Ex. 11. Ask special questions

Ex. 10. Choose the correct tense form.

Ex. 9. Fill in a suitable verb in the Present Perfect Tense.

to give, to become, to show, to draw, to learn, to find, to be, to make, to take, to rewrite

1 They … an attempt to overcome difficulties of this complicated procedure.

2 The science adviser … the whole situation under control.

3 They … not all the examination material yet.

4 I … this article on Maths very helpful.

5 In the given example he … the validity of these principles.

6 The post-graduate … the previous chapter of his report.

7 He … a first-year student of the Mechanics and Mathematics faculty this year.

8 My friend … already the diagram which has certain advantages.

9 The teacher … an example of an algorithm.

10 … you … able to name these rational numbers by decimal numerals?

1. (Have you ever heard/ Did you ever hear) about continued fractions?

2. We (have started/ started) learning fractions when we were at school.

3. By the end of the lecture the students (had learnt/ has learnt) that in Higher Mathematics a fraction is viewed as an element of a field-of fractions.

4. I (have looked up/ looked up) in a dictionary just now the meaning of the word ‘a solidus’(a slanting line).

5. She just (has written/ wrote) this mixed number in another way; i.e. as an improper fraction.

6. She (will have studied/ will study) carefully the chapter about complex fractions by the end of the week.

7. When you come back I (will have divided/ have divided) these fractions using the rule “invert and multiply”.

8. I need to subtract two fractions but I (haven’t got/ didn’t get) the least common denominator yet.

9. Before he solved the problem he (had had to/ have had to) convert the repeating decimals into fractions.

10. You (have remembered/ remembered) since school that a fraction is in its lowest terms when its numerator and denominator have no common factor other than one.

1. By 5 o’clock the experiment will have been over. (by what time) 2. By the age of 41 Sophia Kovalevskaya had won recognition of mathematicians all over the world. (whose) 3. Zero concept has got many new applications in modern science and engineering recently. (what kind of) 4. Russian scientists had introduced thousands of new concepts by the end of the 20-th century. (who) 5. The students haven’t attended the course in the history of mathematics this month. (why) 6. They had obtained some equations by using mathematical terms before the teacher collected their papers. (how) 7. For a long time the major task of mathematicians has been to express ancient algebra in modern symbols. (how long) 8. By the end of the year the historian will have written four new books about the work of genii of mathematics. (how many) 9. Man’s technical progress has developed greatly. (what) 10. Most people have come across the term industrial robots. (what, who) 11. Some European mathematicians have tried to prove Fermat’s last theorem ever since it became known. (since when) 12. Pr. Smirnov’s postgraduates will have finished the experiment before he comes. (whose)

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