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The Fast Track processor (FTK) has been proposed for high-quality track finding at very high rates (Level-1 output rates) for the LHC experiments. Fast, efficient and precise pattern recognition has been studied using a silicon 7-layer sub-detector, including a subset of the pixel and SCT layers. We tested the FTK algorithms using the ATLAS full simulation. We compare the FTK reconstruction quality with the tracking capability of the offline iPatRec algorithm. We show that similar resolutions and efficiencies are reached by FTK at a speed higher than iPatRec by orders of magnitude. With FTK full events are reconstructed at the Level-1 output rate. Bo s rarr mu + mu- events are fufly simuiated together with background samples. We show that a low Level-2 rate is allowed by FTK, even using a singie 6 GeV Level-1 muon selection trigger. FTK provides the full-resolution track list ready for the Level-2 BBo s identification. All selection cuts performed by the Event Filter can be easily anticipated at Level-2. We present the Bo s rarr mu + mu- efficiency gain and related Level-2 rates.