UNAUTH PENETRATION OF AIRSPACE. PROX OF CLASS B AIRSPACE APCH RTE.

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WE TOOK OFF FROM ADDISON (N OF DALLAS; TX) ARPT HDG NW IN ORDER TO AVOID DFW'S CLASS B AIRSPACE. WE WERE GOING TO DENTON ARPT; APPROX 300 DEG HDG. AS I WAS LOOKING AT MY DFW VFR TERMINAL AREA CHART TO TUNE IN THE DFW 40 DEG RADIAL; I ASKED MY STUDENT TO LOOK FOR THE DENTON ROTATING BEACON. THE STUDENT SAID 'I HAVE IT' AND PROCEEDED TOWARD IT. ABOUT 1 MIN I SAW LOTS OF LIGHTS (FROM AIRBORNE ACFT) ON MY R; ABOVE ME. I LOOKED L AND VIEWED DFW'S RWYS 17L/R. IT WAS A VERY CLR DARK NIGHT AND I HAD A LEWISVILLE LAKE ON MY R. I IMMEDIATELY TURNED THE PLANE TO THE N AND DSNDED TO 1000 FT MSL. OUR COCKPIT LIGHT WAS SO DIM YOU HAD TO USE A FLASHLIGHT TO READ THE INSTS; AND I FOUND THAT THE DIRECTIONAL GYRO PRECESSED 30 DEGS OUT OF PHASE; HENCEFORTH; MY STUDENT PICKED THE INCORRECT BEACON TO FOLLOW. THE DIRECTIONAL GYRO SHOWED 300 DEGS; BUT IN REALITY IT WAS APPROX 270 DEGS. BECAUSE OF NIGHT TIME AND BEING UNFAMILIAR WITH THE AREA (FIRST NIGHT TIME FLT); I'M NOT SURE IF I WAS IN THE 100/SFC CLASS B AREA OR 100/20 AREA. AT NO TIME WERE WE CLOSE TO ANY OTHER ACFT. THIS TRAINING ACFT HAS 1 BASIC RADIO. I SHOULD HAVE TUNED INTO REGIONAL APCH 124.3 FOR RADAR VECTORS; BUT THOUGHT I COULD STAY WELL N OF THE CLASS B AREA. ALSO; THE WIND WAS E AT 20 KTS. THE WINDS; MY LOOKING AT CHARTS; TUNING RADIO; STUDENT MISTAKING WRONG BEACON; ALL WERE THINGS WHERE I SHOULD HAVE BEEN MORE ON TOP.