Mitchell had been travelling 96mph in a 60mph zone seconds before impact, the original court hearing was told.
Driving a Mini Cooper, she attempted to overtake three vehicles at once before trying to abort the manoeuvre and hitting the taxi.
Whelan, a history teacher from Woodford in London, had been on the way to a wedding of one of her school friends at the time of the crash.
Mitchell also pleaded guilty to three counts of causing serious injury by dangerous driving in relation to the incident, which happened when she was 18.
The court also heard she had filmed herself speeding just days before the crash.
She was jailed at Gloucestershire Crown Court in February, and her sentence was increased at the Court of Appeal on 28 July.
