Remember 3 other important test-driving rules:
Ignition: Turn the key and see if the car starts easily. Is it easy to remove the key? As you start the ignition, the airbag light should switch on and then off.
Transmission: Pay attention to transmission shifting, make sure it is easy and has no clunks or whining sounds. If it’s an automatic, shifting from park to drive must be easy.
Alignment & rims: Find a flat spot and when the road is safe and nobody is driving close to you, take your hands of the steering wheel and see if it pulls to the left or right. If it does, this car has alignment problems. A shaking steering wheel implies bent rims, that will be a big problem while driving at high speed. Rims can be straightened out and then balanced, but that means extra expenses. And of course, the rim will be slightly weaker where it was bent.
Wheel bearings: Listen for howling sounds coming from the wheels, that means bad or worn down wheel bearings. Take 2 medium speed gentle turns to the left and right and listen for humming noises coming from front wheels. This also means that the bearing are about to go bad.
Shocks, joints and stabilizer links: Rind a spoiled, uneven part bumpy part of the road, listen for noises coming from the front end. That mean bad bolt joints, bad shocks or just bad stabilizer links (the latter is easier and cheaper to replace). Some cars have stabilizer links in the rear end, so pay attention to sounds coming from there. The car shouldn’t wiggle.
CV joints: If it’s front wheel drive, take it around sharp corners in both directions and listen for clicking sounds coming from CV joints. They won’t be repaired, only replaced.
Dashboard: make sure the engine, airbag and ABS lights are not on, check speedometer and other device readings.
Engine & brakes: Find a long, flat spot on a highway, press the acceleator hard, speed up to 60mph. See if the motor is still running smooth. Press the brakes (of course, you should warn the owner before doing so). The brakes must feel firm. This test helps to learn if the car has front-end alignment problems. Again, see if it pulls to the left or right, which indicates alignment problems.
Stereo: don’t play it loud all the way, you have to listen attentively to other noises. Add volume several times to hear if there is distortion in the speakers..
Climbing: Check if the car climbs easily on a long rise and if the engine sounds normal.
Park the car. Check the visibility because parking environment visibility resembles that of a busy highway.