i trust my mom, and she trusts me, that is enough for her. and about making a mistake and not telling her, it's no need for that, she always says "that is what mistakes are for, if i'll always tell you that this is wrong and this is right it's only going to confuse you, you have to realize yourself if you did a right or wrong thing."
and if you do make a mistake, since mistaking it's only human, no one will cut off your head even if your parents might scold you, at least my mom always encourages me when i fail an exams, since i'm feeling totally down saying " it's not the end of the world, that is what exams are for, to pass or fail", so i can freely talk to her about anything.