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I. Match the words in column a with their equivalents in column b.

1. pure mathematics

a) функция

2. axiom

b) дифференциальное уравнение

3. geometry

c) доказывать

4. theorem

d) аксиома

5. differential equation

e) выводить

6. concept

f) геометрия

7. calculus

g) концепция

8. deduce

h) вычисления

9. function

i) теорема

10. prove

g) чистая математика

II. Fill in the blanks with the proper words.

1. ... constitute the second major component of any branch of mathematics.

a) geometries                                             b) theorems

c) differential equations                            d) axioms

2. The objective of mathematical activity consists of the ... deduced from a set of axioms.

a) functions                                                 b) theorems

c) concepts                                                  d) notions

3. The … of number give rise to the results of algebra.

a) axioms                                                      b) functions

c) calculus                                                   d) geometries

4. Mathematical ... must be deductively established and proved.

a) axioms                                                      b) concepts

c) theorems                                                  d) numbers

5. Some mathematicians claim that ... is the most original creation of human mind.

a) pure mathematics                                   b) geometry

c) theorems                                                  d) concepts

III. Choose the right answer to the question.

1. What is the second major component of any branch of mathematics?

a) axiom                                                        b) concept

c) notion                                                       d) theorem

2. What was considered as the basic self-evident truth about concepts up to the 19th century?

a) proofs                                                      b) axioms

c) calculus                                                   d) theorems

3. What may very logically follow from the axioms?

a) functions                                                 b) axioms

c) theorems                                                  d) set of notions

4. How is scientific knowledge produced?

a) by deductive reasoning                        b) by experience

c) from a set of axioms                               d) by mathematical calculus

5. How do mathematicians nowadays investigate algebra and geometry?

a) with immediate application                   b) with no immediate application

c) without any application                        d) with one application

IV. Choose the proper title to the text.

a. Mathematical theorems

b. Axioms as the second major component of any branch of mathematics

c. Mathematical concepts

d. Geometry as the second branch of mathematics