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WorksheetsHOM MIDTERM
Total questions: 100
Worksheet time: 1hrs 8mins
represented by a coil of rope.
(a)
Discovered in 1960 by Belgian archaeologist Jean de Heinzelin de Braucourt while exploring the Belgian Congo. It was discovered in the Ishango area near the Semliki River
(a)
it only uses 2 numeral symbols
(a)
10000?
10?
1000?
were based on seven symbols that can be arrange to represent any positive numbers.
(a)
number system is our system that we used today
(a)
the inherent value of the symbol.
face value
place value
value ko
the power of the base which is associated with the position that the digit occupies in the numeral
value ko
value nya
place value
face value
A written version of a concrete counting system using material objects.
(a)
answer be
^^^^<<<^^<<^^^;^^^<<^^^^
(a)
convert mga be sa base 60
76897
(a)
also known as base 60
(a)
first to develop transfinite numbers, set theory, logarithms, fundamental laws of indices, cubic equations, quadratic equations, sequences and progressions, permutations and combinations, squaring and extracting square roots, and finite and infinite powers.
egypt
greek
india
china
Greek mathematics is thought to have begun with
(a)
the most famous woman of the Pythagoreans.
(a)
He is recognized as one of the greatest mathematicians of all time and the best of the ancient world
(a)
it is a using the board, each compartment has its own value
(a)
provides knots that represent each value. It also helped for doing computations. For the single knot, it represents ten thousands, thousands.
tying knots
wallknots
the quipu
base knot
It used a positional vigesimal (base-20) numeric system.
(a)
Ancient Egyptians developed a writing system with pictures
hieroglyphs
hieroglyhps
hyroglyphs
hierroglyphs
Which ancient artifact is estimated to be over 20,000 years old and was initially believed to be a collection of prime numbers but is now thought to potentially be a lunar calendar?
the ishango bone
Hieroglyphic Numeration
mayan calendar
plimpton 322
what is the first period in greek mathematics
– influenced by Pythagoras
Plato and his school
– Alexandrian School flourished in Grecian Egypt and extended its influence to Sicily and Palestine
who didn’t like algebra?
mayan
greek
china
ako
What fundamental idea did Thales introduce to geometry?
plane geometry
a geometry of lines
deductive geometry
a logical proof
thales in known for his theorem on what
PYTHAGOREAN THEOREM
EUCLEDIAN THEOREM
INTERCEPT THEOREM
NUMBER THEOREM
For him the base of mathematics is logic, but the nature of mathematical relations is completely specified by postulates that dictates the physical experience
plato
aristotle
thales
archimedes
he proposed the geocentric theory, suggesting that the Earth was at the center of the universe
(a)
he is called the grandfather of science.
(a)
he came up with a radical way of looking at the Universe. His heliocentric system put the Sun (helio) at the center of our system.
(a)
He was able to use this telescope to prove the truth of the Copernican system of heliocentrism.
(a)
Branch of mathematics concerned with specific functions of angles and their application to calculations. There are six functions of an angle commonly use in trigometry. Their names and abbreviation are sine(sin),cosine(cos), tangent(tan).cotangent(cot),secant(sec), and cosecant (csc).
(a)
What ancient civilization is known for developing the concept of zero?
Mayan
Greek
Indian
Chinese
Who is credited with the development of the earliest known trigonometric table?
Hipparchus
Ptolemy
Euclid
Archimedes
Which ancient civilization is associated with the Rhind Mathematical Papyrus, a famous mathematical document?
Egyptian
Greek
Chinese
Indian
What was the original name of Ptolemy's astronomical manual "The Almagest," and how did it come to be known by its Arabic name?
The Mathematical Arrangement; it was adopted due to its Arabic translation
The Astronomical Compilation; it was named by Ptolemy's students
The Celestial Guide; it was titled by European astronomers
The Greatest; it was a title given by Ptolemy himself
In Ptolemy's geocentric model described in "The Almagest," what is at the center of the universe according to his view?
The moon
The sun
The earth
The star
Which section of "The Almagest" mainly deals with the prediction of the Sun's position in the zodiac at any given time? book number?
1
2
3
4
What was the primary purpose of Books 7 and 8 in "The Almagest" by Ptolemy?
