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Worksheets7 chapter
Total questions: 50
Worksheet time: 25mins
What is the Suan shu shu, discovered in a tomb nearZhangjiashan?
A. A collection of poems
B. A mathematics text on bamboo strips
C. A historical chronicle
D. A text on astronomy
Which dynasty standardized weights,
measures, and written script?
A. Zhou
B. Qin
C. Han
D. Tang
The term Nine Chapters on the
Mathematical Art refers to:
A. A philosophical text
B. A foundational Chinese mathematical
treatise
C. An astronomical guide
D. A manual for surveying
What base system did ancient Chinese use
for numbers?
A. Binary
Base-10
Hexadecimal
Base-12
What method was used to represent
negative numbers in early Chinese
mathematic
A. Red rods for positive, black for negative
B. Dots for positive, dashes for negative
C. Circles for negative numbers
D. None; negative numbers were not used
The earliest recorded Chinese method for
reducing fractions resembles:
A. Prime factorization
The Euclidean algorithm
Division by successive subtract
Multiplication of reciproc
Liu Hui improved upon the calculation of
which mathematical constant
e
Pi (π)
Square root of 2
Golden ratio
Liu Hui calculated the area of a circle by
using which technique
A. Approximation with polygons
Monte Carlo method
Integration
Algebraic expansion
The Chinese algorithm for square roots
was based on the equation:
x2+2xy+y2
x2−y2x^2 - y^2
x3+y3x^3 + y^3
x+y\sqrt{x + y}
Which of the following was not part of the
Ten Mathematical Classics?
Nine Chapters on the Mathematical Art
The Arithmetical Classic of the Gnomon
The Mathematical Classic of Master Sun
The Elements by Euclid
What principle did Zu Geng use to
calculate the volume of the sphere?
Archimedean principle
Cavalieri's principle
Binomial theorem
The Pythagorean theorem
What method did Chinese
mathematicians use for solving linear
equations
Gaussian elimination
Newton-Raphson method
Double false posi
Integration
The Haidao suanjing was written by:
Zhu Shijie
Liu Hui
Qin Jiushao
Yang Hui
The primary purpose of the Haidao
suanjing was to:
Explain philosophical concepts
Solve surveying problems
Predict eclipses
Study planetary motiOn
Yi Xing is known for creating the first
recorded table of:
Cosines
Tangents
Sines
Logarithms
What distinguished the Chinese method
of solving equations from Babylonian
methods?
Use of place-value decimals
Focus on numerical algorithms
Symbolic representat
Logical axioms
In what year was the Precious Mirror of
the Four Elements by Zhu Shijie writt
1247
1303
1261
1299
What mathematical problem type does
the Sea Island Mathematical Manual
address
Arithmetic sequences
Geometric constructions
Distance and height calculations
Polynomial solutions
What was the primary use of counting
rods in ancient Chinese mathematics?
Writing complex equations
Representing numbers for calculations
Measuring distances
Recording astronomical data
What mathematical principle was used
extensively in the Nine Chapters to solve
geometry problems?
A. Newton's laws
B. The Pythagorean theorem
. Integral calculus
Arithmetic mean
The method of double differences in the
Haidao suanjing was used to calculate:
Areas of irregular shapes
The height of a distant object
Cube roots
. Decimal approximations
What type of equation does the rule
x3+ax2+bx+c=0x^3 + ax^2 + bx + c = 0
represent
Quadratic equation
Polynomial equation
Linear equatioN
Exponential equation
Which dynasty introduced the imperial
examination system that required
knowledge of mathematic
Zhou
Han
Tang
Song
Which of the following Chinese
mathematicians developed Cavalieri's
principle independently
Qin Jiushao
Zu Geng
Yang Hui
Zhu Shijie
The Chinese method of solving
polynomial equations inspired the later
development of:
Horner's method
The quadratic formula
Differential equation
The Fourier transform
What innovation allowed the Chinese to
represent intermediate zeros in numbers
by the 12th century?
Colored rods
B. A small circle symbol
The abacuS
Dots in a vertical column
What was the relationship between the
volume of a sphere and its circumscribed
cylinder according to Liu Hui?
