This letter presents a study of the inclusive production of plus a recoil, using simulated samples of pp collisions at for an integrated luminosity in the range between and . The case for experiments to include un-prescaled b-tag multijet triggers for this topology is made and the ideal jet thresholds are discussed. The sensitivity to the Standard Model Higgs boson with a transverse momentum of at least 200 GeV is evaluated with respect to a continuous background, dominated by multijet processes. The mass of b-jet-pairs is analysed, quoting sensitivity to cross-sections in the range from 1 to 2 pb, for , covering the total Higgs-boson production cross-section of 1.8 pb. The trigger strategy presented in this letter is compared to triggers already in use, showing an increase on the signal efficiency for masses below 200 GeV and a performance comparable to a logical OR of all the currently available akin triggers for higher masses. The robustness of the expected sensitivity against systematic uncertainties is estimated by considering various typical sources, such as those on the fitting parameters of the continuous background, shape uncertainties affecting the signal acceptance and the background modelling. The accuracy of the Higgs-boson production cross-section measurements is also discussed, quoting sensitivity to deviations of 50% for and 10% for .