A new version of the test taken by foreign nationals who wish to become UK citizens "focuses on values and principles at the heart of being British", the Home Office has said. The revised 'Life in the UK' test covers topics as sport, music and history.
The Migrants' Rights Network said the test was "like an entry examination for an elite public school".
The new handbook will form the basis of the modified 45-minute exam being introduced in March, which all those wishing to attain British citizenship must pass.
The overhaul of the test is aimed at focusing less on the practicalities of daily living in Britain and more on the nation's culture and past.
Ten sample questions offered by the Home Office include "Which landmark is a prehistoric monument which still stands in the English county of Wiltshire?" and "What is the name of the admiral who died in a sea battle in 1805 and has a monument in Trafalgar Square, London?"
The Home Office said the test and handbook had been "completely re-written, removing questions on topics that those living in the UK should already be aware of like public transport, credit cards and job interviews".
Immigration minister Mark Harper said: "We've stripped out mundane information about water meters, how to find train timetables, and using the internet.
"The new book rightly focuses on values and principles at the heart of being British. Instead of telling people how to claim benefits, it encourages participation in British life."
He added: "This is just part of our work to help ensure migrants are ready and able to integrate into British society and forms part of our changes which have broken the automatic link between temporary and permanent migration.
"We have made radical changes to the immigration system and are determined to reduce net migration from the hundreds of thousands into the tens of thousands by the end of the Parliament."
But Don Flynn, director of the Migrants' Rights Network, which campaigns in support of migrants in the UK, said: "This looks to us like a big step backwards from the concerns with integration which the government is supposed to have in this area.
"Naturalisation procedures have already been sharply criticised for coming up with tests which have very little to do with the things that most British people feel are important about their lives.
"Now the Home Office has come up with something that looks more like an entry examination for an elite public school. It is very difficult to think that this is a positive move."
However, Alp Mehmet, of the MigrationWatchUK think tank which is concerned about the scale of immigration into the UK, said the "underlying principle and thought process" behind the citizenship test was "absolutely right".
"People who want to come to live in this country should know a little about the country they're joining," he said.
More than 150,000 Life in the UK tests were taken nationally last year, with 77,000 of those in London.
Labour's Chris Bryant said the home secretary was "missing the point".
"Having a citizenship test that teaches people about life in the UK is important, but Theresa May has many other issues in her department that are far more important to focus on," the shadow immigration minister said.
"Rather than coming up with gimmicks, Theresa May should be spending her time sorting out the chaos at the UK Border Agency or finally finding a director general for UK Border Force. She should be focusing on fixing the big problems in her department not wasting time on rewriting the citizenship test."