Assalaamu alaykum wa rahmatullaahi wa barakaauhu. I have heard that if I say, for example, 'I will fail the exam', and the angels that are with me say, 'Ameen', then Allaah will really make me fail; is this true?

All perfect praise be to Allah, The Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad is His slave and Messenger. 

We are not aware of any evidence which indicates that this statement is true.

A Muslim should have good expectations of Allah, hope good from his Lord, and ask Him of His Favor.

It is not permissible to supplicate against oneself or one's family or wealth, lest this would coincide with a time when Allah responds to supplications, and then one’s supplication would be a reason for the occurrence of evil.

Jaabir, may Allah be pleased with him, narrated that the Prophet said, “Do not supplicate against yourselves or against your wealth or your children, lest you happen to do that at a time at which when Allah is asked for something, He grants it, and thus He answers your supplication.” [Muslim]

For more benefit, please refer to fatwa 197743.

Allah knows best.