Mxsmanic wrote:

Where does this exam take place? Is it in a classroom, or in a testing
center, or is it actually in the aircraft?

It's usually done at the point of the checkride, inside the FBO in some
convenient place where you go over the paperwork and then outside in the
vicinity of the aircraft, typically the candidate being asked questions
while demonstrating the checkride.

When you are asked math-type questions, are you expected to answer with just a
ballpark figure or an exact answer? In the latter case, can you use a
calculator, or pencil and paper, or must you do it in your head?

You're not typically asked math-type questions. Generally questions are
asked about aircraft systems and your preflight planning is examined.
In flight, you might be asked to compute some things as part of your
normal cross country navigation. Accuracy to what you can get on the
whizwheel is accceptable.

If I'm asked how long it will take to go 84 nm at 120 kts, I know that it's
about 40 minutes, but if an exact answer is required I don't see how I could
practically provide that without a calculator.

Whizwheels were the classic, calculators are acceptable.