First is an inquiry I had made regarding division by zero. I never felt that division by zero was quite fully explained to me in high school and prior, so I did some number fiddling and consulted with the Dr. Math program about it. It ended up turning out that division by zero wasn’t always as undefined as high school made it out to be.
Second was an inquiry regarding the average rate of change. Our teacher had taught something that wasn’t working out in practice, so I inquired about it. Turns out the teacher was wrong, but looking back on it, I could see an out of practice teach confusing averaging the derivatives between the end points with averaging the derivatives of the end points.
There was a problem of the week program too that I found interesting and participated in on occasion. It’s not as free as it once was, but it was exciting and helpful to me.