawaatur. It is not
permissible to change any word of it by altering the vowels or changing the
letters, replacing one letter with another. End quote. 

Based on that, it is not
permissible for a student to write a word or a letter that he knows is not
part of the Qur’an or that does not belong in this verse; rather he should
either try hard to remember, or he should leave the parts that he has
forgotten blank. He can also apologize for that by explaining that he forgot
where this word goes and that he did not want to write something of which he
was not certain in this case. 

And Allah knows best.