Firms that offer private tutoring and standardized-test preparation are scrambling to cash in on what could be a multibillion-dollar bonanza created by the No Child Left Behind Act, which requires public schools to expose students to an unprecedented battery of assessments and offer tutoring and remedial instruction to those who fail.

Districts nationwide have turned to the private sector for help complying with the law, and in doing so have created a “supplementary educational services” industry that barely existed five years ago, executives said. Princeton Review Chief Executive John Katzman said the company’s K-12 division, which runs after-school programs and helps students prepare for standardized tests, now has 2,000 client schools, up from none two years ago. The division now produces about 15 percent of the company’s business. Within three years, Katzman said he expects it to represent 25 percent.

Other tutoring firms, like Baltimore-based Sylvan Learning Systems, report a surge in demand from schools looking to implement extended-day programs. And New York City-based Edison Schools, best known as the nation’s largest for-profit manager of public schools, said it is planning a rapid expansion of its fledgling summer-school and after-school program divisions. Within three years, it expects those operations to produce $100 million annually.

Supporters have hailed those developments, saying the private firms are riding to the rescue of schools that don’t have the personnel to tutor kids themselves.

But Monty Neill, executive director of FairTest, a group that has opposed increased standardized testing, said the changes have happened too fast, with too little scrutiny of whether the new services actually help kids learn.

“These private companies are really like vultures, descending on what they see as a feast,” he said. “We’re worried that we are going to be hearing stories about schools not being able to buy library books because they are spending money on test prep.”

The law requires that schools that don’t meet federal achievement standards set aside between 5 percent and 20 percent of their federal antipoverty money for tutoring.

There is some question about whether parents will take advantage of the programs at the levels the companies hope. School districts are required to offer services to qualified students, and to pay for them, but students are not always required to participate. In New York City, for example, fewer than 10 percent of the 240,000 students eligible for the first round of free tutoring signed up.

In other cities, private firms have made instant inroads. In Philadelphia, 22,000 students were enrolled this year in an after-school reading program run by a Dallas firm, Voyager Expanded Learning. Philadelphia schools chief Paul Vallas said Princeton Review is working with the district to offer a similar after-school program in math.

“I think you are going to see more outside consultants, more outside educational providers serving children, as a result of No Child Left Behind,” Vallas said. “There are a lot of outside firms that can do a better job than we can … I think it is the wave of the future.”