No one has yet claimed responsibility for the attacks.
An interior ministry official said 12 of those killed in Dora were students at a nearby technical college.
The remaining three victims were policemen working at the checkpoint.
The Iraqi parliament held an emergency session to discuss the bombings. Many MPs have condemned the government's handling of the security situation in the capital.
They also condemned the government for failing to provide a senior security minister to answer MPs' questions.
Tuesday's bombings come two days after the Iraqi parliament passed a new electoral law paving the way for parliamentary elections on March 7, 2010.
Iraqi and US military officials have expressed concern about a possible spurt in attacks aimed at destabilising the government before next year's polls.
Zeina Khodr, Al Jazeera's correspondent in Iraq, said the attacks are another embarrassment for the government.
"We just spoke to a high raking official who said he was worried that the security forces were infiltrated," Khodr said.
"This is a blow to the security forces and prime minister Nuri al-Maliki, who is running for re-election on a platform that he has improved security across the country.
"Attacks have become part of daily life, not only in Baghdad, but across the country. Security is not only fragile, it is deteriorating."
On Monday, eight people were killed when a bomb exploded at a school in Baghdad. The dead included six children, 41 people were wounded in the attack.
On the same day gunmen stormed a checkpoint near Tarmiyah, north of Baghdad, killing five members of an anti-al-Qaeda group, police said.
The men were members of the Sunni Awakening Council, one of many Sunni groups that have begun taking on al-Qaeda in Iraq.
The US has 115,000 soldiers in Iraq, but that figure will drop to 50,000 next year as all of its combat troops are pulled out before a complete withdrawal by the end of 2011.