David Cameron stars on Late Show with David Letterman
David Cameron has become the first serving British prime minister to appear on popular US chat show the Late Show with David Letterman.
Mr Cameron faced questions on British history and culture during the show, which aired on Wednesday in the US.
The PM got many questions right but was unable to say what Magna Carta meant in English or who wrote the words and music of Rule Britannia.
Earlier at the UN, he appealed to world leaders for more action on Syria.
In the keynote speech to the General Assembly, he cited a recent report documenting torture and murder of children by regime forces and said more should be done to stop the "atrocities" of president Bashar Assad's government.
He also urged leaders to back the emerging democracies of the Arab Spring.
'A falling out'
Mr Cameron had planned to use his subsequent appearance on the Letterman show - one of the most watched in the US with some three million daily viewers - to "bang the drum" for British business and encourage Americans to visit the UK.
Mr Letterman has been a prominent fixture on late night US television for 30 years. Past political guests include Barack Obama, London Mayor Boris Johnson and Tony Blair, who has appeared twice since leaving 10 Downing Street.
In Wednesday's show, Mr Cameron was welcomed by a band playing Rule Britannia, and dry ice being pumped into the studio to represent a London fog.
Asked briefly about the Arab Spring and his UN trip, the prime minister then faced questions about the composer of Rule Britannia, guessing incorrectly at Edward Elgar.
The right answer, he was informed by Mr Letterman, is Thomas Arne - setting words by James Thomson to music.
Mr Cameron was also unable to provide an English translation of Magna Carta, which means great charter.
Hesitating before naming Runnymede as the place it was agreed, he correctly answered 1215 as the date the Magna Carta was drawn up and told Mr Letterman about its significance in the origins of democracy.
The show's host later questioned Mr Cameron about Britain's four nations.
Mr Letterman said: "What is the deal on Wales? Did they vote for you, the people of Wales?
"Some of them did," Mr Cameron replied.
The prime minister raised a laugh in the studio when he joked about the UK's relations with the US.
"There were some good bits and some less than good bits, and obviously we had a bit of a falling out. I like to think we've got over that now."
'Not very popular'
During the programme, Mr Cameron also drew cheers from the audience when he mentioned London's hosting of the 2012 Olympic and Paralympic Games.
But he avoided commenting on US Republican presidential candidate Mitt Romney, who had questioned London's preparations for the Games.
"The idea that two major world class athletics events took place in London... who would have bet against that going off flawlessly, as it seems to have done?" Mr Letterman asked.
Mr Cameron prompted the loudest applause of the evening when he explained that Britain does not allow political advertising, a big issue in the US where multi-billion dollar attack ads are being used in the presidential campaign.
However, he added that he was first recognised in the US because of television, when a passer-by spotted him on a New York street and shouted: "Hey, Prime Minister's Questions - we love your show."
Mr Cameron later said he wanted his appearance on the Late Show with David Letterman to help "bang the drum" for British business in the US.
He spoke about the creation of one million private sector jobs by his government over the past two years.
But he also admitted he is "not very popular at the moment", pointing to austerity measures and cuts as a possible explanation for his low ratings.
In a keynote speech to the United Nations General Assembly earlier, he urged world leaders to take more action to stop the "atrocities" of President Bashar al-Assad's government in Syria.
A recent report documenting the torture and murder of children by regime forces was a "stain on those who have failed to stand up" to Syria, he added.