"shouldn't it be "J'ai eu peur que nous ne soyons arrivés trop tard?" The correct answer did not include ne."

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Hi Ann,
this is a question of register. In formal French you would use the ne, whereas in spoken French, often you don't use it. With or without ne, the meaning remains unchanged.

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But shouldn't it be marked correct as we don't know whether the tester wants the formal or the dialogue? This way one does not have to go through several exercises to prove one understood

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I think in the context of the lesson, which is trying to get students to learn the ne-explétif, it is understood to use the "ne" whenever appropriate.

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So the answer is wrong. The 'ne' should be there. We have to assume formal language, unless told otherwise!