The tests were administered by the school and consisted of maths, verbal and non verbal
The tests vary from school to school, as it is up to them what they examine. (Some might test curriculum subjects only, e.g. English, Maths, Science, some use a mixture, and at least one - I think - uses reasoning tests only.)
Except where immediate entry is being sought (by families moving into the area), tests for year 10 entry are usually taken during the summer term of year 9 (at the individual grammar schools).