MATH 4109 COMPREHENSIVE EXAM TWO
TEST PAPER 2026 DETAILED QUESTIONS
AND THOROUGHLY EXPLAINED
ACCURATE SOLUTIONS GRADED A+
⩥ What was Viete's contribution to the development of the modern
symbolism of algebra? Answer: He used letters to represent unknown
quantities.
⩥ Bombelli wrote "It was a wild thought in the judgment of many; and I
too for a long time was of the same opinion." Bombelli was referring to
what set of numbers? Answer: Imaginary numbers
⩥ What strategy did Girolamo Cardano use to solve cubic equations?
Answer: With a particular substitution, he transformed the cubic
equation into a quadratic equation which he did know how to solve.
⩥ In which stage of algebraic development did Diophantus make
contributions? Answer: Syncopated
⩥ Which mathematician used the letters at the end of the alphabet to
represent unknown quantities and the letters at the beginning of the
alphabet to represent known quantities or constants? Answer: Rene
Descartes
, ⩥ Who is sometimes called the "father of algebra?" Answer: Diophantus
⩥ Who is the father of English cryptography? Answer: John Wallis
⩥ 12) what is the heavenly body that is at the center of the Copernican
model of the universe? Answer: the sun
⩥ In the Ptolemaic model of the universe, the equant is the center of the
epicycle that moves around the earth. Answer: false
⩥ The Ptolemaic model of the universe is a heliocentric model. Answer:
false
⩥ Who wrote the mathematical text, Almagest? Answer: ptolemy
⩥ What is a chord of a circle? Answer: A line segment that intersects a
circle in two points.
⩥ What is the base in common logarithms? Answer: 10
⩥ According to one of the principles in the Copernican model, what is at
the center of the moon's orbit? Answer: the earth
TEST PAPER 2026 DETAILED QUESTIONS
AND THOROUGHLY EXPLAINED
ACCURATE SOLUTIONS GRADED A+
⩥ What was Viete's contribution to the development of the modern
symbolism of algebra? Answer: He used letters to represent unknown
quantities.
⩥ Bombelli wrote "It was a wild thought in the judgment of many; and I
too for a long time was of the same opinion." Bombelli was referring to
what set of numbers? Answer: Imaginary numbers
⩥ What strategy did Girolamo Cardano use to solve cubic equations?
Answer: With a particular substitution, he transformed the cubic
equation into a quadratic equation which he did know how to solve.
⩥ In which stage of algebraic development did Diophantus make
contributions? Answer: Syncopated
⩥ Which mathematician used the letters at the end of the alphabet to
represent unknown quantities and the letters at the beginning of the
alphabet to represent known quantities or constants? Answer: Rene
Descartes
, ⩥ Who is sometimes called the "father of algebra?" Answer: Diophantus
⩥ Who is the father of English cryptography? Answer: John Wallis
⩥ 12) what is the heavenly body that is at the center of the Copernican
model of the universe? Answer: the sun
⩥ In the Ptolemaic model of the universe, the equant is the center of the
epicycle that moves around the earth. Answer: false
⩥ The Ptolemaic model of the universe is a heliocentric model. Answer:
false
⩥ Who wrote the mathematical text, Almagest? Answer: ptolemy
⩥ What is a chord of a circle? Answer: A line segment that intersects a
circle in two points.
⩥ What is the base in common logarithms? Answer: 10
⩥ According to one of the principles in the Copernican model, what is at
the center of the moon's orbit? Answer: the earth
