MATH 4109 EXAMINATION TWO ACTUAL
CERTIFICATION SCRIPT 2026 EXTENSIVE
QUESTIONS WITH PRECISELY WELL
DEFINED CORRECT ANSWERS GRADED A+
⩥ Which empire transmitted the Indian numeration system to the west?
Answer: Islamic empire
⩥ What motivated the standardization of symbols in our numeration
system? Answer: The invention of the printing press
⩥ What was the most famous and important invention of Indian
mathematicians? Answer: base ten numeration system
⩥ how was geometry used in the religion text, the Vedas? Answer:
geometry was used to construct altars
⩥ under what circumstances did the ancient Indians use the Pythagorean
Theorem Answer: the theorem is used to find the length of the diagonals
of squares and rectangles
⩥ what prompted the ancient Indians to invent their numeration system
Answer: we do not know
,⩥ what are the Vedas Answer: religious texts
⩥ how did the writing materials of the ancient Indians affect the
development of their algorithms for computing Answer: the small
writing space required the ability to erase a digit as soon as it was no
longer needed
⩥ what is the primary feature of the numeration system in ancient India
Answer: it was a place value system
⩥ 8) What strategy did the Chinese use on their counting boards to avoid
confusion between consecutive places? Answer: Alternating the
orientation of the rods
⩥ Why did Chinese mathematics develop independently of Western
cultural influence for so long? Answer: The geography of China isolated
the region from the rest of the world.
⩥ Chinese Square Root Algorithm: If a, b, and c are the digits
(respectively) of the square root of x, then which of the following is
equal to squareroot(x)? Answer: 100a + 10b + c
⩥ True or False: The Chinese numeration system that required the use of
a counting board and rods was not a positional system. Answer: false
, ⩥ We have used the word "gnomon" in several places during this course,
particularly during the module on ancient Chinese mathematics. What
letter of the alphabet is a gnomon shaped like? Answer: L
⩥ The Nine Chapters on the Mathematical Art was central to the
development of mathematics in which country? Answer: China
⩥ The method that Liu Hui used to approximate the value of π was
similar to the method used by which Greek mathematician? Answer:
Archimedes
⩥ Which set of numbers was used on the counting boards of the ancient
Chinese? Answer: Integers -- both postive and negative
⩥ Why is the book Nine Chapters on the Mathematical Art significant in
the history of mathematics? Answer: It is central to Chinese
mathematical activity for hundreds of years.
⩥ How was ancient Chinese mathematics different from ancient Greek
mathematics? Answer: The Chinese mathematics did not have a proof-
based axiomatic development.
⩥ 9) During the period of the Islamic Empire, negative numbers were
acceptable solutions of quadratic equations. Answer: false
CERTIFICATION SCRIPT 2026 EXTENSIVE
QUESTIONS WITH PRECISELY WELL
DEFINED CORRECT ANSWERS GRADED A+
⩥ Which empire transmitted the Indian numeration system to the west?
Answer: Islamic empire
⩥ What motivated the standardization of symbols in our numeration
system? Answer: The invention of the printing press
⩥ What was the most famous and important invention of Indian
mathematicians? Answer: base ten numeration system
⩥ how was geometry used in the religion text, the Vedas? Answer:
geometry was used to construct altars
⩥ under what circumstances did the ancient Indians use the Pythagorean
Theorem Answer: the theorem is used to find the length of the diagonals
of squares and rectangles
⩥ what prompted the ancient Indians to invent their numeration system
Answer: we do not know
,⩥ what are the Vedas Answer: religious texts
⩥ how did the writing materials of the ancient Indians affect the
development of their algorithms for computing Answer: the small
writing space required the ability to erase a digit as soon as it was no
longer needed
⩥ what is the primary feature of the numeration system in ancient India
Answer: it was a place value system
⩥ 8) What strategy did the Chinese use on their counting boards to avoid
confusion between consecutive places? Answer: Alternating the
orientation of the rods
⩥ Why did Chinese mathematics develop independently of Western
cultural influence for so long? Answer: The geography of China isolated
the region from the rest of the world.
⩥ Chinese Square Root Algorithm: If a, b, and c are the digits
(respectively) of the square root of x, then which of the following is
equal to squareroot(x)? Answer: 100a + 10b + c
⩥ True or False: The Chinese numeration system that required the use of
a counting board and rods was not a positional system. Answer: false
, ⩥ We have used the word "gnomon" in several places during this course,
particularly during the module on ancient Chinese mathematics. What
letter of the alphabet is a gnomon shaped like? Answer: L
⩥ The Nine Chapters on the Mathematical Art was central to the
development of mathematics in which country? Answer: China
⩥ The method that Liu Hui used to approximate the value of π was
similar to the method used by which Greek mathematician? Answer:
Archimedes
⩥ Which set of numbers was used on the counting boards of the ancient
Chinese? Answer: Integers -- both postive and negative
⩥ Why is the book Nine Chapters on the Mathematical Art significant in
the history of mathematics? Answer: It is central to Chinese
mathematical activity for hundreds of years.
⩥ How was ancient Chinese mathematics different from ancient Greek
mathematics? Answer: The Chinese mathematics did not have a proof-
based axiomatic development.
⩥ 9) During the period of the Islamic Empire, negative numbers were
acceptable solutions of quadratic equations. Answer: false
