Summary:
I entered KLVK airspace during my check ride about one mile before
contacting them on the radio, mostly because I was overloaded and didn't
have a good visual estimate of how close I was (my GPS had been turned
off by the examiner)

What happened:
Basically, I know that while I can be very smart, my mental abilities are 
very uneven, and go way down with lack of sleep (much faster than others)
or other physical reasons. I failed to be in the top 1/10,000 students in
France and had to settle with 1/1,000-ish mostly because of costly and
punctual silly errors due to lack of centrations.  This has plagued me
my entire life, and obviously it comes up in flying.
My goal however is to have my skill level be high enough that I will manage
to do the right thing even if I suddenly become very tired or otherwise
start losing mental "sharpness" while in flight (I shouldn't have left
otherwise) and get overloaded with bad situations on top of that.
However, not surprisingly, on my check ride day, I was both feeling
physically bad, and felt quite tired due to a very restless night.

Ground went fine, mostly because I knew much more than what was actually
required and asked.

Flying, well, I only managed what I knew out cold and could do in my sleep,
since my abilities were not much higher than that.
The first part of the excercises were done at PAO, and I passed them
mostly because I knew how to do them very well, and did well enough even
with reduced capacities.

We then went for the X-country where I flew slightly off course to stay below
clouds and go more towards the low side of sunol.
Mike, the examiner, then diverted me to KLVK, turned off the GPS and my
workload got interesting at that point.
While I wanted to stop and circle, I was in an unsafe spot to do so (in
the middle of the pass), so I went towards calaveras reservoir while
starting my calculation work.
I was:
- inside the pass so I had to watch traffic
- flying a bit low (2000 not climbing) due to clouds
- recomputing heading on the terminal chart, calculating distance
- quick calculation in my head: 12 miles is a 10th of an hour at 120knots,
  or 6 minutes, which is less than 1 gallon of fuel. I gave that to Mike
  along with the approximate heading by the time I had reached calaveras
  reservoir, I turned for that heading so that my time would be correct.

While checking my heading, altitude (descending) and getting ATIS for KLVK, I
tuned the tower and Mike told me I had busted their airspace by the time I
was pressing on the button to call them. Thanks for playing...

Mistake #1: I knew to divide the distance by two on a terminal chart, I even
told myself to do it after measuring, except I never did it. See my comment
about "costly lapse of concentration" comment above. In the end, I had
measured 12 miles when the actual distance was 6, so 3 miles later, when
I made the call, I had just entered Delta.

Mistake #2: diversion to close-by airport when you have to pretend you don't 
know where it is and do those computations instead of focussing on flying
there and doing what you should do, has never been my forte. This is something
that has always required a fully working brain for me. I didn't have that
at that time.
Obviously, my biggest judgement mistake was to try and get to KLVK quickly
and worry about making the numbers I had just computed (based on a regular
120knots cruising speed) instead of staying over calaveras and circling
there until I had everything together. In the end, I was only about 1mn
short (i.e. would have called KLVK in time 1 minute early)

Mistake #3: I have never really been able to tell what a mile is, never mind
4. As a result, putting away my sectional chart instead of looking at
how close I was to the airspace, was obviously stupid since the GPS was
off (I put it away in an attempt to clean up the cockpit and work on my
descent checklist).

I landed at KLVK without problems, and the tower operative (female) told
me on my way out that I had contacted them only 3 miles out and that I
should be more careful next time (considering it cost me a check ride,
I'm not exactly likely to forget)