To describe the construction of astronomical instruments
To explore the motions of the moon
To outline the theory of solar and lunar eclipses
To provide information about fixed stars and their coordinates
Which significant achievement is attributed to Ptolemy in "The Almagest" regarding the planetary motions?
Introduction of the heliocentric model
Formulation of the laws of planetary motion
Use of advanced mathematics to predict the orbits of planets
Combined epicycle and eccentric methods to model planetary motions
all are Heron of Alexandria's notable inventions except one.
First Ever Steam Engine
Developed Syringes
wind mill
ater operated device to open and close temple doors
Heron's formula for finding the area of a triangle includes:
The length of all sides
The sum of the sides
The semi-perimeter and side lengths
The angles of the triangle
How does spherical geometry differ from Euclidean geometry?
Both have similar theorems and results
The theorems are false in spherical geometry
Results in Euclidean geometry are false
Both are identical in nature
What mathematical concept did Heron of Alexandria contribute to?
geometry
calculus
algebra
trigonometry
Heron of Alexandria developed a method for finding the square root of any number. What was this method called?
The Pythagorean Theorem
The Euclidean Algorithm
The Heronic Mean
Iteration Formula for Square Roots
Book VI deals with
Similar rectilinear figures
Number theory
Magnitudes
Ratio and proportion
What did Euclid define in Book VII of his Elements?
Divisor
even number
odd number
Number as a multitude composed of units
What characterizes a perfect number?
Equal to the sum of its own parts
Has only two factors: 1 and itself
Can be divided into three equal parts
Is an odd number that is a multiple of 3
When three magnitudes are proportional, the first is said to have to the third the ___________ ratio of that which it has to the second.
Duplicate
Triplicate
Proportional
Equal
What is the quote associated with Archimedes related to levers and moving the world?
"Give me a lever long enough and a place to stand, and I can move the Earth."
"With the right lever, I can move anything."
"The lever is the key to the world's movement."
"Give me a lever, and I can change the world."
The Pythagoreans displayed numbers as figures, with the most important figures being the:
(a)
Which lever class has the fulcrum placed between the effort and the load?class number?
1
2
3
4
What term is used to describe the sum of the first N terms of a sequence?
(a)
Which lever class has the load positioned between the effort and the fulcrum?
(a)
What type of approximation did Archimedes use for the irrational number π?
Rational approximation
irrational approximation
Precise approximation
Geometric approximation
In Archimedes' approximation of π, what value did he use?
3.34
3.14
25/8
22/7
Euclid's famous mathematical treatise, the Elements, consists of how many books?
(a)
In Book XII of Euclid's Elements, what relationship is described between pyramids of the same height with triangular bases?
They are always congruent to each other.
The bases are similar in shape.
Their volumes are equal
Their areas are identical.
What property of numbers does the statement "If a number is a square, then all its powers are squares as well" refer to?
(a)
Which geometric figure's area is calculated using Heron's formula?
(a)
Which statement accurately describes the relationship between pyramids of the same height with triangular bases?
Their volumes are equal.
Their bases are congruent.
They have different volumes.
Their areas are equal.
Which ancient civilization was able to solve quadratic equations in algebra?
Babylonian
greek
egyptian
mayan
If the sides of a triangle measure 9 cm, 12 cm, and 15 cm, what is the triangle's area using Heron's formula?
(a)
What was a fundamental limitation of Greek Algebra?
Rejection of positive rational numbers
Rejection of negative and complex solutions of equations
Consideration of irrational numbers as standard numbers
Geometric interpretation of all algebraic problems
The Cairo Papyrus, dating around 300 B.C., allowed the solution of:
Linear equations with two unknowns
Quadratic equations
Systems of degree equations
Exponential equations
Which ancient civilization learned algebra from Egypt and later studied Mesopotamian geometric algebra from the Persians?
Babylonians
Egyptians
mayan
greeks
What type of algebraic method did Egyptian and Babylonian algebra primarily utilize?
(a)
What concept did Greek Algebra refuse to consider as numbers, although they recognized their existence?
(a)
Which mathematician's work in the 3rd century CE marked the culmination of Greek algebra?
(a)
In Euclid's Elements, what is a point defined as?
