1.A
B错在从句的时态应该和主句的found保持一致,即它必须使用一般过去时it was...,而不是一般现在时it is...
I found that maths problem hard to work out.
= I found that maths problem was hard to work out.
= I found (that) it was hard to work out that maths problem.
= I found it hard to work out that maths problem.
2.C
该题如果选用ABD,它们都是使用定语从句修饰先行词the days,但是它们的关系词都错误.
A不能用when.因为the days在定语从句中充当had的宾语,所以必须选用关系代词which/that或不填,而不能使用关系副词when,因为此时该句不缺时间状语,而是had后面缺少宾语；
B同样不能用when.因为the days在定语从句中充当spent的宾语,所以必须选用关系代词which/that或不填,而不能使用关系副词when,因为此时该句不缺时间状语,而是spent后面缺少宾语；
C不能省略不填关系代词.因为the days在定语从句中we stayed together in that remote village中充当时间状语,所以必须选用关系副词when,而不能使用关系代词which/that或不填.因为此时该句缺时间状语,而不是缺少宾语.
所以答案为C,用过去分词短语spent together in that remote village直接做the days的后置定语.因为spend和the days之间是被动关系,而且该动作已经发生,所以用过去分词形式spent.
3.D
固定短语practise doing sth“练习做某事”,排除AC；
该句为被动句,换成主动时为Sb listened to the girl sing songs at the room.它采用了不带to的不定式（即动词原形）sing做宾语补足语.
但是,该结构变为被动语态后,必须补回缺省的不定式符合to,所以排除B,正确答案为D.
