Sit on the edge of a chair with your feet flat on the floor. Then only using your pelvis and core muscles tip the chair forwards. Easier said than done! It really shows you if your core muscles are up to scratch or not.
Another one to test your core, stand on the ground with your feet apart like you're on a horse. Bend your knees a little, then keeping that position (all your lines etc straight.... ear shoulder hip heel and elbow wrist hand) lift your heels off the ground (stand on the balls of your feet), hold it for a few seconds then go back down again and repeat a few times. You CANNOT shift your position from the knees bent or loosing any of your straight lines, so the strength to lift your heels actually comes from the core.
I know so many people that cannot do this really very straight forward exercise, and sure enough, they are typically those who struggle to get engagement on their horses and to half halt using their back ;)