Hello, Echantress!
Don't worry. I used to be like you. I got a score of 5.1 when I was in Year 8 and was extremely unfit. In Year 10 I earned a score of 9, so yes it is possible and yes you can do it in 4 weeks even though I'm a nerd and my personal example took 2 years to reach my goal.
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Firstly this might be a bit long for you to read so I'll just let your watch a video first if you don't have the time. Pay attention to the advice given on pulls ups, sit ups, push ups and running.
YouTube - Special Forces testing
Anyways, on to business. Running is the hardest part of any physical fitness test. To be good at it, like anything else, you need to be dedicated and to practice the exercise frequently. First thing to do is to organise yourself. Ask yourself, when am I available to run? Where can I run? What time should I run (I recommend running in the evening than in the morning since running in the morning is very demanding due to the cold air) In what clothes should I run in (a beanie, a long sleeved shirt and track suit pants should do together with comfortable shoes. You don't need to wear one of those tank tops like other women do. Some guys will perve at you from their cars and you don't want that, do you)? After answering those questions find the time to be able to run at least 15 minutes a day, five or six times a week. Don't do less than this because you probably improve that much unless if you're really knackered.
Anyways, now on to the running. I don't know how far you can run but guessing you can run at least 3 km without walking. From this, run about 2 km for the first week each day (except on Sunday where I recommend you should go swimming for leisure) WITHOUT TIMING YOURSELF. The key here is to not pressure yourself to get a PB but to get comfortable running. You should run at your own pace WITHOUT WALKING. Distance over speed. While you're running you should also try what is call HIIT. This stands for High Intensity Interval Training. For this you jog for the first 400 metres and then sprint 3/4 of your all out speed for 50 metres and then return to jogging for the next 200 metres etc. This running method really works, especially if in your situation where you need to improve in a short amount of time. Be careful though and don't push yourself too hard the first week because you will get a stitich if you do sprint a bit too hard. (if you do get a stitch clench your fists as firmly as you can in the punching position with your knuckles out and continue running. For some reason this works and your stitch pain will alleviate). I recommend you do HIIT for one running day and then jog for 20 minutes at your leisure on your next running day. This should be your relaxing day from HIIT.
After that on the second week put it up to 2.4 km and then halfway through on the week push it up to 3 km. I reccomend you should be able to run at least 2 miles (3.2 km) without walking before you do the test. From that you should be fine and you'll reach 7.5 easily.
For push ups, the first thing to do is to make you're doing them correctly. A test to see if you're doing them right is to put yourself in the push up position. Looking down on the ground in front of you check if your hands are in line with your face. If they are, you're in the wrong push up position i.e. your ass is sticking up in the air. Your hands shuold be in line with your chest. This is done to ensure that your body is straight throughout the exercise. Get this right first before continuing on. The worst thing to do is practice doing push ups and then arriving on the day to find them not counted because you were not doing them correctly!
Anyway, on to improvement. Personally what works for me is to do push ups in intervals. Do half of of what you can and rest (or do sit ups/crunches) and then do them again and see how many sets you can do before you're knackered. For example.
6 push ups.
Rest 30 seconds-1 minute. (or do 20 sit ups)
6 push ups
Rest 30 seconds-1 minute. (.)
etc.
Then the next day rest and do them again on the following day after your rest day. Also, if you want to improve quicker incline yourself and do your push ups. To do this, put your feet on your couch and get on the push up position on the floor. This should put more gravity on your chest and therefore increase your core body strength and endurance for you to be able to do more push ups!
Doing pull ups also will help with your push score as it works on your triceps. For this though I don't recommend you get straight to the bar and do them. Start doing pull ups from a bar from with your feet on the ground. These modified pull ups are usually easy to do than the real ones which take long to master the perfect technique. Do about 10 and then rest yourself for some time and then come back to do them again. Do 4 sets of these and you would have done 40 pull ups in one day! Do this about 2 times a week if you have the time or at your leisure.
Finally, on one day of the week before you go to bed try to do as much as you can and you should improve. If you don't, tell me and I'll make another plan for you. The most important thing to remember though is to NOT DO WEIGHTS.
I'm guessing you need to do sit ups as well so I'll help you there also. Put your feet up against a wall at 90 degrees on your bed, with your hands cupped behind your ears and start doing sit ups there aiming to touch your thighs with your elbows. Keep your eyes on the walls in front of you without looking at your legs. Do this slowly and do about 50. This should work on your upper abdominals which the normal sit up and crunch positions don't work on that much.
That's about it and as the battle cry of the 6th Airborne goes 'GO TO IT!'
