Jade Clark was riding a red scooter that was in collision with a car at around 8.20pm on Sunday night between the Verwood on-slip road and the A338 off-slip road.
She was pronounced dead at the scene and next of kin have been informed, police said.
Chris Edwards, headteacher at Ringwood School, said Jade left the school in July 2012 to follow her love of hairdressing by starting a college course.
“She had a lively, bubbly personality and was always full of life,” Miss Edwards said.
“She will be remembered as someone who had a ‘huge heart’, always willing to help others in difficulty – a really positive force for good.
“Jade was always grateful for everything life had to offer.
“She wanted to improve herself, and refused to let things hold her back.
“She dropped in to see us on a regular basis to let us know how she was getting on, and to thank people for their help and support.
“It was a real joy to see the progress she had made, an independent, confident young woman enjoying life to the full.
“Our thoughts and best wishes go to her family and friends at this difficult time.”
This morning commuters faced chaos as the A31 was closed westbound from Ashley Heath to junction two of the M27. A rolling road-block was taking traffic through the New Forest with reports of heavy congestion on diversion routes.
All lanes were reopened around 1.10pm.
The road was closed at around 8.20pm on Sunday after the collision.
It happened on the stretch between the northbound A338 Salisbury Road and Ashley Heath interchange.
A lane of the eastbound carriageway was closed to allow for investigation work but has now been reopened.
A spokesman for Dorset Police said: "Family liaison officers are currently working with the relatives of the deceased.
"We would like to apologise for any incovenience these road closures cause, but this is an extremely serious and complex road traffic collision.
"We would like to thank motorists for their patience."
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