At least a half-dozen companies got an unexpected boost in marketing their brands to New York’s children this week — with free product placement on the state’s English exams.

Teachers and students said yesterday’s multiple-choice section of the eighth-grade tests name-dropped at least a handful of companies or products — including Mug Root Beer, LEGO and that company’s smart robots, Mindstorms.

IBM, the comic book and TV show “Teen Titans” and FIFA — the international soccer federation — were also mentioned in the test booklets, some of them with what educators referred to as out-of-place trademark symbols.

“I’ve been giving this test for eight years and have never seen the test drop trademarked names in passages — let alone note the trademark at the bottom of the page,” said one teacher who administered the exam.

How long before corporate education boosters push for companies to pay for advertising within standardized tests?