A shape with no length
A shape with no width or breadth
A shape with no breadth
A shape with no part
Which angle type is greater than a right angle according to Euclid's Elements?
obtuse
acute
right
straight
What term refers to a figure contained by straight lines, such as trilateral or quadrilateral?
multilateral
rectilinear
In which book of Euclid's Elements are topics like the Pythagorean theorem and the sum of angles in a triangle covered?
i
ii
iii
iv
What is the definition of a straight line according to Euclid?
A shape with breadth
A shape with one dimension, length
A shape with no length
A shape with two dimensions
In Book II, a parallelogram is said to be contained by two straight lines containing a right angle. What geometric property does this describe?
Equilateral sides
Right angles
Equal diagonals
Perpendicular bisectors
According to Book III, when are circles considered equal?
When their circumferences are equal
When their diameters are equal
When their areas are equal
When their radii are equal
In Book IV, what does it mean for a rectilinear figure to be inscribed in another figure?
A.
B.
C.
D.
All sides are equal.
All angles are equal.
Respective angles lie on respective sides.
The figure is centrally symmetric.
What construction is concluded in Book 2 of Euclid's Elements regarding a square and any rectilinear plane figure?
(a)
Who is often considered the "father of Algebra"?
(a)
Which statement rephrases Euclid's fifth postulate?
A line and a point can intersect at one point.
Given a line and a point, it's impossible to draw a parallel line.
It's impossible to draw exactly one line through a given point parallel to a line.
Any line and point can have multiple parallel lines
What did Bolyai and Lobachevsky realize about non-Euclidean geometries?
They cannot be consistent
They are irrelevant to mathematics
They contradict the Elements
They are entirely self-consistent
What is Euclid's fifth postulate about?
Proving other postulates
Defining geometrical properties
Establishing general assumptions
Drawing lines parallel to a given line
Which of the following does Euclid's Elements start with?
Five postulates
Definitions
The axiomatic method
Common notions
What is the significance of Diophantus' "Arithmetica"?
It introduced geometric algebra.
It focused on solutions of algebraic equations and the theory of numbers.
It discussed the geometry of conic sections.
How many problems did Diophantus present in "Arithmetica," and how were they solved?
(a)
What did Diophantus contribute to algebraic notation?
introduced Roman numerals.
developed symbolic styles of writing.
promoted verbal descriptions for equations.
used geometric shapes to represent variables.
What did Hindu mathematicians recognize about quadratic equations?
.They have no real roots.
They have 2 real roots.
They have 1 real roots.
.They have negative real roots.
What is Hindu Algebra known for inventing that is still in use today?
Decimal System
Coordinate
Roman Numerals
Universe
How did Hindu mathematicians represent debt in their numerical system?
(a)
What is the literal translation of "al-jabr w’al-muqabala," the title of Al-Khwarizmi's work?
Algebraic Principles
Restoration and Compensation
Geometrical Equations
The art of mathematics
What was Al-Khwarizmi's contribution to quadratic equations?
He could only solve linear equations
. He introduced symbolic notation for quadratic equations
developed a rhetorical approach to quadratic equations
He solved cubic equations
What did Omar Khayyam classify and provide geometric solutions for in the 11th century?
Linear equations
Quadratic equations
Cubic equations
Quartic equations
Who is often called the father of "modern algebra" in the 16th century?
Omar Khayyam
Abu Kamil
Viete
Al-Karaji
What did Viete introduce in his mathematical writings that revolutionized algebraic notation?
Geometric symbols
Latin phrases
Letters for both constants and unknowns
Arabic numerals
Which mathematician introduced symbolic algebra to its full maturity, using letters for unknowns and constants?
(a)
What equation introduced by Descartes is still used today to describe the equation of a line?
ax^2 + by^2 = c
. ax + by = c
5aⁱⁱⁱ +7bⁱⁱ
a^3 + b^2 = 5
At which stage of algebraic development did symbolic algebra reach full maturity?
Rhetorical
Geometric
Symbolic
Syncopated
How is classical algebra characterized?
Solving Rubik's Cube permutations
Manipulating symbols using arithmetic operations
Studying abstract algebraic structures
Exploring vectors in three-dimensional space
Who is credited with developing the concept of a group in abstract algebra?
(a)
