Fast magnetosonic wave absorption by fast alpha particles at small concentrations during an approach to ignition in ITER-like fusion plasmas is examined for the fundamental deuterium heating scheme. Numerical results are obtained using a full-wave code which solves coupled second order differential equations for the wave fields in a slab geometry. The fast alpha particle velocity distribution is approximated by a Maxwellian, chosen so that its velocity space density of resonant particles equals that of a slowing down distribution when both are evaluated at the absorption peak. For the cases considered, the thermal gyroradius of the Maxwellian alpha distribution satisfies the condition (k_⊥ρ_αf)²/2 < 1. Significant absorption of the fast wave by the alphas can occur in a parameter window characteristic of startup conditions. This is because the Doppler broadened alpha particle resonance zone encompasses the deuterium-tritium hybrid resonance where the left hand circularly polarized component of the wave electric field peaks