Can a high school math tutor be paid for from a 529 plan?

No. But read below. You may have been thinking of the Coverdell Education Savings Account (CESA). This type of account does allow for tax free distributions to pay for tutoring the beneficiary who is attending elementary or high school.

If some part of the 529 distribution is taxable (i.e., the distribution includes both a return of capital as well as earnings), then there would be an additional 10% tax as a penalty on the taxable portion of the distribution.

IRS Pub 970 explains the 529 and CESA rules. It includes examples on how you determine what is taxable and whether the 10% penalty applies.

I would say no. Looking at

Eligible educational institution. For purposes of a QTP, this is any college, university, vocational school, or other postsecondary educational institution eligible to participate in a student aid program administered by the U.S. Department of Education.

So high school does not qualify.

I would expect that a college tutor also would not qualify under other provisions relating to the expense being required. There might be an exception for certain music programs where "private" lessons in your instrument are required by the university.

Disclaimer: I have no particular tax preparation training.

Thanx to everyone who replied, you confirmed what I thought was the situation.