Beginning with students who enter high school in 2009, the state will require every student to take four math courses before graduation.
Some parents said adding more academic hurdles might ultimately hurt at-risk students.
"We think children will either be retained more (or) will drop out, and we have a cause to be concerned about this," said Calla Wright, who heads the Coalition of Concerned Parents for African-American Children.
Overall, 68 percent of North Carolina's public high school students graduate in four years. But only 60 percent of African-American students earn diplomas in that time, compared with 73.6 percent of white students.
Wright said she is frustrated by the achievement gap and thinks it might grow with higher standards.
"We're saying that the children can meet the challenge. But if the resources are not there, if the support is not there, then we have a problem," Wright said.
But North Carolina Board of Education Chairman Howard Lee said schools must raise standards to better prepare students for college and careers.
State education leaders have set a goal to raise the graduation rate by 60 percent in the next few years.
Lee called the 68 percent graduation rate "unacceptable," and said pushing all students to learn more while pulling up those prone to fall behind are not competing goals.
"Standards in and of themselves are not the main reason kids drop out of school," Lee said. "I frankly reject the notion that just raising standards itself would have a negative impact on black kids."
Lee agreed with Wright that dropout prevention programs, combined with focused family and community support, are the formula for success.
"If we raise the expectations, these kids will respond," he said.