There was a rise of 23 per cent in rape cases over the year, largely down to an increasing number of victims coming forward in historic cases after high-profile celebrity sex abuse claims.
These historic rapes accounted for 36 per cent of all reports, while an increase in domestic rapes also contributed.
In road traffic accidents, culpable homicide cases - which include causing death by dangerous or careless driving - went up by 73 per cent.
During 2013/14, 191 people were killed on Scotland's roads, an increase of 14 per cent. Both motorcyclist and pedal cyclist deaths increased by half, while child fatalities also went up from two to eight.
Chief Constable Sir Stephen House said: "The data clearly shows rises in sexual crime including the number of rape cases reported to us and investigated. We said from the outset of the single service that such crimes were under-reported and that we wanted to instil confidence in those who suffer at the hands of sexual offenders.
"Measures were put in place to ensure that not only could victims have the confidence to be able to come forward and report to us, but that those who offend in this way would be targeted in a more consistent way.
"The result of these approaches can be seen in the information published today. More victims of sexual crime including rape are willing to report to the police and more offenders are being caught by officers."
However, a spokeswoman for Rape Crisis Scotland warned that while some of the cases may be the result of more people coming forward, it did not account for the total increase.
She said: "It's very difficult to know exactly how to account for an increase in these cases.
"It's certainly true that the police have taken steps to improve things. There's a national rape task force and a great deal of partnership working. But we cannot discount the possibility that at least some of this is due to increased perpetration and that really is worrying."
A total of 1,690 rapes were reported to the police over the year. However, it is estimated that around 75 per cent of attacks go unreported.
The figures showed that almost one-quarter of rape victims were under 15 at the time they were attacked, while 18 per cent were asleep. Just five per cent of victims were raped by a stranger.
The detection rate for rape increased by 10 per cent to 71.8 per cent.
Despite a reduction in both serious and minor injuries in road traffic accidents, Sir Stephen said the road fatality figures pointed to a "bad year" on the country's highways.
Superintendent Iain Murray, head of road policing, added: "Research from Road Safety Scotland show that there is still a very high number of drivers who continue to wilfully engage in dangerous behaviour - a figure of almost three quarters.
"And in fact more than 55 per cent admit to engaging in illegal behaviour on the roads.
"These drivers don't see themselves as having a social impact and that's something that needs to change."