Assalamu Alaikum wa rahmatullah wa barakatuhu. I have a question concerning non-muslims at school. 1. Is it permissible to do the homework of a kaafir teacher that told you to do it? 2. Is it permissible to explain something to a kaafir student (while being yourself a student) or he (the kaafir student) explains it to me. 3. Can we joke and talk with this kaafir student, while hating him from inside, and trying to go away from him. 4. If the principle or headteacher is a kaafir and orders you to do something do we listen to him? 5. Is it permissible to call a teacher sir, or miss if she was female. 6. Ruling on knowing how to calculate riba (interest) in maths, but just learning, all of the questions are hypothetical and untrue. (Learning formula for example)
All perfect praise be to Allah, The Lord of the Worlds. I testify that none is worthy of worship except Allah and that Muhammad, is His slave and messenger.
All the things mentioned in the question involve no sin.
As for the first four, they involve no sin because it is not prohibited for a Muslim to extend physical acts of kindness and justice to a disbeliever or help him in doing something beneficial. The prohibited is when a Muslim likes a disbeliever for his Kufr (disbelief) and the falsehood he is following. However, it is allowed to love a disbeliever for a specific reason, such as kinship relations, marriage, their manner of dealing, or for the sake of the knowledge or benefit he offers to others. Such love is not prohibited and it does not contradict hating the disbelievers for religious reasons or disassociating oneself from their disbelief.
As for the fifth point, it involves no sin because the Arabic word “Sayyid” used in the Hadeeth reading: “Do not address a hypocrite with the title ‘Sayyid’,” is translated as (Master) or (Chief) and not (Sir) or (Mr.). The two words (Master and Chief) are titles of glorification and praise that conform to the meaning of eminence and prestige intended in the Hadeeth, meaning a master or chief who is obeyed by people and who has high status, unlike the other two titles (Sir and Mr.) which are merely used as titles of respect and decorum when addressing others.
There is also no sin in the sixth point, because it does not fall under the category of Riba or helping others deal in it. There is nothing wrong in learning how to calculate the interest as part of the curricula, merely for the purpose of study and not to apply it in actual Riba-based transactions.
Allah knows best.
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