Full-contact chess? j/k
Why not?
There’s all kinds of permutations.
Basketball where the height of each team’s net depends on their grades from a quiz right before the game. New quiz at halftime.
Football where the highest scoring quizzer is the quarterback, 2nd highest is the wide receivers, and a minimum score for anyone trying to be a lineman. If your linemen are too dumb, you end up with only 2 on the line rather than 4.
Cross country, where you run to each post where there’s a quiz question and you can’t leave until you get the question correct. Combine that with what they’ve already combined: Golf + cross country, where you run to each hole carrying your clubs and it’s a combined time score + golf score, each stroke costs 1 minute or sumthin like that.
Boxing, where you punch into a target during the match and you have to hit the right target answer on the other side of the ring to get your single point.
Soccer. No goalies but the size of the goal is determined by how many right answers the team gets on the quiz for each quarter. Same with hockey.
Robot wars with 3 or 4 functions blocked, unblocking them requires the player to answer quiz questions correctly.