(Part 1)

1. According to the passage, Egyptian mathematics merged with Greek and Babylonian mathematics to give rise to mathematics of…

a) ancient China.

b) India and Pakistan.

c) Hellenistic period.

d) the Islamic Caliphate.

2. The R-hind papyrus suggest the simplest of underpinnings to analytical…

a) geometry.

b) algebra.

c) linear equation.

d) the circumference of the circle.

3. Ancient Egyptians said that the area of a circle is repeatedly taken as equal to that of the square of 8/9 of the…

a) golden ratio.

b) Pythagorean theorem.

c) radius.

d) diameter.

4. The word frustum means

a) "the truncated cone or pyramid".

b) " the truncated cone or cylinder".

c) " the truncated circle or pyramid".

d) " the truncated cone or cotangent".

5. Which of the following would be an appropriate title for this passage?

a) History of Egyptian Algebra.

b) Ancient Egyptian Mathematics.

c) History of Islamic Mathematics.

d) Early Egyptian and Hellenistic Mathematics.

6. The word combination right cylinder in the text is closest in meaning to …

a) a geometric figure having circular bases and a surface perpendicular to the bases.

b) a geometric figure having circular bases and a surface parallel to the bases.

c) a geometric figure having circular bases and no surface perpendicular to the bases.

d) a geometric figure having perpendicular bases and a surface circular to the bases.

7. The word underpinnings in the text is closest in meaning to …

a) opinions.

b) amounts.

c) fundamentals.

d) volumes.

8. According to the text, the ancient Egyptians extracted …

a) the volume of a right cylindroid and the area of a triangle.

b) the volume of a right cylinder and the perimeter of a triangle.

c) the volume of a right cylinder and the area of a triangle.

d) the volume of a circumference and a value of π.

9. What can you state as the main idea of the text?

a) Ancient Egyptians possessed rather deep knowledge of mathematics.

b) Ancient Egyptians suggested the simplest of underpinnings to analytical geometry.

c) Egyptian mathematics merged with Greek and Babylonian mathematics to give rise to Hellenistic mathematics.

d) Egyptians recorded an instruction manual in arithmetic and geometry and other mathematical texts on papyrus.

10. The word papyrus in the text is closest in meaning to …

a) any ancient document or manuscript on papyrus.

b) a tall water plant of the sedge family.

c) a writing material.

d) an ornamental.

(Part 2)

1. According to the passage, "Babylonian mathematics" means any mathematics of the peoples of …

a) present-day Iran.

b) present-day Iraq.

c) present-day Ireland.

d) present-day Mesopotamia.

2. Now we know that the Babylonians used very high system of calculation in …

a) commerce and agriculture.

b) commerce and military affairs.

c) commerce and practical mensuration.

d) algebra and geometry.

3. What topics do the majority of recovered clay tablets cover?

a) fractions, algebra, the calculation of Pythagorean triples, and solving various equations up to the fourth degree.

b) Pythagorean Theorem.

c) usage of 60 seconds in a minute, 60 minutes in an hour, and 360 degrees in a circle.

d) a true sexagesimal place-value (positional) numeral system.

4. The word tablet in this passage means

a) "a small flat piece of solid compressed medicine".

b) "a thin flat leaf of wood, stone or metal shaped for specific purpose".

c) "a flat baked clay plate used for inscriptions".

d) "a writing or drawing pad consisting of sheets of paper glued together at one edge".

5. Which of the following would be an appropriate title for this passage?

a) History of Ancient Clay Tablets.

b) Babylonian Mathematics.

c) Babylonian Algebra.

d) Deciphering the Wedge-Shaped Letters.

6. The word combination isosceles triangle in the text is closest in meaning to …

a) a three-sided geometrical figure with one right angle.

b) any three-sided geometrical figure.

c) a three-sided geometrical figure with two equal sides.

d) a three-sided geometrical figure with one obtuse angle.

7. The word unknown in the text is closest in meaning to

a) strange.

b) unaware.

c) unfamiliar

d) mysterious.

8. According to the text, the early Babylonians used to draw …

a) triangles on baked clay plates with needles

b) triangles on wet clay plates with needles

c) triangles on dry clay plates with needles

d) triangles on wet stone plates with needles.

9. What can you state as the main idea of the text?

a) More than 400 unearthed clay tablets prove that early Babylonians had rather deep knowledge of mathematics.

b) Elementary concepts of mathematics have been discovered and utilized by early Babylonians.

c) Unlike the Egyptians, Greeks, and Romans, the Babylonians used very high system of calculation in commerce and agriculture.

d) Mathematics in ancient Babylonia is the earliest in the world.

10. The word combination decimal place in the text is translated into Ukrainian as

a) десяте місце.

b) розміщення десятків.

c) десятковий розряд.

d) десяткове місце.

7. Answer the following questions:

1. What archeological findings enabled us to know about the knowledge of mathematics in ancient Egypt and Babylonia? 2. Which ancient Egyptian manuscript represented the manual in arithmetic and geometry? What topics did it cover? 3. What did Babylonians lack in their numeral system? 4. What mathematical knowledge of present-day use derived from Babylonian numeral system? 5. What geometrical underpinnings did the R-hind papyrus contain?

8. Translate the following sentences into English:

1. У давньому Вавилоні застосовували шістдесяткову позиційну систему числення в якій числа, записані зліва, представляли більші величини, так само як у десяткових дробах. 2. Стародавні єгиптяни вміли визначати об’єм прямого циліндра, усіченого конуса та піраміди, а також площу трикутника. 3. На відміну від єгиптян, греків і римлян вавилоняни застосовували високорозвинену систему обчислення в торгівлі та сільському господарстві. 4. В одній із задач наводиться метод знаходження об’єму усіченого конуса. 5. Глиняні таблички також містили таблиці множення, тригонометричні таблиці та методи розв’язування лінійних і квадратних рівнянь. 6. Вавилонська геометрія тісно пов’язана з практичними вимірюваннями. 7. Давні вавилоняни знали алгебру, дроби, вміли розв’язувати квадратні та кубічні рівняння, а також рівняння з двома невідомими. 8. Папірус, датований 2000-1800 р. до н.е., містив "словесні" задачі, створені для розваги. 9. Давні єгиптяни знали множення, ділення, операції з дробами, формули обчислення площі та об’єму різних фігур, а також мали досконалу теорію чисел. 10. Ще один важливий математичний текст – навчальний посібник з арифметики й геометрії, – було знайдено в папірусі, датованому приблизно 1650 роком до н.е.

9*. Write a short summary of the text (about 200-250 words).

10*. Speak about the main achievements of ancient civilizations of Egypt and Babylonia in mathematics.