Battery light

About a week ago I was getting ready for work when I started the car to get it warming up before leaving. About ten minutes later as I was walking out the door I noticed the car was off and would not start or do anything. Jumped battery and started right up with battery light on. Later that day after leaving work the battery light was off. About a week later I was idling on the side of the road waiting for my sons bus to come in the morning and the radio went out, the lights dimmed and the wipers started going slow. Turned the car off and after the bus came it started and drove fine but with the battery light on again. Went to the O'reilly's and they tested the alternator and out of three tests it passed twice and once it failed on output. They also tested the battery and it passed but said "low charge" Going to clean connections this weekend but looking for other ideas in case that does not help.