how can I check that my alarm battery is dead?

hello can somene one give me some information. My accenta 8mini alarm was not working. Got the engineer in, he said I needed a new battery (Yucell 2.1 12 volt), The cost for coming out and fitting was £55.00. Can you tell me if I can check that the battery taken out is still working, I ask this because I switched the electricty supply off at the mains, yet the outside lights ie red and green were working, and all the sensors were working. Would appreciate any information you can give me many thanks