What are some ways to improve my upper body strength?

Do push ups and pull ups.

Make sure your diet is right and you are well hydrated, because it will improve your strength. Do some training at home and rep out those push-ups till failure (assuming that the test requires X number of push ups to be completed) , but let your muscles recuperate to 100% before you do another work-out.

Another important factor is the way you do them, trying to even out the load on your chest, shoulders and triceps so you are getting the most out of them

1.) you are gonna have to take in more protien to help with muscle development try to stay away from fatty foods.

2.) now if u work out ur chest = working out ur back or u can have some problems if u dont so if ur going to the gym you can start with bench press 3 sets- of 6 wat ever weight is comfertable

then do some pull ups for the back mind u this is just for some pointers.

3.) do the same set 3 sets=6 reps inclined press with dumbells. then do some shoulder shrugs with heavy dumb bells then just shrug. of course the push up lol just do that whenever u have some free time.

4.) keep it up these will definetly help you can always look up some more or ask but these are core builders. have fun !