1.

At school children study subjects like the mathematics and the history, and learn how to take their place in the society.

At school children study subjects like [the] mathematics and [the] history, and learn how to take their place in [the] society.

2.

The young people can learn a lot from the old.

[The] young people can learn a lot from the old.

3.

She wants to be actress like girl next door.

She wants to be AN actress like THE girl next door.

4.

In the morning he plays the squash before he goes to the work.

In the morning he plays [the] squash before he goes to [the] work.

5.

New houses are within easy reach of shops, public transport and leisure centre just opened by mayor.

THE new houses are within easy reach of THE shops, public transport and THE leisure centre just opened by THE mayor.

6.

Twice a week there are lectures in the library on the life and culture of the British Isles.