Pete and Kate are going to stay in a hotel this weekend. (Subject-verb agreement)
They are not going to finish the work before next week. (Missing auxiliary verb 'are')
I'm not going to be at the party next week. (Missing verb 'be' after 'going to')
He is going to visit the Opera House in Sydney in the summer. (Subject-verb agreement)
I'm not going to study French next year. (Missing infinitive marker 'to' after 'going')
There is going to be a computer course next week. / There are going to be... (Missing 'is/are' and 'be' after 'going to' depending on context of computer course - singular/plural). Assuming singular: There is going to be.
Are you going to play football this weekend? (Missing infinitive 'to play')
You are going to eat at that new restaurant this weekend? (Missing auxiliary verb 'are')