In quiz bowl, this is a common abbreviation for "For Ten Points" as used at the end of questions. Most questions used in NAQT-style tournaments have a pyramidal structure, where the most obscure facts come at the beginning and the giveaway is towards the end. Questions (sometimes) have a power mark, before which the question is worth 15 points; around the time FTP is encountered, many average players might be able to get it.
To demonstrate where FTP might be used, here's a sample question (from the packet at http://www.naqt.com/IS-packet.htm)
His unrestricted personal life and literary lyricism earned him comparison to fellow poet Lord Byron, and like Byron he denounced the reactionary movement which had set in after the Napoleonic Wars. During his exile in southern (*) Russia, he wrote The Prisoner of the Caucasus, which followed his first major work, Ruslan and Ludmila. FTP name this poet, who took many of his themes from Russian folklore and was killed in an 1837 duel after writing the verse drama Eugene Onegin.
answer: Aleksandr (Sergeyevich) Pushkin
Variants of FTP include FAQTP (For A Quick Ten Points), FFP or F5P (For Five Points), F15P (For Fifteen Points), FTPAP (For Ten Points APiece) and FTSNOP (For The Stated Number of Points; pronouced "fits-nop").