1) Enthusiasm. The examiners want to see your interests and passion in Math exploration in your everyday life. So, do research, get inspired and look for mathematic application in your interests before you decide your topic.
2) logical and concise organazation. Make sure your exploration is in chronological order, everything clearly labled and easy to understand. Yes, logical reasoning is the key in Mathematics.
3) self- reflection. Remember your whole assignment is a self exploration, therefore you need to reflext on what you find out and learn through your journey. Basically, include everything you feel and think about your experiementaions in your exploration if relevant.