Congratulations on getting the interview! The first thing is don’t panic - a month is a long time to get prepared!
In terms of what to do:
1. Become comfortable using frameworks.
What I mean by this is I’d recommend learning three frameworks with will cover most cases: profitability, business situations (eg new market entry, new products); and capacity change (eg mergers, opening a new factory). I have a crib sheet which I’m happy to share if helpful.
Once you’re comfortable with these, practice cases where you address general business issues. Learn how to draw on the buckets you’ve learnt to inform your thinking of how to answer the question.
Then when you’re comfortable with that, drop the frameworks all together and practice more non traditional cases (eg non profit, government). You’ll realize that you’ve learnt how to create structured thinking without having to parrot off frameworks.
2. Brush up on your mental maths. Get to grips with your 12 times table, multiplying and dividing big numbers, calculating percentages.
3. Brush up on reading charts - lots of these are in cases, or look at publications which have charts like the economist and practice drawing insights from them.
4. Get ready to answer the PEI questions. Have two answers prepared to demonstrate each of times you’ve led, times you’ve had disagreements with people, times you’ve gone above and beyond what’s expected of you, and times you’ve faced big changes in your work.
Let me know if I can help, and good luck!