Checklist when looking at a 2nd hand car - anything to add?

[Hodders]

Looking to get a small car for my kids to learn to drive in.

There is a Hyundai i10 locally that is insurance group 01a. 8 years old, 40k miles at a decent price.

Seller is upgrading after finishing uni, car has been in family since new.

Everything checks out on vcheck. MOT has 7 months to run. Partial service history.

I've got a sort of check list below - anything I can add?

MOT will spot stuff like worn/thin brakes, split gaitors. Emissions test would hopefully spot any gasket issues.

So my list of pokes and prods is fairly limited:

Check V5 matches VIN
Check V5 registered keeper ID
Check engine number
Check 2 keys
Locking wheel nut

Receipt

Check air-con works
Any dashboard lights
Seatbelt warnings
Electrics - windows, wipers etc
Spare tire
Road tires for uneven wear/damage
Oil level and filler cap for mayonaise
Exhasut on cold start-up
Check all lights
Engine compartment/driveway free of oil leaks

My insurance does cover me to drive another vehicle 3rd party - so I guess:

Lock to lock - check for noises
Smooth gear change
Clutch bite point and slipping
Brake straight no pulling
Check hand brake