The 13+ usually refers to an entrance exam taken by children in Year 8, aged 12-13, who plan to enter a school at Year 9. However, "13+" is an umbrella term which can apply to any of the following:
i) The 13+ Common Entrance exam set by ISEB.
This consists of up to ten subjects. English, Mathematics and Science papers are always sat, and students take additional papers on humanities, languages and classical subjects. The syllabi can be viewed here. Unfortunately, sample papers are not free, but must be purchased from Galore Park.
The Common Entrance exam is still used by many top schools including Eton, St Paul's and Westminster. However, in the last ten years many schools have begun to also set pre-tests, which are taken in Years 6, 7 or 8. The pre-tests are often considered the 'sticking point' of the admissions process, with the Common Entrance mark just acting as a fail-safe to be sure the student has not slacked off since.
ii) Individual 13+ entrance exams set by the school
These exams almost always include a Mathematics paper, an English paper, and may include reasoning or science. Schools often make these papers freely available each year, and well established tutors will have a large database of past papers. These papers might be quite different in style to one another, although they all test the same core knowledge. Examples:
City of London School for Boys Maths Paper
City of London School for Boys English Paper
iii) The 13+ pre-test
The pre-tests for 11+ and 13+ can also be referred to as "the 13+". This usage is less common, and, in my opinion, liable to promote confusion. If discussing pre-tests, the term "13+ pre-test" is preferable. For more about pre-tests, please click here.
GETTING HELP
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I prepare my students for the specific exam they will be sitting, as well as working to develop the whole child academically. This means they will be fully ready for life at public school as well as for the tests.