Even on critical patients don't rush in and out: hurrying makes you forget things, gives you a chance to trip over something, and make you look like a goof in front of people.
Work out a way to evaluate every patient; and do it the same way every time. do it with family members and friends and co workers until you can do it in your sleep, because there will be times that you will be asleep and doing it.
Mine is: (no matter what the incident, trauma, (even on sprained ankles), medical, etc.
Check what outside of house and inside of house looks like on way to patient: (look to see if there is junk all over, if rotting food is lying around, mouse/rat droppings etc {look to see if Social Services need to be notified after run}).
As you walk up to patient introduce yourself in normal tone of voice, and ask their name and what happened: if they look at you and respond normally it tells you what their mental state is and if they understand english or can even hear. Also, look for skin color, respiratory effort (normal person wont be working to breathe)
Squat down next to them (if they are sitting) (especially if they are pedriatic) and slowly reach out and check a pulse in wrist: don't check for actual heart rate; I am checking to see if they have a pulse in wrist, if it is rapid or slow, weak or strong, regular or irregular. Also tells you skin temp (hot, cool), condition ( dry, or diaphoretic). Also check to see how long cap refill is when you release their wrist (CR doesn't have to be done in nail bed)
Continue to talk to the patient, letting them know what you are doing "Mrs Jones I am going to check your pulse for a few seconds" while you are doing this you can also ask more details of what happened, and when it started, what makes it better or worse, etc.
Like I said do it with every patient every time, and it works great, less than 30 seconds and you know their mental state; skin color, temp, condition, basic pulse info, cap refill and the basics of what happened or why they called you today
and also remember that yes you are responding to a "emergency" but not every call you are rushing in and out because a pt is critical. Take your time get all the info you need and slow down everything from patching over the radio to moving your own body. Always be early and particpate actively in rig check familarlize yourself with the ambu equipment, if in between calls instead of watching tv go out just go check out the ambu. Also very important if you don't know how to do something or cant here at BP NEVER fake a reading! just ask your partner to double check this can happen in the back. I would also very much consider buying a good scope. My scope is a 3m littman select $45.00 plus shipping it is worth the $! 
