We study binary black hole mergers in the extreme mass-ratio limit. We
determine the energy, angular momentum, and linear momentum of the post-merger,
remnant black hole. Unlike previous works, we perform our analysis directly in
the test-particle limit by solving the Regge-Wheeler-Zerilli wave equation with
a source that moves along a geodesic. We rely on the fact that toward the
merger, small mass-ratio binary systems follow a quasiuniversal geodesic
trajectory. This formalism captures the final premerger stages of small
mass-ratio binaries and thus provides a straightforward universal description
in a region inaccessible to numerical relativity simulations. We present a
general waveform template that may be used in the search for gravitational wave
bursts from small and intermediate mass-ratio binary systems. Finally, this
formalism gives a formal proof that the recoil velocity is quadratic in the
symmetric mass ratio $\nu$. Specifically, the velocity is given by $V/c\approx
0.0467 \nu^2$. This result is about $4\%$ larger than previously estimated.
Most of this difference stems from the inclusion of higher multipoles in our
calculation.
