Sounds like you've been put forward for your test too early. If the aircraft is trimmed in pitch and yaw then it should just keep going in a straight line, unless yours is badly bent or you're carrying a fuel imbalance.
Assume a C152 does 90kts (1.5nm/min makes the maths easy). It it doesn't, slow it down (or speed it up if you've got a crap one) until it does. Ditto mph if that's what your speedo is calibrated in. I know of people who have worked out a table of distance and time before - I can't remember if the time to diversion needs to be corrected for wind but in any case it's not going to make a huge amount of difference.
It should take you no longer than a minute to work out where you are, where you are going and the heading to steer. If it does - see my first point. Get it going the right way then work the timing out. Break the task down into little bits.
You're never going to be more than a mile and a half away multiplied by the time flown since from where you last knew you were.