SACRAMENTO — Thousands of students who failed the California High School Exit Exam since its 2006 debut would be eligible to receive their diplomas — if they meet all other graduation requirements — under last-minute changes Gov. Jerry Brown requested to a bill the state Legislature is considering.

On Friday, Assemblywoman Susan Bonilla, D-Concord, said Brown’s office asked that SB172 provide an Exit Exam exemption for all students, regardless of when their class graduated. SB172 seeks to suspend the test over the next three years so that the state can consider updating it to reflect the Common Core standards now being taught.

The governor’s request came after he signed a different bill last month to retroactively award diplomas only to students from the class of 2015 who had met all other graduation requirements but had not passed the written test, which was canceled in July by the state over concerns that it was outdated.

If approved by the Legislature and signed by the governor, SB172 essentially would make the Exit Exam irrelevant during the decade it was required.

Brown’s office declined to comment Friday on whether the request signals support for the legislation.

But students who have tried for years to pass the test found hope in the revised bill.

Arlene Holmes of Vallejo said she is crossing her fingers. The 21-year-old estimates she has taken the math portion of the Exit Exam 20 times since her sophomore year of high school in an attempt to pass it. Holmes said she passed the English portion of the test on her first try.

She has come within a few points of passing the math test.

“I moved around a lot when I was younger, and I went to a bunch of different schools,” said Holmes, who would have graduated with the class of 2012. “I retained English, but math was always tricky for me. I’m not good with math tests.”

Holmes said having a high school diploma will open up career opportunities for her.

“I would apply for higher-paying jobs, and I would definitely start going to school for other (trade) programs that require a diploma that I couldn’t do before,” Holmes said.

State education officials canceled the July test instead of renewing a contract that expired in May due to ongoing concerns that the test is not aligned to what is being taught in schools under the new Common Core standards. California began requiring the Exit Exam in 2006.

Many students in the class of 2015 were required to pass the July test as a condition of being accepted into four-year colleges, the military and some job-training programs. But Brown’s signing last month of SB725 allowed districts to begin issuing the diplomas to their recent graduates. San Francisco and Oakland had already gone ahead and awarded the diplomas before the law was enacted.

The bill to exempt all students from the test requirement, SB172, has to pass the state Assembly and Senate before the legislative session ends Sept. 11. The bill could be taken up as early as Tuesday in the Assembly.

If passed, the bill would become effective Jan. 1.

Melody Gutierrez is a San Francisco Chronicle staff writer. E-mail: mgutierrez@sfchronicle.com. Twitter: @MelodyGutierrez