Pupils will be expected to memorise maths formulae and concentrate more on spelling, punctuation and grammar

The new curriculum for GCSE maths will see pupils in England spending more classtime studying the subject and memorising mathematical formulae, such as Pythagoras's theorem.

The revised maths curriculum – which comes into force in September 2015 – expands the range of topics that pupils are expected to learn, while the new curriculum for GCSE English literature and language courses will place a greater emphasis on spelling, punctuation and grammar.

The education secretary, Michael Gove, said the introduction of a more demanding maths curriculum was to improve the attainment of pupils in England compared with their counterparts in other advanced industrial countries.

"The new mathematics GCSE will be more demanding and we anticipate that schools will want to increase the time spent teaching mathematics," Gove said in a written statement to parliament announcing the changes on Friday.

"On average, secondary schools in England spend only 116 hours per year teaching mathematics, which international studies show is far less time than that spent on this vital subject by our competitors. Just one extra lesson each week would put England closer to countries like Australia or Singapore, who teach 143 and 138 hours a year of mathematics respectively."

According to the Department for Education (DfE), the new maths syllabus adds a section on ratio, proportion and rates of change, as well as vectors and conditional probability. Students will have to learn key formulae, such as the quadratic formula, sine and cosine rules. Under the existing syllabus, the formulae are provided in exam papers.

An international survey of adult skills published last month found that 16- to 24-year-olds in England ranked 21st for numeracy out of 24 countries. Pupils in England were ranked 27th in maths in the international assessment known as Pisa conducted by the Organisation for Economic Co-operation and Development in 2009.

The new curriculum for GCSE English literature will see pupils studying at least one play by Shakespeare, at least one 19th century novel, a selection of poetry since 1789 that includes Romantic poetry, and British fiction or drama from 1914 onwards. The revised exam will require the analysis of unseen texts, which the DfE says will reward students who have read widely.

The new English language course requirements increase the proportion of marks awarded for accurate use of spelling, punctuation and grammar. It will award 20% of exam marks for spelling, punctuation and grammar, compared with 12% under the current requirements.

"The new GCSEs in English and mathematics set higher expectations. They demand more from all students and provide further challenge for those aiming to achieve top grades," Gove said.

The revised curriculum comes alongside details of new GCSE examinations announced by the exam regulator, Ofqual. The exams – which will first be taken for maths and English in 2017 – will end the use of A* to G letter grades in favour of a numbered scale from nine to one, with nine being the highest grade.

Ofqual confirmed that course modules and assessment would be dropped, with grades determined by a single end-of-course examination for most GCSE subjects.

The DfE said it wopuld announce the revised curricula for most of the remaining GCSE subjects in spring next year.