Teachers will have to complete English essays and answer questions on maths topics including algebra before they can start training, it has been announced.
Ministers have unveiled details of plans to overhaul tests taken by prospective teachers, saying they want to raise the status of the profession.
Under the proposals, from next September, anyone who wants to train as a teacher will have to complete revamped tests in English and maths.
A paper on verbal, numerical and abstract reasoning is also due to be introduced in the next few years.
Calculators will not be allowed and the pass marks for both the English and maths tests will be raised again, the Department for Education (DfE) said.
The plans have been recommended by a review group of headteachers and education experts, which was set up in March.
The government said at the time they wanted to toughen up the tests taken by trainee teachers due to concerns that many took several attempts to pass.
The current tests, in literacy and numeracy, are taken towards the end of teacher training, with the latest figures showing that 98% of people pass.
From this autumn, trainees have been limited to two re-sits for each paper and the pass mark has been raised for the first time.
It is to be raised again over the next three years, with candidates eventually needing to score the equivalent of a grade B at GCSE to pass, the DfE said.
The new maths test is likely to include questions on topics such as algebra and graphs, while the English paper will ask candidates to answer open-ended questions, with marks for spelling, punctuation and grammar.
The new tests were unveiled as Liberal Democrat education minister David Laws said teachers were failing to encourage pupils to "reach for the stars" and show students top roles are not unobtainable.
“Teachers, colleges, careers advisers have a role and a responsibility to aim for the stars and to encourage people to believe they can reach the top in education and employment,” Mr Laws told the Daily Telegraph
“That’s not happening as much as it should do at the moment.
Teachers were blamed holding back children, leaving them with "depressingly low expectations" of what they could expect to achieve in life.
Official figures show that rising numbers of trainee teachers are passing the new tests on the first attempt.
In 2010/11, 30,624 people passed the literacy test on the first go, compared to 29,266 the year before. Some 1,903 people took three or more attempts, down from 2,483 in 2009/10.
Some 29,531 candidates passed the numeracy test at the first attempt, up from 29,287 in 2009/10.
A total of 3,329 took three or more goes, up slightly from 3,313 in 2009/10.
Education Secretary Michael Gove said: "These changes will mean that parents can be confident that we have the best teachers coming into our classrooms.
"Above all, it will help ensure we raise standards in our schools and close the attainment gap between the rich and poor."