This file photo shows a student leaving after taking the SAT at Upper Arlington High School in Upper Arlington, Ohio. (Paul Vernon/AP)

Is SAT angst easing? There are signs of a more intelligent attitude toward what has been America’s most-feared test, a test for which the Class of 2015 had the lowest average composite scores in a decade.

Fewer colleges are requiring that applicants take the SAT or its rival college admission exam, the ACT. More of the students who yearn to attend the most selective colleges are realizing that their SAT or ACT scores are not the most important factor for getting in.

I know how scary those tests can be. I suffered a panic attack near the end of the SAT that was much worse than anything I experienced while serving as a soldier in Vietnam. But I also know that the best preparation for the SAT and the ACT is just listening in class and doing your homework.

To dispel further pre-test terror, I have a few tips from an accomplished college counselor on the changes in the math sections of the PSAT and the SAT. The advice from Perry Youngblood of Southern Pines, N.C., was originally sent to me by Shirley Bloomquist, a private college counselor in Northern Virginia. She used to be the guidance director at the Thomas Jefferson High School for Science and Technology, which has the highest SAT average in the country.

Youngblood said he found few surprises in the new PSAT, usually taken by 10th-graders as preparation for the SAT. The emphasis will be on algebra, particularly on linear and quadratic equations.

“Students really need to understand what makes up a linear equation,” Youngblood said. “They should be able to explain in words what a slope of a certain value means in the context of the problem. Many problems in the new test deal with these concepts.”

He found many more surprises in the prep book for the new SAT released in June. “Several of the math concepts included are typically taught in pre-calc [or pre-calculus] as opposed to Algebra 2,” Youngblood said. “Students need to understand the remainder theorem of polynomials. They need to understand the relationship between the zeros of a polynomial and its binomial factors. They must be able to take a quadratic equation or an equation of a circle in whatever form and convert it, perhaps by completing the square, to a form so that they can analyze the graph.”

Concepts will be important, he said. One practice question he saw gave the formula for the height of an object under ballistic motion as a function of its initial vertical velocity and time, and asked when the object would return to the ground.

“Other SAT topics that are either new or more difficult include histograms, scatter-plot interpretation, unit analysis, inference from a sample, two-way tables, exponential functions or compound interest,” he said.

Useful practice problems and tests developed by the Khan Academy can be found on the College Board Web site. Long before the SAT and ACT existed, students feared tests. But examinations, even those as annoying as the SAT, are part of the learning process. You are more likely to master facts and concepts if you review them later. That is what testing is all about.

I don’t see any lasting harm from the fright that such tests, from my 10th-grade geometry final to the SAT, have inflicted on students wanting to go to college.

Some parts of the application process, such as demonstrating interests pursued outside the classroom, help give teenage life needed depth.

Selective colleges’ demands for extra-curricular activities help students persuade parents that taking homework time to play basketball, write songs, bake bread or design video games adds to their attractiveness to colleges. Those after-school activities, as well as teacher recommendations and grade-point standing in the high school class, will have more weight in admissions to a selective college than the SAT.

They also will have at least as much benefit as understanding the relationship between zeros of a polynomial and its binomial factors.