Mayor Bill de Blasio’s agenda-setting speech Wednesday could have been titled: What comes after pre-K? In a word, his answer was college.

After the mayor’s widely heralded expansion of full-day pre-kindergarten, which accompanied the launch of a turnaround program for struggling schools and a reorganization of the education department, many critics and parents were waiting for a clear vision for improving the rest of the school system.

In his speech at a high-performing Bronx high school, de Blasio sought to offer one, saying that his disparate school initiatives would operate in tandem to propel students toward college.

After pre-K, new programs will ensure students can read fluently by third grade and take algebra by ninth grade. In high school, every student will have access to advanced courses and help with college applications. And at all levels, students will learn the basics of computer science, which should make them more competitive as college applicants and job seekers.

The end goal of the these efforts — which are expected to cost $186 million annually when fully in place — is that a decade from now 80 percent of students will graduate high school each year and two-thirds will leave prepared for college-level work, the mayor said. Today, 68 percent of students graduate within four years, and less than half are considered ready for college classes.

[Read more about the specific initiatives, and their timelines, here.]

The speech seemed to strike the right chords. Observers said it balanced ambitious targets with student-focused initiatives that filled in policy gaps and are likely to appeal to parents and outside partners, such as technology companies and philanthropists.

“We can finally see a working vision for school reform taking shape under Mayor de Blasio’s leadership,” said Zakiyah Ansari, a public-school parent and advocacy director for the Alliance for Quality Education, in one of dozens of statements from advocates, businesspeople, and politicians that City Hall sent to reporters.

Still, the policy speech came with a heap of caveats and questions.

Most of the new programs won’t launch until next fall — after state lawmakers will have had to decide whether or not to extend his control over the city school system — and he will be out of office by the time his 2026 graduation deadline arrives.

Will the city be able to pull off the new programs, which will require extensive teacher hiring and training along with philanthropic funding? And even if the efforts go as planned, will they guarantee that students read proficiently and graduate high school in record numbers?

“Those are lovely goals,” said New York University research professor Leslie Santee Siskin, “but it would take a lot of work and reconfiguring of practice to make them reachable.”

The essence of de Blasio’s new agenda, he said, was summed up in the giant banner that hung over him in the Bronx Latin auditorium Wednesday: “Equity and excellence.” The idea is to improve the quality of all city schools, while making sure every student has access to the same learning opportunities.

That means that all second-grade students will eventually be able to get help from an on-site reading specialist, all eighth-grade students will be able to take algebra at their schools, and all high-school students will be able to take a range of Advanced Placement courses, according to the mayor’s plan. In addition, all 1.1 million city school students will get a chance to study coding, robotics, and other aspects of computer science.

Kim Nauer, education research director at the New School’s Center for New York City Affairs, said the mayor made a convincing argument that every school should offer stronger reading, math, and computer programs.

Those “struck me as something that the middle class and upper-middle class have always assumed for their children,” she said. “And so here he’s saying, all kids should have access to this quality of curriculum.”

Still, each program faces formidable challenges.

The city is proposing that within six years the reading specialists, combined with teacher training, will be able to more than double the number of incoming third graders who are proficient readers — from 30 percent today up to 66 percent. At the same time, more than 15,000 more eighth-graders who lack access to algebra classes and nearly 40,000 high-school students without AP options will need to receive them.

Meanwhile, the system-wide computer science classes will require some 5,000 trained teachers, officials estimate. And it will cost $81 million over a decade, with half that amount coming from private sources. So far, only about 30 percent of the private money has been committed, officials said.

Even if the city pulls off the extraordinary amount of hiring, training, and curriculum development that those programs will demand, it’s far from certain that they will lead to a 12-point increase in the graduation rate within a decade.

Aaron Pallas, a sociology and education professor at Teachers College, recalled a national education panel in the 1990s setting the goal of a 90 percent U.S. graduation rate by 2000. By 2013, the rate had hit 81 percent. While Pallas commended de Blasio for setting an ambitious target, he said detailed plans are needed.

“It’s easy to set those kinds of aspirations,” he said. “It’s harder to figure out the specific strategies.”