A few days ago my grandson Robbie was doing his homework in our den. My pal asked me to go over his history and math homework with him.

Of course I was delighted to give him a hand and listened as he told me of the Aztec ruler Montezuma and his losing battle in Mexico facing the Spanish conquistador Hernan Cortes in the 1500s.

From history he switched to math. Perusing his math textbook I was stunned by the areas covered by fifth- and sixth-grade teachers and their pupils these days. From identifying prime numbers, recognizing and naming geometric solids to using fractions and converting units of liquid measure, all I could say was “Wow!”

I hadn’t faced those challenges until I was deep into high school. Here and now I realize that the students of Kolbe Academy-Trinity Prep and other Napa Valley schools leave us 1940s and ’50s students in the dust in the neverending search for knowledge.

But before Robbie’s books were packed away in his duffle bag and we left the den, my grandson — who forgets nothing in terms of schoolwork — asked me a question. “Grandpa, a few months ago before my fifth-grade final exams, you told me about the exams you took and how you were taught to approach them. You promised to tell me about the toughest exam you ever took. Could you tell me now?”

“Sure,” I said, “there is one exam I’ve never forgotten.”

I had studied hard for NYPD’s 1970 lieutenants exam, along with two friends and fellow sergeants: John Loughery who was sharp and funnier than his Bronx high school buddy Regis Philbin; and Bob Muir, a no-nonsense guy and the glue that held our small study group together.

We were sergeants and friends in the same lower Manhattan command in 1970, and our studying was at times broken up by the many demonstrations, disorders and riots in those bitter anti-Vietnam War years. But somehow we hung tough in terms of preparing for the lieutenants exam.

We’d meet at each other’s houses, at the police academy’s in-service classes, at a tutorial school we paid for and in the back rooms at our command after a tour of duty — in short almost anywhere.

New York State’s Penal Law and Code of Criminal Procedure had received its first major overhaul since 1909, and we took the new laws apart. A desk lieutenant in any of NYPD’s 75 precincts above all else had to know the law to correctly charge and book prisoners. We also agonized over the department’s rules and procedures, criminalistics, investigatory procedures, forensics, supervision and management and even current events out of the New York Times (no friend of ours.)

The tutorial school was big on test-taking techniques, and we listened and learned. “Pick off the answers that pop right out, you should have 40 to 50 answered in the exam’s first hour. Then go back, but don’t bog down on a single question. Keep on going.” Finally, we were taught to never change an answer unless we misread the question. The school told us that changing your first choice in two out of three cases would lead you from right to wrong. We never knew where the school got those statistics from, but we listened.

On the morning of the exam, about 2,000 sergeants were on hand and knew the ground rules. The mark of the top 200 sergeants, plus ties, would be the passing mark, and everyone wanted to make that list. But as the starting bell rang and booklets were opened, all bets and techniques went out the window.

Some Machiavellian minds in the city’s Personnel Department had prepared an exam that would test the courage of a saint. The four-hour exam consisted of 135 questions — no problem— but the monkey wrench thrown into the exam became obvious and ominous immediately.

No problems tackling A to D choices, but E was the horror. If none of the above answers were correct, or if more than one choice was correct, then the answer was E. This cute trick raised the level of difficulty tenfold at least.

The degree of difficulty on that exam produced a list of 200 lieutenant eligibles with the passing mark of 54 percent. Unheard of in civil service testing before or since.

Horror stories abounded in the weeks and months that followed the posting of the key answers and the publication of the list of successful candidates. Guys had walked out or blacked out on test day, others tore up their booklets. The police academy’s young hotshot sergeant, who taught the promotion classes, had failed the exam and seemed to just fade away.

When John, Bob and I gathered at my car after the exam, we shook our heads and smiled. If we didn’t do that, we’d have sat down on the curbstone and cried.

My grandson Robbie asked me if I passed that exam. Somehow I did, but on the day the key answers were released by the city, I thought my 100 correct answers out of 135 questions, or 74 percent, would not be good enough.

However, months later when the lieutenants list was published I, among others, was astounded that the pass mark was an unbelievable 54 percent. I had worried needlessly and finished 20 points above the cutoff mark.

So I told Robbie that if he studied, I mean really dug into his books, good things will happen. I told him that if he was having trouble on an exam he’d studied for, he could be certain that his classmates were in the same boat. I said “Robbie, the trick is to study hard and never give in!”

Postscript: John Loughery and I were promoted to lieutenant in May 1971, the same day Black Panthers ambushed and murdered two young NYPD officers at the Polo Grounds project. (They should never have torn down the ballpark.) Bob Muir was promoted six months later. All three of us had refused to give up.

Ev Parker can be reached at evjenpar@mailbug.com or 224-9956.