The 14 students studying A-level statistics at Shrewsbury Colleges Group were given the formula booklet for the mathematics paper during the exam on June 18.
Principal James Staniforth apologised for the mistake and said the programme leader contacted all students immediately after them exam to apologise and reassure them at the correct booklet would be provided for the second paper.
He added: "The exam board have confirmed that they applied special consideration to all students marks for that paper.
" In addition, we wrote on behalf of all students who had applied to university to explain what had happened and we are very pleased that all the students who studied the statistics course and applied to university have secured their places.
"This was both a very rare and extremely unfortunate mishap and we are very sorry for the distress it may have caused some students.
"In ensuring special consideration was applied by the exam board and by contacting the relevant universities we have taken every step to mitigate the impact."