Alright, since you're joining the army...
I'm in the US Army, and when I joined I could only do 45 pushups in 2 minutes. In Korea, when I did the Pyramid Push-up program, at my peak , I did 105 push-ups in 2 minutes, but my LT who was counting took 15 off, because I did some of them wrong.
Now, assuming the canadian pt test is anything like the American one, here's some things to remember
There is a difference between a "push-up" and an "army push-up"
If you wanna max out on the PT test for your age group, start with your hands a little lower, beneath your pecs is usually where I go, at about shoulder width. This lets me use other muscles/joints, and when I tire those out, I spread my arms a little wider and use different ones so I can score higher.
Remember, since your push-ups are going to be GRADED by someone who doesn't like you, doing 1 perfect push-up is ALOT better then 10 shitty ones that wont be counted.
****Keep your back straight, DO NOT ARCH OR SAG IN THE MIDDLE while coming up or going down. That means you gotta keep your abs and lower back stable, so work on those too. It is 100x easier to do this if you just look straight forward with your head as opposed to keeping your head down with your eyes looking at the ground.
But yeah, what worked for me was doing something like a pyramid. After we would get off working the road, I would go to the gym mat and do 40 push-ups, and then 40 sit-ups, 39 push-ups and then 39 sit-ups. I would go all the way to 1. I guess you could call it half a pyramid :icon_lol:
But anyway, after I finished with that, my reward was hitting the weights. My goal was too get past that fucking torture so I could go into the air conditioned gym.
Hell, you could even do deck of cards PT. For red cards do push-ups, black cards do sit-ups, jacks, queens, kings and aces could be alternate exercises or an increased amount of push-ups/ sit ups. I mean, its really all up to you man. You're only limited by your imagination.