The final was tough, and I did ace it. There was one final question that was this big scary horrible-looking integral that refused to yield to any of the usual techniques for simplification. I refuse to be scared off by marks on paper, and I figured I had plenty of time and nothing better to do. So I dove in and integrated the mess. And sure enough, the whole thing fell apart in the process, leaving the final answer to be something trivial like "2". It turns out the star pupils both were too frightened by the monster equation and didn't even attempt it!
For example, she pulled out our most recent test, which contained a problem involving proving that the four points provided were the corners of a square. I had done something involving line lengths and reciprocal slopes. My mom had shown that the diagonals were the same length and perpendicular. Whereupon I pointed out that this didn't constitute a proof of squareness - unless the diagonals were perpendicular bisectors, you could have a figure known as a "kite", not a square. The teacher was boggled she hadn't even seen the flaw in the reasoning, but let my mom keep the credit for her answer.