STUDENT PLT ON FIRST SOLO FLT OUTSIDE OF TFC PATTERN AT HEF BECAME DISORIENTED; EXITED AND THEN REENTERED DC ADIZ WITHOUT OBTAINING DISCRETE CODE NOR MAKING CONTACT WITH PCT.

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I DEPARTED MANASSAS REGIONAL ARPT RWY 16R FOR MY FIRST SOLO FLT IN THE PRACTICE AREA (OUTSIDE THE PATTERN). MANASSAS GND HAD ADVISED ME TO SQUAWK XXXX; AND TO CALL PCT UPON DEP. THERE WAS A BREAK IN THE ATC CONVERSATION WHEN I WAS AT APPROX 1000 FT; AND I CONTACTED PCT. I HAD DIFFICULTY HEARING THE CTLR AND I ATTEMPTED TO FIX THE VOLUME. I DEPARTED THE PATTERN AFTER 1200 FT. I DID NOT HEAR PCT CONFIRM THAT I HAD CLRED THE ADIZ; ALTHOUGH I HAD BEEN FLYING FOR AT LEAST 10 MINS AND PASSED LANDMARKS THAT ARE OUTSIDE ADIZ. I BECAME CONCERNED AND CALLED PCT. THE CTLR SAID THAT THEY HAD CALLED ME; BUT I DID NOT RESPOND. I BELIEVE THEY ALSO TOLD ME TO SQUAWK 1200 WHICH I DID. SINCE I WAS OUTSIDE THE AREA WITH WHICH I AM FAMILIAR; I CHKED MY MAP TO SEE IF I COULD IDENT ANY LANDMARKS. I WAS UNSUCCESSFUL AND FLEW A HEADING OF 060 DEGS TO RETURN TO THE PORTION OF THE PRACTICE AREA WITH WHICH I AM FAMILIAR. I DID NOT TUNE CASSANOVA VOR BECAUSE IT WAS OTS ON THIS DAY. IN RETROSPECT; I SHOULD HAVE CONSIDERED WAITING UNTIL CASSANOVA WAS OPERABLE TO MAKE MY FIRST SOLO FLT IN THE PRACTICE AREA. AT THIS POINT; I SHOULD HAVE CALLED THE MANASSAS TWR TO LET THEM KNOW THAT I WAS LOST. HOWEVER I THOUGHT I WOULD EVENTUALLY RECOGNIZE A LANDMARK. I SPOTTED A LARGE LAKE AND MISTOOK IT FOR HORSEFEATHER. IN FACT; IT WAS LAKE MANASSAS. AT THIS POINT PCT CALLED ME AND TOLD ME TO SQUAWK 1200. I TOLD THEM PCT ALREADY TOLD ME TO SQUAWK IT. I DIDN'T REALIZE I HAD BROKEN THE ADIZ. HE ASKED ME TO TAKE DOWN A NUMBER. I WAS HAVING DIFFICULTY HEARING; AND I WAS GROWING INCREASINGLY CONCERNED THAT I COULD NOT FIND MY POS ON THE MAP. I HAD DIFFICULTY COMMUNICATING WITH THE CTLR BECAUSE OF THE PROB WITH THE VOLUME. I WAS ALSO CONCERNED THAT I WAS TAKING UP TOO MUCH AIR TIME. AFTER SOME ADDITIONAL CONVERSATION WITH THE CTLR; I RECEIVED 2 HEADINGS TO RETURN TO MANASSAS ARPT. I SHOULD HAVE ASKED HIM TO PROVIDE ME WITH DIRECTIONS EARLIER; BUT I THOUGHT I WOULD EVENTUALLY FIND THE LAKE ON THE MAP. I PROMPTLY CALLED THE NUMBER I WAS GIVEN WHEN I LANDED.