Our pre-sch does what's already been said plus...
Writing: attempting to mark paper with pen, form letters (possibly with a pencil but also 'writing' in sand with finger etc), hold pencil correctly.
Reading: learn to recognise own name (useful for clothing labels, cloakroom peg etc), first letter sounds - ie. dog begins with 'duh' (and not the hard sound 'dee'), recognise some of the alphabet.
Maths: Counting sing-song style up to 20ish, counting items by pointing at each one individually up to about 10 or so. Knowing basic 2D shapes. Knowing 'bigger than' 'smaller than' and sorting into size order.
Science: can't remember!
Other: Colours, joining in with group activities, attempt to use scissors, have some independence in choosing activities and getting on with it, speaking in front of others.
All our children have Profiles which their key workers write comments in, tick boxes and generally monitor learning - it is handed to their Reception teacher when they go up to school.
But they don't HAVE to learn any of this. We have children that leave that can tell the time and count backwards from 100 and add-up and we have children that leave that don't know what letter their name begins with or know grey from pink. By the end of Year 1 or 2 they are all mostly at similar levels.