The question asks what happens to the CAS when an aircraft is climbing
through an isothermal layer at a constant Mach. You are therefore looking for a
CAS / Mach relationship.
Mach = Dynamic pressure/Static pressure = CAS/Static Pressure
Using this equation you do not need to take account of the temperature,
but purely the affect of altitude.
As the aircraft is climbing the static pressure will be decreasing and
therefore to maintain a constant Mach the CAS must also decrease, which is the
answer to this question.
Conversely if the aircraft is descending then the
static pressure will increase, so CAS will increase to maintain a constant
Mach.
If the aircraft remains at a constant flight level then the static
pressure will remain constant and the CAS must also remain constant to maintain
a constant Mach.
Furthermore if the question is related to TAS and Mach use the following
formula;
Mach = TAS/LSS where the LSS is solely dependent on temperature.
If an aircraft is climbing at a constant Mach through an isothermal
layer the temperature will remain constant, so the LSS will remain constant and
TAS will remain constant.
Conversely if an aircraft is climbing at a constant Mach through an
inversion what will happen to TAS. With increasing
altitude the LSS will decrease, but because the aircraft is flying through an
inversion the temperature will increase, which will cause the LSS to increase
and therefore the TAS to increase.