Cold Temp Altitude Corrections for INRAT

[Iliopolus_1]

I notice practice INRAT questions have two types, Cold Weather corrections for say IAF FAF PT MDA MA etc, that are HIGHER than 5,000 when RAC 9.1 only shows up to 5,000.
What do you do when you have altitudes that are far higher?

Then there is the classic Question of Cruising at 9,000 crossing a mountain peak of 6,000 with a 9,000 OAT of -30 etc. The solution speaks of 4% of the total altitude for each 10 Degrees of ISA deviation.

The answers I come up with are wrong and I'd like to see an explanation for how to accurately calculate the difference.

These questions seem to assume "with that Altimeter reading 9,000 ft by how much will you clear the mountain top... when obviously, the aircraft flying at 9,000 indicated is at a lower actual altitude AMSL.

[PositiveRate27]

This is a common interview question asked of guys who have only flown the prairies when they come out west and Sector altitudes are in the teens, let alone above 5000'.

Lets say you need to do a correction on an alt of 7000'. Find the correction for 5000', then the correction for 2000'. Combine them and apply it to the 7000' altitude.

[photofly]

The blurb below the table (9.1 in AIM RAC) says the linear equation (which gives the data in the table) is acceptable for use up to 12000 feet. So adding two table entries is ok with TC up to that altitude.

There's a more accurate equation given for use up 36000 feet. If you're worried about terrain clearance in the Himalayas.