1. Mathematicians have used mathematical formulas in solving these problems. 2. By the end of the lesson we’ll have been able to obtain the modified definition of the function. 3. Scientific theories have often suggested directions for mathematical investigations. 4. Physical objects and observed facts had often served as a source of the postulates in Maths. 5. Einstein was able to achieve some of his results after Maths had suggested new ways of thinking about space and time. 6. Abel had hardly reached the age of 22 when he made two of his most famous discoveries. 7. Algebra has become the science that can deal effectively with anything. 8. By the end of June the students will have passed their exams and gone on holiday. 9. Throughout the centuries people have improved their ability to record, process and communicate information. 10. When you come, I will have solved these equations with fractions. 11. This century scientists have made a lot of discoveries about the universe.