If you have only one month, and your goal is improving this only for the mentioned exam, and assuming that all other aspects of your English speech are adequately good, there are a few quick fixes that I can think of.
Method 1: Enunciate (which is to pronounce every word clearly) and exaggerate (which is to overstress the words you'd normally stress, well, normally :-).
One month is perhaps too short a time frame that you can really fix your accent. (Well, I believe that you could if you are willing to do it, but it's hard work and it's very demanding.) So instead of trying to imitate native speakers (which is actually the ideal, in the long run), keep doing enunciation and exaggeration could help you find your own pace when you speak. Naturally, enunciate each word crisply will force you not to speak too fast, and exaggerate the words you want to emphasize will naturally improve your intonation. The catch? This process will mend your accent. If you keep practicing this long enough, it will be much more difficult in the future to correct (or lose or reduce) your accent.
NOTE: It is okay to ridiculously overstress and over-enunciate when you practice. Once you're used to it, your normal speech is easier to understand and has better intonation.
Method 2: Intonation analysis
I call it "analysis" because it is the main idea of this method. Usually, learners work better with eyes than ears. So it's a good idea to use visual aids to improve your speech.
This method is rather easy, but tedious. Here is what you will need to do:
Find a good video clip on YouTube. (As a side note, those English teaching clips usually speak too carefully, and might be less natural sounding. It might be better to look for a clip that has a native speaker talking about anything you find interesting.) In that clip, find a few sentences that you think you might say. Then for each sentence, try to duplicate it. Try to say it yourself exactly the way they say it.
Unfortunately, this is easier said than done. So, we need visual aids. You can create visual aids yourself like this. Write the sentence you chose down on a piece of paper (anything you can write on is fine), then mark each syllable you think they (the speaker) emphasized by drawing a circle around it. Draw a line under each syllable you think it's in a very low tone (in short, underline it). Draw a line over each syllable in a very high tone. Cross every word that you can notice a change in its tone (e.g. rising, falling, rise-and-fall, or fall-and-rise) with a diagonally upward arrow, or a diagonally downward arrow, or an up-then-down arrow, or a down-then-up arrow. These are your visual aids.
Then try to speak the sentence again, with your visual aids. Repeat the sentence until you think you get it right. Then, move on the the next sentence. You can choose any sentence from any video clips you can find. You can also repeat this very same process as much and as often as you like.
Method 3: Sing a lot!
This is perhaps the easiest and the funnest one! Assuming that you can speak English good enough already, but your intonation is off (which usually implies that your rhythm is off too), the fix is simple, just sing a lot TM :-).
You don't have to sing difficult songs, or sing any songs the way professional singers do. You just want to feel the melody and rhythm! Embrace them. Absorb them. Let them flow into you. Virtually, any songs you like are equally good. But here is my big secret: the simpler the song is, the more useful it would be for you. So, nursery songs and rhymes are good. Oldies is good. Slow rock, pop, country songs are good, too, in my opinion. It's up to you. It's your choice. Just pick something you like that is not too fast, and not too slurred, and sing along.
Good luck!
