Saying its college admission exams do not focus enough on the important academic skills, the College Board announced on Wednesday a fundamental rethinking of the SAT, ending the longstanding penalty for guessing wrong, cutting obscure vocabulary words and making the essay optional.

The president of the College Board,David Coleman, criticized his own test, the SAT, and its main rival, the ACT, saying that both had “become disconnected from the work of our high schools.”

In addition, Mr. Coleman announced programs to help low-income students, who will now be given fee waivers allowing them to apply to four colleges at no charge. And even before the new exam is introduced, in the spring of 2016, the College Board, in partnership with Khan Academy, will offer free online practice problems and instructional videos showing how to solve them.

The changes are extensive: The SAT’s rarefied vocabulary challenges will be replaced by words that are common in college courses, like “empirical” and “synthesis.” The math questions, now scattered across many topics, will focus more narrowly on linear equations, functions and proportional thinking. The use of a calculator will no longer be allowed on some of the math sections.

The new exam will be available on paper and computer, and the scoring will revert to the old 1,600-point scale — from 2,400 — with top scores of 800 on math and 800 on what will now be called “evidence-based reading and writing.” The optional essay, which strong writers may choose to do, will have a separate score.

Once the pre-eminent college admissions exam, the SAT has lost ground to the ACT, which is based more directly on high school curriculums and is now taken by a slightly higher number of students. Last year, 1.8 million students took the ACT and 1.7 million the SAT.

The new SAT will not quell all criticism of standardized tests. Critics have long pointed out — and Mr. Coleman admits — that high school grades are a better predictor of college success than standardized test scores. More colleges have in recent years become “test optional,” allowing students to forgo the exams and submit their grades, transcripts and perhaps a graded paper.

For many students, Mr. Coleman said, the tests are mysterious and “filled with unproductive anxiety.” And, he acknowledged, they inspire little respect from classroom teachers: only 20 percent, he said, see the college-admission tests as a fair measure of the work their students have done.

Mr. Coleman came to the College Board in 2012, from a job as an architect of the Common Core curriculum standards, which set out the content that students must master at each level and are now making their way into school.

He announced plans to revise the SAT a year ago and almost from the start expressed dissatisfaction with the essay that was added in 2005. He said he also wanted to make the test reflect more closely what students did in high school and, perhaps most important, rein in the intense coaching and tutoring on how to take the test that often gave affluent students an advantage.

“It is time for the College Board to say in a clearer voice that the culture and practice of costly test preparation that has arisen around admissions exams drives the perception of inequality and injustice in our country,” Mr. Coleman said Wednesday. “It may not be our fault, but it is our problem.”

While test-preparation companies said the SAT was moving in the right direction, with more openness and more free online test preparation, the changes were unlikely to diminish the demand for their services. “People will always want an edge,” said Seppy Basili, a vice president of Kaplan Test Prep. “And test changes always spur demand.”

The suggested changes were well received among many educators, but Mr. Coleman’s comments about the ACT drew harsh words from an executive of that company.

“David Coleman is not a spokesman for the ACT, and I acknowledge his political gamesmanship but I don’t appreciate it,” said Jon Erickson, president of ACT’s education division. “It seems like they’re mostly following what we’ve always done.”

Philip Ballinger, the director of undergraduate admissions at the University of Washington, said he admired Mr. Coleman’s heartfelt “damn the torpedoes, full speed ahead” approach to improving the SAT and appreciated the effort to tame the test-prep industry.

“It’s absurd, and that’s the nicest thing I can call it, how much test prep has grown and how guilt-ridden parents have become about trying to prepare their kids for the test,” Mr. Ballinger said. “If this helps test prep become learning, not gaming, well, shoot, that’s great. “

Some changes will make the new SAT more like the ACT, which for the last two years has outpaced the SAT in test takers. Thirteen states administer the ACT to all public high school juniors, and three more are planning to do so. The ACT has no guessing penalty, and its essay is optional. It also includes a science section, and while the SAT is not adding one, the redesigned reading test will include a science passage.

But beyond the particulars, Mr. Coleman emphasized that the three-hour exam — three hours and 50 minutes with the essay — had been redesigned with an eye toward reinforcing the skills and evidence-based thinking that students should be learning in high school, and moving away from a need for test-taking tricks and strategies. Sometimes, students will be asked not just to select the right answer but to justify it by choosing the quotation from a text that provides the best supporting evidence for their answer.

The revised essay, in particular, will shift in that direction. Students now write about their experiences and opinions, with no penalty for incorrect assertions, even egregiously wrong ones. In the future, though, students will receive a source document and be asked to analyze it for its use of evidence, reasoning and persuasive or stylistic technique.

The text will be different on each exam, but the essay task will remain constant. The required essay never entirely caught on with college admissions officers. Many never figured the score into the admission decision and looked at the actual essays only rarely, as a raw writing sample to help detect how much parents, consultants and counselors had edited and polished the essay submitted with the application.

The Key Changes

These will be among the changes in the new SAT, starting in the spring of 2016:

■ Instead of arcane “SAT words” (“depreciatory,” “membranous”), the vocabulary definitions on the new exam will be those of words commonly used in college courses, such as “synthesis” and “empirical.”

■ The essay, required since 2005, will become optional. Those who choose to write an essay will be asked to read a passage and analyze the ways its author used evidence, reasoning and stylistic elements to build an argument.

■ The guessing penalty, in which points are deducted for incorrect answers, will be eliminated.

■ The overall scoring will return to the old 1,600-point scale, based on a top score of 800 in reading and math. The essay will have a separate score.

■ Math questions will focus on three areas: linear equations; complex equations or functions; and ratios, percentages and proportional reasoning. Calculators will be permitted on only part of the math section.

■ Every exam will include, in the reading and writing section, source documents from a broad range of disciplines, including science and social studies, and on some questions, students will be asked to select the quotation from the text that supports the answer they have chosen.

■ Every exam will include a reading passage either from one of the nation’s “founding documents,” such as the Declaration of Independence or the Bill of Rights, or from one of the important discussions of such texts, such as the Rev. Dr. Martin Luther King Jr.’s “Letter From Birmingham Jail.”