A complete sample of quasars at B = 19.80

A quasar candidate spectroscopic UV-excess survey with B less than 19.80 has yielded 35 quasars in the 1.75 sq deg region studied. The X-ray data for the 35 quasars are used to show that quasars with B lower than 19.80 and z lower than 2.2 constitute 24 + 10, -8 percent of the observed X-ray background at 2 keV. This sample is combined with one containing 22 quasars with B values lower than 18.25, and it is noted that fits of evolution and luminosity functions are substantially similar to previous results, although the confidence limits for the model parameters are reduced by a factor of 2. Pure luminosity evolution models are found to produce very good fits to the observed N(less than B) data, and are used to estimate the overall contribution of quasars to the X-ray background.