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The remote-controlled bomb was planted at the outer wall of the government-run middle school in the outskirts of Mardan town in troubled Khyber Pakhtunkhwa province.
The bomb exploded after police arrived to investigate complaints about a suspicious plastic bag outside the school, which was closed at the time.
"One policeman was killed and eight other people including five civilians were wounded," Zeshan Haider, Mardan police chief, told AFP by telephone.
Three policemen were also wounded but no pupils were hurt.
Haider said the target was the school.
"The outer wall of the school was also destroyed," he added.