How to "know" if I have a passion?

If you were really passionate about something, you'd know because you'd want to do it in exclusion of all else. You think about that thing even if you're bathing, eating, etc.

Having said that I can understand what you're asking because if we define passion this way, precious few people would be passionate about anything that they can actually make a living from. That includes academics - e.g. this question

I just want to get married, and have weekends and evenings off, and chill out and play board games, and have nice conversations with friends, and have time to exercise and eat good food, and partake in hobbies, and read books and play computer games and watch movies and write a novel or two.

And from there it's just a short way to "I just want to get married and have my entire week off ..."

So now what? I suggest:

1. Can you imagine yourself doing it as a career? You don't have to like it more than board games, conversations with friends, etc, but you should like it enough that you can do it for upwards of 40+ hours a week. On the other hand if it starts getting painful to go to work every day, it's not a good idea to do it.
2. Are you good at it? If you are, then you can get results even if you aren't passionate (by above definition) about it.

It may not be a popular position, but you can certainly base your career around things that you aren't passionate about (by above definition). For example, my mother became a doctor because that's traditionally what all good students at her high school did. She didn't particularly like it any more than other careers, but she studied it, did well at it, became a trained doctor, became a specialist, and eventually managed her own department. She would often complain about her work at the dinner table, and talk about e.g. how she would rather teach language at a local high school, but by all metrics she still had a successful career.

I suppose the point of this answer is to reject the notion that having a passion for area X is any sort of prerequisite for working in area X and having a successful career. I should make clear that I'm an assistant professor of mathematics at Oberlin College, a small liberal arts college in northeastern Ohio. My job affords me a balance between teaching and research that I love and wouldn't give up for the world. Whether this counts as success is obviously a matter of opinion.

Throughout college (and grad school) I met math majors that knew they wanted to study math for the rest of their lives from the age of 12 or 13. Myself, I became a math major because my engineering pre-major advisor thought that taking two math classes in the spring of my freshman year was a bit much and thus I registered for five math classes to spite her. I had many interests as an undergraduate (mostly in history, foreign languages and literature), and feel that I probably could have gone on to a successful career in any number of them that I would have ultimately found rewarding.

Now there's no way to get around the fact that to succeed in grad school you're going to have to work very hard. In fact you'll probably work so hard that you'll convince yourself that it's a blessing you're even being paid because you'd gladly do this work for free.

I guess my point is that if you really enjoy a field and have a talent for it then you shouldn't discount going on to grad school for it. Even if your passion for the subject doesn't coincide with the romantic notions of some of your classmates. At the end of the day hard work is likely the stronger predicter of success in any event.

Most students encounter a life-changing decision during their undergraduate years. That is either to choose a high-paying career, yet such that they might not be passionate about or a career they like but is unlikely to be high paying.

This is false, on many levels:

• Students face the choice of what to do after having finished their studies. You don't choose your entire career at once (although certain choices obviously draw you away from certain career paths).
• Passion is not something binary (have it / don't have it), nor even a spectrum (have zero, little, lots, maximum passion). People have mixed and ambivalent feelings about their pursuits.
• In a sense, you can usually not really develop passion for something you will do later in life - in your actual career - when it's not what you do during your studies. As a student, you study, you don't practice. (Exception: Some degrees have a practical experience phase.)

Now my question is, What is the sufficiency precisely in this context? ...I think I feel passionate for mathematics.

That's rather general and abstract. It may be enough to consider an M.Sc. (if that's customary in your country; in some countries, those are discouraged as opposed to direct Ph.D. tracks) - you'll spend 2-3 years on getting deeper into one particular subject and experiencing research in math. Actually, that's not a very representative experience of what research is like later, but it should be enough to help you decide if you're really into it.

Alternatively - try to think of something you would like to use math for, or apply math in. If there is something like that - consider looking for relevant work in that field. That might arouse your "passion" either for more applied, industrial work or for more academically-oriented research work.

How can I come to "know" whether I truly have a passion for mathematics or whether I was merely deluded into thinking that because I was made to feel that I am good at mathematics by the relevant education system?

You're assuming these two options are distinct. Have you considered they might overlap, or be one and the same? At any rate, my suggestions above are what I'd do to be able to better know.