The Chicago Public Schools are putting $40 million into Hyde Park Academy High School to improve programs and facilities at the school across from the planned Obama Presidential Center, Mayor Rahm Emanuel and CPS CEO Janice Jackson said Tuesday.

But it isn’t a new investment in the school at 6220 S. Stony Island Ave. The $40 million — which Emanuel and Jackson held a news conference at the school to announce — counts $20 million in capital funding that CPS approved last year and another $20 million the school system allocated over the summer for Hyde Park.

A similar event was held last week as the outgoing mayor, who has cited improved schools as a key part of the legacy he’ll leave as mayor, announced investments at Prosser Career Academy High School that had been approved by the Chicago Board of Education in July.

Facing a crowded field and potential fallout from the murder trial of the white Chicago cop charged with killing an African-American teenager, Laquan McDonald, Emanuel announced last week he won’t seek a third term.

The money being spent on Hyde Park is meant to shore up the open-enrollment high school, which community groups had feared would be sold to developers to take advantage of the economic boost the Obama center is expected to bring.

“Hyde Park represents our strategy for improving schools in Chicago,” Jackson, who graduated from the South Side high school, told students Tuesday. “There are new things happening in this community with the Obama library, and we’re all excited about that, but we also want to respect the institutions that have been here educating kids for hundreds of years and making sure there’s a good synergy between the two.”

Neither she nor Emanuel would take questions. Asked as she walked away how her old high school was chosen for such a large investment, Jackson kept walking and didn’t answer.

Hyde Park’s principal, Antonio Ross, said he has long lobbied for roof and tuckpointing repairs for the more than century-old building, said he wasn’t sure what got CPS to invest in the school, but added, “I think our new neighbor helped out a lot.”

Hyde Park had about 740 students last year, nearly all of them African-American.

Many of the improvements there already have been done. The school has had its smaller gym redone, classrooms painted and new lighting installed throughout the building, work that Ross said “just changes the entire feel of the building.”

Over the summer, the mayor and Jackson, his fifth schools chief, announced plans for nearly $1 billion in capital spending citywide, including building a new high school on the Near West Side that would serve the rapidly growing, high-income West Loop. The mayor also championed the controversial conversion of the highly rated National Teachers Academy elementary school, with a largely black, low-income student body, into a high school for the wealthier families populating the booming Near South Side.

Some parents and the Chicago Teachers Union have questioned why CPS is adding capacity to schools as enrollment across Chicago continues to fall, particularly among African-American families who have left the city. CPS has lost about 33,000 students since Emanuel took office in 2011, about 31,000 of them black.

Jesse Sharkey, president of the Chicago Teachers Union, blamed Emanuel for ignoring neighborhood schools like Hyde Park.

“Emanuel has starved this school community and surrounding neighborhoods for years — and now, as these communities confront gentrification and increasing displacement, he’s prepared to offer what this school and students should have had eight years ago,” Sharkey said.