# College Board omits two PSAT math problems, but reasoning is unclear, confidential

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When the sophomores and juniors received their 2016 PSAT scores online on Dec. 12, several noticed something surprising: in addition to the usual breakdown of subscores, percentiles and question difficulties, there was a note that said questions no. 4 and no. 17 on the non-calculator math section had been omitted.

Of course, this isn’t the first time this has happened. Questions are frequently omitted from scoring on standardized tests, usually due to unforeseen ambiguity.

But that’s just the thing – neither of the two unscorable questions appears ambiguous. In fact, they seem to be among the most straightforward questions on the test.

No. 4 is a multiple-choice question that gives a simple polynomial; the student must choose the equivalent factorization.

No. 17 is a free-response question that gives a system of equations with two variables; the student must solve for y.

Since neither is a word problem, ambiguous wording seems unlikely as the reason for omission.

Mathematical ambiguity is also not the reason, as both problems quite clearly have only one correct answer, according to AP Calculus BC teacher Glenn Mangold, who examined the questions.

“They’re not redundant equations,” Mangold said in reference to the system of equations in no. 17. “I don’t see a problem.

“There doesn’t seem to be anything wrong with (no. 4), either.”

Of course, there are other reasons questions are omitted.

For example, a question could be thrown out if deemed out of scope.

However, in this instance, that can’t be the issue either. For the PSAT, anything from Algebra II or below is fair game. So solving simple systems of equations and factoring polynomials are concepts well within the test’s scope.

Another possible reason is that the College Board, which creates the tests, saw a need to readjust the weighting of the subscores.

As it stands, the math section is broken into three subscores: Heart of Algebra, Problem Solving and Data Analysis, and Passport to Advanced Math. Each section has its own scope of topics.

If the College Board realized post-test that particular topics – factoring polynomials and solving systems of equations, in this case – were being weighted too heavily, they might throw out questions to restore proper weighting.

That said, it seems odd that the College Board would make such weighting miscalculations.

College counselor Jane Bauman suggested that the questions could have been experimental ones for future tests, which would result in their omission from scoring.

According to TestMasters.net, however, unlike the SAT, the PSAT has never had experimental questions. And even if there were experimental questions on the PSAT, they certainly wouldn’t include no. 4 and no. 17. The same problems (though with different numbers) have likely been on every College Board math test since the company’s creation.

So what’s going on here?

Adam Ingersoll, co-founder and principal of the Compass Education Group, has the answer to one of the mysteries – a tiny technicality that wouldn’t have been caught by anyone but test makers and critiquers very familiar with the test.

No. 17 reads: “4x – 9 = -y. 2x = 3y – 5. According to the system of equations above, what is the value of y?” It’s unlikely that any student would be thrown off by the way the question is phrased – math teachers often write problems that are even more concise, like “4x – 9 = -y. 2x = 3y – 5. Solve for y.”

However, the College Board must be precise.

“The problem did not specifically say that the equations solve for the variable,” said Ingersoll. “Without that assurance, the equations could do many things.”

In other words, the question should have said something along the lines of “If (x, y) is the solution to the system of equations above, what is the value of y?”

As for no. 4, though, even Ingersoll doesn’t know the answer.

“We’ve been unable to identify a math-related flaw in the second problem that was thrown out,” he said.

“Our best guess is that there was some other sort of technical problem – perhaps a misprint only affecting certain test booklets, or a problem that they had unintentionally reused from a prior test without realizing it until later. (That) happened on an SAT last spring.”

In any case, nothing can be confidently confirmed or denied as the College Board won’t reveal the reason.

An Octagon reporter who called the College Board five times asked the same question to every representative who answered: “Why were those two problems omitted on the non-calculator math section of the 2016 PSAT?”

And five times the rep gave the same answer: he or she was not permitted to discuss the details of specific questions.

When former college counselor Patricia Fels, who worked with Country Day students for 18 years, heard of the College Board’s resistance to answering something so seemingly inconsequential, she said she wasn’t surprised.

“The College Board was always pretty secretive and dictatorial in my experience,” Fels said. “And for a long time it could afford to be as it pretty much had students over a barrel since there was no other testing option.

“Now, however, the ACT is really giving the SAT a run for its money, so I think the College Board needs to be more open and transparent, especially when it’s the Board’s mistake.

“Students spend a lot of money on taking and retaking College Board tests like the PSAT, the SAT and the Subject Tests. They deserve to know why particular questions aren’t being scored.”

Had the questions been scored as intended, junior Atsuo Chiu would have received credit for both. (To confirm that he arrived at the “correct” answers, he had to check his test booklet because the College Board website doesn’t have the students’ unscored answers on record.)

Chiu said that it is unfair to compromise students’ scores because of the test makers’ mistakes.

“I think that my score should be changed,” he said, examining his booklet. “To be honest, (no.) 4 was an easy question because it was just factoring common terms. But it seems like I had some problems with question 17 because there are three times I did the problem. The first time, it looks like I got it wrong because I scratched it out and did it again. I did it the third time to make sure because there was spare time, and I still wasn’t 100 percent sure about it.

“So, yes, I think I should get the points that I didn’t get awarded.”

Despite his disagreement with the way the College Board handles its mistakes, Chiu acknowledged that there isn’t much to be done.

“I feel a little annoyed, but I don’t really care much because it’s something that won’t change,” he said.

—*By Marigot Fackenthal*

I had a question on problem 24 on the calculator section. It is one of three questions related to a table showing intervals of investments and how many people got those earnings after taking $25,000 and investing. The question is someting like a person at random is chisen from those who got AT LEAST $13,000, what’s the pribability the person at least doubled their money.

This is a conditional probability, so we need to find how many people got at least $13,000. This has an issue in that the intervals given do not limit to exactly $13,000. There are 5 people with $6,000-$9,999 and 17 people from $10,000-$13,000. This means we can be certain of 5 people, but how many of the 17 we are not. However, even if we use the lowest number like 6 or highest 22, using those give us a range. 10/995 or 10/979 are both really close to .01 which would be 1%. The answer was given as 6%. I really don’t see it getting that large. 6% of 995 or 989 are 59 or 60 .. Now if we add in more, like the 35 from the $14,000-$17,000 that gives still 10/944 but that is still around 1%. I don’t get thier answer at all.

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