Here’s a thing, no amount of puja and prayers will help you score good in exam if you haven’t prepared for it. And also, you wouldn’t need to obsess god and the chants before exam if you are well-prepared.
Nothing can replace hard work. So study hard and give exam. Have faith in God that S/He will look after your goodwill. But don’t obsess and overly rely on them, thinking it would help you score big. Remember, God only helps those who help themselves.
As for your question, of course, worshipping Maa Sarasw
Chanting Gayatri Mantra 108 time’s also brings good vibes. It not only keeps you focused but also keeps your morale high.
Putting Chandan tikka and doing diya regularly also helps.
Don’t do any extravagant puja that requires money and time. The money and time you save here, invest that in helping other in-need people like street side dwellers and poor.
Contrary to the popular belief of Pundits and religious leaders, this will appease God even more than a pretentious puja.
Have God in your heart, work hard and see good things follow without any formal puja. If things don’t go right this time on your result day, have faith in yourself more than the God for the next term.
Not only this, every action he performed in Ramayan will teach us something.
Lord Hanuman is the symbol of strength and self confidence. Blessings of him will help us to face any hurdles in life :)
For kids, I would suggest the mother or father are the prime Guru. If it's the mantra, then parents can approach a capable guru, under supervision learn and then transfer it to the children. Else, I would suggest reading, 15 poem of Soundarya Lahari regularly without mistakes. This will definitely help your kids in building good memory, concentration, Bhakthi and improve speech.