Some standardized tests administered to D.C. students this week included confusing instructions that city officials sought to clarify after teachers and principals — some of whose jobs depend on test results — reported the problems.

Directions for one section of an eighth-grade math test said that students could use calculators only on the first 16 questions, when, in fact, they were allowed to use calculators on questions 17 and 18 as well.

On a fifth-grade math exam, a picture of a stop sign printed on students’ answer sheets directed them to stop after answering Question 49. But the section actually continued on the next page to Question 52.

And on a sixth-grade math exam, both parts of a two-part question were labeled “49A” in the test booklet, but answer sheets labeled them as “49A” and “49B.”

CTB/McGraw-Hill writes the tests under a contract with the Office of the State Superintendent of Education, the city agency responsible for administering standardized tests. The publishing company received $3.4 million this year to develop, print and analyze the city’s annual tests.

Jesus Aguirre, who leads OSSE, called the problems “minor typographical errors” that affected only a small number of questions. Aguirre said agency staff provided guidance as soon as they heard about the issues after testing began this week.

Aguirre said CTB will analyze each question and throw out those for which students provided a statistically skewed number of incorrect answers, as they do every year. “We’re pretty sure that we’re going to get valid testing results,” he said.

Pete Weber, chief of data and strategy for D.C. Public Schools, which is required to administer the tests received from OSSE, said school system officials are “very disappointed and frustrated about these errors.”

“This is already a very stressful time for our teachers and school staff, and these issues do not help,” Weber said. “We are providing guidance and support for schools to deal with the errors, and we hope that no more come up during this test administration.”

Students who had already taken the flawed sections of the sixth-grade and eighth-grade exams before OSSE clarified instructions are not allowed to go back and revisit them.

Fifth-graders who stopped at Question 49 instead of 52, as the answer sheet directed them to do, are able to go back and answer those three questions. Proctors giving that exam have been told to remind students that they should turn the page past the stop sign, the kind of assistance that teachers have been trained not to offer to avoid accusations of cheating.