A note next to one of the explosive formulas said "the type used in Oklahoma".
"A piece of music isn't a pure mathematical collection of formulas," said Donald Martino, a composer and an emeritus professor of composition at Harvard.
Some Republican colleagues of the governor, who has also urged Congress to accept threat-based formulas, said they hoped Mr. Pataki would use the bully pulpit more often on the issue.
"People have a lot easier time getting an intuition from pictures than they do from numbers and tables of formulas," said Stephen Wolfram, a physicist who formed Wolfram Research Inc. to develop a software tool to permit mathematicians and students to view equations as three-dimensional images.
This year's test was based on the new core curriculum, which focuses more on applying concepts to the real world than individual physics formulas, said Michael Herzog, a retired physics teacher who helped create the new curriculum and test with a statewide committee.
"The scheme is aimed at helping users understand not only complicated functions of mobile phones but also complicated pricing formulas," said an official at the telecoms ministry.