Exactly equal
Less than π/4\pi/4 of the cylinder's
volume
Greater than π/4\pi/4 of the cylinder's
volume
No relationship was established
Which famous mathematical constant did
Zu Chongzhi calculate to seven decimal Places
Pi (π\pi)
Euler's number (ee)
)
C. Square root of 2
Golden ratio
In Chinese mathematics, the volume of a
pyramid was calculated as
A. V=13×base area×heightV = \frac{1}{3}
\times \text{base area} \times \text{height}
B. V=14×base area×heightV = \frac{1}{4}
\times \text{base area} \times \text{height}
C. V=base area×heightV = \text{base area}
\times \text{height}
D. V=12×base area×heightV = \frac{1}{2}
\times \text{base area} \times \text{height}
Who was known for advancing the
solution of polynomial equations in the
13th century?
Li Ye
Yang Hui
Qin Jiushao
Zhu Shijie
Which mathematical work by Zhu Shijie
incorporated solving systems with up to
four unknowns?
Nine Chapters on the Mathematical Art
Precious Mirror of the Four Element
Sea Island Mathematical Manual
Mathematical Treatise in Nine Sections
Chinese mathematicians used the term
“gou-gu” to describe:
Addition of fractions
Properties of right triangles
Calculation of roots
Decimal notations
The counting board was mainly used for
Writing philosophical texts
Performing calculations
Creating astronomical tables
Developing calendars
What was Qin Jiushao's Mathematical
Treatise in Nine Sections mainly about
Astronomy
Polynomial equations
Trigonometry
Geometry
What was the Chinese approximation for
π\pi used in the Nine Chapte
3
3.143.14
C. 22/722/7
3.14159263.1415926
Which problem-solving approach is akin
to modern-day Gaussian elimination
Method of double false position
Counting board matrix manipulation
Polynomial expansion
Geometric proofs
What was the primary contribution of Jia
Xian
The development of the Pascal triangle
B. Introduction of trigonometric methods
Creation of tangent tables
Study of eclipse patterns
The Sea Island Mathematical Manual
focuses on solving problems involving:
Polynomials
Heights and distances
Volume calculation
Astronomical cycles
Which dynasty oversaw the annotation of
the Ten Mathematical Classics
Han
Tang
Song
Ming
Liu Hui's commentary on the Nine
Chapters introduced the concept of:
Cavalieri's principle
Decimal fractions
Approximating π\pi with polygons
Binomial expansion
What mathematical achievement is
associated with Zu Chongzhi
Invention of the abacus
Calculating π\pi more accurately than
previous approximations
Writing the Nine Chapters
Introducing algebraic symbols
What geometric figure was used by Liu
Hui to approximate the area of a circle
Triangle
Dodecagon
Hexagon
Square
What significant mathematical
advancement did Qin Jiushao's work
contribute to?
Differential calculus
Solving high-degree polynomial
equations
Creating logarithmic tables
Astronomical computations
The Chinese term for calculating a square
root was based on
Geometric diagrams
Approximation using the Pythagorean
theorem
Numerical algorithms
Recursive subtraction
How did ancient Chinese astronomers
contribute to mathematics?
Inventing the decimal system
Creating tangent and sine tables
Solving cubic equations
Developing integral calculus
What was the purpose of the Jiuzhang
Suanshu (Nine Chapters)?
To compile philosophical essays
To provide practical solutions to
mathematical problems
C. To serve as an agricultural guide
To record military strategies
Which mathematician formalized the use
of Cavalieri's principle in China?
Yang Hui
Zu Geng
C. Qin Jiushao
Zhu Shijie
48. What was the primary content of the Sea
Island Mathematical Manual?
Astronomy and celestial calculations
Geometric methods for surveying
Solutions to algebraic equations
Financial mathematics
Liu Hui’s commentary introduced which
numerical concept into Chinese
geometry?
The ratio of circumference to diameter
Binomial expansions
Decimal fractions for areas
D. Approximation through iteration
What was one limitation of early Chinese
mathematical methods as seen in the Nine
Chapters?
Lack of symbolic notation
No use of negative numbers
Inability to solve cubic equations
Ignoring practical applications
