All of the attacks occurred on Saturday.
An Interior Ministry official, speaking on condition of anonymity, said a soldier was killed and three others were wounded when a roadside bomb went off at around noon near an Iraqi army patrol in the town of Taji, situated 30 kilometers (20 miles) north of Baghdad, Xinhua reported.
In another incident, gunmen broke into a house in a village near the city of Samarra, some 120 kilometers (75 miles) north of Baghdad, and shot dead a man and injured two members of his family.
Earlier in the day, a policeman was killed and another wounded by a roadside bomb that exploded near their patrol car in the city of Fallujah, some 50 kilometers (31 miles) west of Baghdad.
Elsewhere, a school teacher was killed and four children wounded in the city of Saadiyah, located 120 kilometers (75 miles) northeast of Baghdad, when a magnetic bomb attached to a school minibus went off.
In addition, four people, including a woman, were killed when a bomb exploded near vendors selling vegetables and fruits on a main street of Saidiyah, a neighborhood in southwestern Baghdad.
Eleven others, including three women, were injured in the blast.
Bombings and shootings have recently increased across Iraq, and many believe that the attacks are being carried out to undermine the central government.
Official figures show that September was the bloodiest month in Iraq in almost two years, with attacks killing 365 people, the highest monthly death toll since August 2010.
The statistics, which were compiled by the health, interior, and defense ministries, show that 182 civilians, 88 police officers, and 95 soldiers were killed in attacks in September.
The violence reached a crescendo on September 8 and 9, when more than 30 attacks killed at least 88 people and injured more than 400.
September 30 was the second deadliest day of the month, with a death toll of 33 and 106 injured.
Violence has increased in Iraq since December 2011, when an arrest warrant was issued for fugitive Vice President Tariq al-Hashemi, who has been charged with running a death squad targeting Iraqi officials and Shia Muslims.
In response, the government has stepped up efforts to increase security across the country over the past few months.