Airflow through a converging$-$diverging nozzle results in a shock downstream of the throat but upstream of the nozzle exit. The inlet area, temperature, pressure and stagnation pressure are, respectively, $6$ cm$2,300$ K$,200$ kPa and $298\mathrm{.}95$ kPa. The nozzle area at the location of the shock is $24\mathrm{.}26$ cm$2,$ and the exit temperature is $330\mathrm{.}6$ K$.$

What is the Mach number just upstream of the shock, the temperature just downstream of the shock, the exit pressure, and the exit area?