INSTRUCTOR WITH ATP STUDENT FLYING IN THE SVFR AREA INADVERTENTLY ENTERS TCA.

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FLYING FOR THE FIRST TIME WITH AN ELDERLY DOCTOR; WHO HOLDS AN ATP AND A CURRENT BFR; FROM LGB TO CMA THROUGH LOS ANGELES SFRA AT THE REQUIRED 4500 FT MSL. WE HAD ASKED FOR THE SHORELINE RTE AT 2500 FT; BUT WERE DENIED. I WAS HIGHLY DISTRACTED BY THE DOCTOR'S DIFFICULTY IN TRIMMING THE ACFT AND IN HOLDING A HDG/TRACKING THE SMO 132 DEG RADIAL. AFTER PASSING SMO WE DID NOT GO FAR ENOUGH NW BEFORE TURNING TOWARD VTU; AND DID NOT DSND FROM 4500 FT. I WAS UNAWARE OF ENTERING THE TCA UNTIL WE RECEIVED WORD FROM MAGOO APCH THAT LAX APCH HAD CALLED. PART OF MY DISTR RESULTED FROM MY EXASPERATION AT THE SUBSTANDARD PERFORMANCE OF MY HIGHLY QUALIFIED AND EXPERIENCED STUDENT. SECOND; THIS WAS MY FIRST TRIP THROUGH THE LOS ANGELES SFRA (I USUALLY AM IFR IN TURBINES). MY UNFAMILIARITY KEPT ME GLUED TO THE TCA CHART; BUT THE CHARTING IS THOROUGHLY CONFUSING; EVEN TO THIS EXPERIENCED IFR PLT. YOU ARE REQUIRED TO BE ON A SEPARATE PANEL OF THE CHART; WHICH DOES NOT SHOW THE NEED TO IMMEDIATELY DSND TO BELOW 4000 FT BEFORE TURNING NW. FINALLY; WHY MUST THE TCA BE DOWN TO 4000 FT IN THAT AREA; WHEN 5000 FT WOULD SEEM MORE REASONABLE IN LIGHT OF THE 4500 FT SFRA.