I need help finding examples of hopelessness and hope in "A Raisin in the Sun" by Lorraine Hansberry in Act 1

Answer 1

I haven't read this work, but if you read the first of the themes here, you should get some ideas:
http://www.sparknotes.com/lit/raisin/themes.html

Answer 2

I can't pinpoint them by page (your pagination Is probably different than the copy I have), but look at Mama's speeches for hope, her son's for both (his dreams are hopeful), Ruthie's for some hopelessness or disdain for her husband's dreams.