State officials touted increases in scores on tough Common Core exams this year but failed to reveal that they had lowered the number of right answers needed to pass half the exams.

The state Education Department dropped the number of raw points needed to hit proficiency levels in six of the 12 English and math exams given to students in grades 3 to 8, officials acknowledged.

“The reason that occurs is because the tests are slightly harder,” Deputy Education Commissioner Ken Wagner told The Post.

Student scores plunged on last year’s statewide 3-8 tests — the first based on the new Common Core standards. Before the 2013 exams, a panel of 95 educators decided how many points, or correct answers, students had to get to demonstrate proficiency.

But the point cutoffs were tweaked after this year’s tests. The state and its testing vendor, Pearson, found six tests were harder and four easier this year than in 2013, Wagner said.

They did so by comparing how students performed on “anchor” test questions — identical items used in both 2013 and 2014. A report on the scoring process will be released in December or January, Wagner said.

The changes raise questions about the validity of the results.

“The information given out about the test questions does not provide a complete picture, making it hard to judge how much progress students made last year,” said Fred Smith, a former testing analyst for city schools.

Score manipulation has erupted in scandal before. Between 2006 and 2009, the state reduced the number of raw points students needed to pass. Then-state Education Commissioner Richard Mills insisted the questions got harder, justifying the lower passing scores. But experts found the test items got easier, inflating scores hailed by then-Mayor Mike Bloomberg, among others, as proof of great progress.

Raw points are converted to scaled scores, which are divided into four levels, with Level 1 the lowest and Level 3 “proficient.”

Last year, fourth-graders needed 38 raw points out of 55 on the English test to hit Level 3. This year’s fourth-graders needed only 36.

The number of points needed to pass also dropped on five other tests: third-grade English and math, fifth-grade math, sixth-grade math and seventh-grade English.

On four of this year’s tests, points needed to pass rose: fourth-grade math, seventh-grade math, fifth-grade English and sixth-grade English.

The points required remained the same on the eight-grade exams.

Overall this year, the number of city students who passed the math exam jumped from 30.1 to 34.5 percent. In English, the number of students rated proficient inched up from 27.4 to 29.4 percent.

“It’s a good day for the whole New York City school system,” Mayor de Blasio declared, adding students and schools shouldn’t be judged on tests alone.