The task is to create a negative sentence using the contraction. The original sentence is 'My mother will cook cookies next Sunday.' The negative contraction for 'will not' is 'won't'. Thus, the negative sentence is: 'My mother won't cook cookies next Sunday.'
Therefore:
{"question": "Постройте отрицательную форму (сокращённую). Напишите предложение целиком. My mother will cook cookies next Sunday.", "answer": "My mother won't cook cookies next Sunday."}