Cameron, who was educated at Eton and Oxford, appeared on the Late Show with David Letterman in what was considered by some in London as a risky move, given the host's biting humour and obvious relish in embarrassing high-profile guests.
Cameron, who announced in a major speech on immigration in Oct 2011 that his government was revising the citizenship test to "put British history and culture at the heart of it", could not answer questions about the Magna Carta and the composer of Rule Britannia.
After fumbling with questions about British history and culture, Cameron, shifting awkwardly in his seat, told the host, "You have found me out. That is bad, I have ended my career on your show tonight".
Letterman, who fired him with questions, first asked him who composed the music for Rule Britannia after the band struck up the music from the Last Night of the Proms. "Elgar," Cameron said uneasily.
"You are testing me," he added. It was the British equivalent of an Indian Prime Minister not knowing who wrote 'Vande Mataram'.
Letterman waited until near the end of Cameron's appearance to point out that Thomas Arne had composed the music and that the poem was by James Thomson. The host then asked him about Magna Carta.
Cameron said "1215," when asked the date it was signed. It took him a few minutes to give the venue where it was signed - Runnymede - but he did not know the English translation for the Latin Magna Carta.
Letterman finally ended Cameron's agony, explaining that it meant Great Charter.
In a major speech on immigration in Oct 2011, Cameron had said, "So let me say one more thing about the journey to becoming a British citizen. We're also going to change the Citizenship test. There's a whole chapter in the Citizenship handbook on British history, but incredibly, there are no questions on British history in the actual test".
He added, "Instead, you'll find questions on the roles and powers of the main institutions of Europe and the benefits system within the UK. So we are going to revise the whole test and put British history and culture at the heart of it".
British newspapers on Sept 27 had a field day reporting on Cameron's inability to correctly answer the questions and hoped that he would not be asked to sit a citizenship test at Heathrow when he returns from his visit.