In order to test the alarm system board, you will need the following two pieces of lab equipment:
A variable dual power supply capable of supplying up to 15V and about 2 amps. The supply should also have current limiting.
A multimeter capable of measuring up to about 15V DC supply with a milliamp scale as well.
Both of these are readily available on eBay and elsewhere. My local hardware store regularly sells multimeters for about $20.
If you don't have or can't afford a variable power supply, use AAA batteries in series to get yourself a 13.5V and a 3V supply. The batteries won't supply enough current to do any serious damage, in case of the 13.5V version.
A 13.5V DC supply consists of nine 1.5V batteries connected together in series.
A 3V DC supply is two AAA batteries connected in series. This will be used to simulate the 3.3V supply from the BeagleBone.