getting fit for the Airforce!

Former Air Force vet here. First off, your standards are a little off. Secondly, are you trying to get a 100% on the test or just trying to pass? Bc the standards you posted are for a perfect score. Max points for run under 10:23, max points for push ups 47, max points sit ups 54. You can already run a 10 min 1.5 which is damn good and max points...you don't get extra points for running it faster. If you want to drop the time I would suggest doing some sprint workouts. As for push ups...you need to do push ups to get better at them. So do as many push ups as you can until failure then get on your knees and continue to push. Adding upper body weight training to that only speeds up the process. Overall, focusing on the push ups is key. The same goes for sit ups...train using the the Air Force standard sit up technique. Again, adding other core exercises will only benefit you. Again, the standards you posted are for a perfect score just bc you don't get above that number you fail...just give it your all. It's pretty easy and you can already run great. Try not to stress about it. Btw, what's your job? Thanks for serving.

From experience, sit back and eat all the pies

But in all seriousness I'd echo the point from sonic above. Go and see the recruiters and find out the actual standards that you need to reach. That figure is somewhat lower than the minimum standard to join the Royal Air Force, but somewhat higher than the best scoring times. That said, the Recruit Fitness Test is a pass/ fail whereas the in-service fitness testing for all three UK services have graded scoring.

As far as preparation is concerned, the advice that I'd normally offer would be to look at the kind of phys that's done in new entry training and aim to replicate that rather than merely the entry tests. The better you can do the phys in training the less likely you are to end up on remedial phys, so you free up time to focus on the other parts of training. It's a very easy win.

That means broadly running, and a fair amount of bodyweight circuit work. For my own service, admittedly not AF, I'd anticipate being able to comfortably run 10Km in the first week of training. If you get yourself onto a plan to run for that distance you should be smashing the new entry standard fairly easily.

Equally, as far as resistance training is concerned, something like You Are Your Own Gym is decent preparation. And the author in that case knows what he's about as he's a former USAF Combat Controller and PTI.

All the best with it

From an US Army perspective, I would agree that incorporating some sprint training or fartlek training will greatly help at improving your overall run times. For pushups, getting into the gym and doing some upper body work will help but so will doing lots and lots of pushups. We used to get into a pushup position with our hands on a scale to find that weight, put that on a bench press and then do as many as we could in our time limit for several sets. I think the most I ever got on a PT test was 127 in 2min. I struggled with situps due to hip issues half the time so proper stretching to be warmed up and doing lots of ab work should help.

Keep in mind that most services do have a minimum and maximum score you need to achieve. Most also have a minimum ENTRANCE score you need to achieve which should be different than the one close to graduation day. I can't vouch for AF but in the US ARMY if you could pass the entrance version, you would do more than enough working out to breeze through the final.