David Carr

The San Francisco 49ers waived third-string quarterback Nate Davis on Monday, just more than a year after drafting him in the fifth round out of Ball State. Shortly after announcing they had parted ways with Davis, the team said it signed quarterback Troy Smith to a one-year deal.

Coach Mike Singletary had been openly frustrated with Davis’ slow development and work ethic despite the quarterback’s dyslexia that makes it difficult to grasp the playbook. Singletary hinted after Thursday night’s preseason victory over San Diego that Davis was a question mark to make the team, but he was still around Friday when the Niners trimmed their roster to the 53-player limit.

The move was made Monday as San Francisco prepares for its opener at NFC West rival Seattle, but announced hours after Singletary addressed the media.

The 49ers already have starter Alex Smith and backup David Carr, two former No. 1 overall picks. Singletary had said they could get by with only two quarterbacks, but opted to add Troy Smith. He was a fifth-round draft pick by Baltimore in 2007 and has appeared in 14 games with two starts in three seasons. The Ravens cut Smith on Saturday.