If you have a flight computer is much easier, but if you want to do it with your brain, hereŽs how it goes. IŽll show you an example with the first one:
First I want to know how fast is Mach 1 at that temperature ( I say temperature because Mach only depends on it).
Mach 1 = 661.5 kts x [square root (absolute ambient temperature/ 273 kelvin)]
Mach 1 = 661.5 kts x [square root (273-48/273)]
Mach 1 = 661.5 kts x [square root (0.824)]
Mach 1 = 661.5 kts x 0.9078
Mach 1 = 600.5 kts
Now, what's your speed, 290 CAS? So we can use a simple flight computer to determine your TAS or you can do approximately 2% of your CAS every thousand feet.
2% x 31 (FL310) = 62%
TAS = 290 kts x 1.62
TAS = 469.8 kts
And finally your Mach number is:
M = TAS/Speed of sound
M = 469.8 kts / 600.5 kts
M = 0.78
The others are the same. Remember that if you are using Total Air Temperature instead of Static Air Temperature you have to take into account the temperature rise, which again you can get it with a flight computer or you can use the simple formula T Rise = 30 x Mach ( This formula isn't very exact).
Cheers