Check the exhaust. Turn on the ignition, on neutral step on the
accelerator a little, get someone to check for any black smoke
coming out or chopper sound(burst exhaust).
Check the radiator and its tung kee for any leakage. You can look
below the vehicle under the bonnet. You can look out for any green
patches(coolant) on the floor and the engine parts. When you turn
on the ignition, the radiator fan should start running and not run
only when you turn on the air con.
Check the handbrake. Pull up the handbrake, should not be more than
three clicks, step on the accelerator a little on first gear, the
vehicle should be prevented from moving off. If the handbrake is
not secure(too many clicks), you'll need to get a mechanic to
tighten it.
Bring the vehicle out for a test drive to feel the overall. When
making a U turn or a junction turn, look out for any 'greg greg
greg' sound coming from the front wheels. If there is some sounds
and vibration, the front shafts are wearing off and will need to
change a pair which can be quite costly. When driving on a straight
road, lift your hands off the steering wheel for a short while and
look out whether your vehicle starts swerving off its track. if the
swerving is substancial, your wheel alignment needs to be adjusted.
Look out for any 'king klunk' sound during gear
engagement(gearbox). Importantly, check the brakes. Look out for
any hissing sound from the front wheels when braking gradually. The
hissing sound could mean the brake pads have worn off.
For some cars, the dealers would already have it accessed by an
accessing centre and such cars have a certificate of accessment.
Alternatively, you can bring the car of your choice to any
accessment centres for a small fee if you are not sure what to
check.