I hope so vs I hope to
 

أنا بشرحها بهذا الشكل

Great thanks Ms Huda for your concern, you know that books and notes avoid dealing with this item completely.
So, What do you think of this example written in one of the books.. I hope you pass your exams. - Yes, I hope so.
Is it a correct one ?

I tell my students if there is a verb in the sentence that proceeds we use I hope to but if there is something we use I hope so.This is my own impression .It could be right or wrong

i will explain it to u as i had the same problem before
as mrs huda wrote
will u join the university ?
i hope to

I think your father will be better soon
i hope so

in the first sen. u can complete it by adding join
so u can say i hope to join

in the second sen. u cant say i hope to
as if u try to add a verb after "To" u won't be able to do that
so u use i hope so
in that case so replaces the whole sen.
so u can say i hope he will be better soon

يعني بالعربي بتجيب to لما تقدر تقول i hope to (a verb)
وبتجيب so لما تقدر تقول i hope (sent.)
ده اللي انا اعرفه برضو بعد ما فضلت الحكاية دي مضايقاني حوالي شهر

اه وبتحاول تجرب i hope to الاول يعني لو نفعت الجملة ب to يبقى متحاولش تحطلها so
لو منفعتش تجيب so
يعني لو الجملة تمشي في الحالتين يبقى to اولى