Would-be 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 resits 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.
Official figures show that rising numbers of trainee teachers are passing the tests on the first attempt. In 2010/11, 30,624 people passed the literacy test on the first go, compared with 29,266 the year before. Some 1,903 people took three or more attempts, down from 2,483 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."
Christine Blower, general secretary of the National Union of Teachers (NUT), said: "All teachers need strong literacy skills and also a good grasp of mathematics. It is however surprising that Michael Gove is showing such interest in the entry requirements for teacher training courses, while at the same time advocating that schools should be free to employ unqualified teachers.
"The real issue is the training and support that teachers are given once they have entered into teaching training. All too often the Government is looking at ever shorter routes to qualifying as a teacher, including on the job training in schools. This leaves little opportunity or time for trainee teachers to be able to learn about child development and pedagogy in depth."