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1ST SEM PRELIMS > MATH 101 REVIEWER > Flashcards

MATH 101 REVIEWER Flashcards

1
Q

Characteristics of the Math language

A

Precise, Concise, Powerful

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2
Q

It creates a complex schedules for sports tournaments, making sure teams have equal numbers of home and away games, and do not travel for too long

A

Mathematics

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3
Q

Why is language important?

A

To understand expressed ideas, to communicate ideas

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4
Q

Objects that we use in Math

A

-Numbers (operations and properties)
-Variables (Free and Bound)
-Operations (Unary and Binary)
-Sets (Relationships, Operations, Properties)
-Relations (Equivalence Relation, Functions)
-Functions (Injective, Surjective, Bijective)

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5
Q

it is changing the grouping of the numbers in addition or multiplication will not change the result

A

Associative Property

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6
Q

In other words adding zero to a number does not change its value

A

Additive Identity Property

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7
Q

Properties of Real Numbers

A

Closure, Commutative, Associative, Distributive, Identity + x, Inverse + x

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8
Q

There exists a unique number 1 such that the number 1 preserves identities under multiplication.

A

Multiplicative Identity Property

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9
Q

For each real number a there exists a unique real number -a such that their sum is zero

A

Additive Inverse Property

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10
Q

For each real number, a there exists a unique real number 1 over a such that their product is 1

A

Multiplicative Inverse Property

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11
Q

It is changing the order of the numbers in addition or multiplication will not change the result

A

Commutative Property

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12
Q

Focused on the “structure”, Structural rules governing.

A

Grammar of Mathematics

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13
Q

explains the
universe, such as why bees have
hexagonal honeycombs, and how
many galaxies there are.

A

Mathematics

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14
Q

In other words multiplying a number by 1 does not change the value of the number.

A

Multiplicative Identity Property

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15
Q

There exists unique number 0 such that zero preserves identities under addition

A

Additive Identity Property

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16
Q

Multiplication distributes over addition

A

Distributive Property

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17
Q

words opposites add to zero

A

Additive Inverse Property

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18
Q

states: a + (b +c) = (a + b) + c

A

Associative Property

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19
Q

it powers graphics software, so that you can draw perfect curves and save pictures digitally.

A

Mathematics

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20
Q

A mathematician, mathematics is a formal system of thought for recognizing, classifying, and exploiting patters.

A

Ian Stewart

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21
Q

Philosopher: Mathematics is the science of quantity, Philosopher and Polymath

A

Aristotle

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22
Q

is the study of numbers, quantities, shapes, and patterns. It involves logical reasoning, problem-solving, and the ability to analyze and interpret data. it also provides the tools and frameworks to understand and describe the world around you.

A

Mathematics

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23
Q

The Science of Indirect Measurements, A mathematician

A

Auguste Cosme

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24
Q

Mathematics teaches logical reasoning, critical thinking, and solving skills. These skills are essential in everyday life for making decisions, analyzing situations, and finding solutions to complex problems.

A

Problem Solving skills

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25
Q

Mathematics is the language in which god has written in the universe. Phycist, engineer, scientist, mathematician, polymath.

A

Galileo Galilei

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26
Q

is a fundamental discipline that plays a critical role in various aspects of life, science, and technology.

A

Mathematics

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27
Q

A mathematician, mathematics is the classification and study of all possible patterns and relationships.

A

Walter Warwick Sawyer

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28
Q

3 Core Concept of Mathematics:

A

Numbers: The foundation of mathematics, including natural numbers, integers, fractions, and real numbers.
Operations: Addition, subtraction, multiplication, division, and more complex operations.
Patterns and Relationships: Identifying and analyzing patterns to understand relationships between numbers and variables.

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29
Q

Mathematics is essential in daily activities such as shopping, cooking, home budgeting, and time management. Understanding basic mathematical concepts helps people navigate everyday tasks more efficiently.

A

Supportive Daily Life

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30
Q

Mathematician, Mathematics is our one and only strategy for understanding the complexity of nature.

A

Ralph Abraham

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31
Q

Are symbols or letters used to represent numbers or other mathematical objects. They are essential in expressing general mathematical statements, equations, and functions, allowing for the formulation of relationships and problem-solving strategies.

A

Variables

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32
Q

Many modern technologies, including computers, telecommunications, artificial intelligence, and cryptography, are built on mathematical theories. Innovations in these fields often require advanced mathematical understanding.

A

Innovation and Technology

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33
Q

it’s not just about numbers, it is a way of thinking, a method of problem-solving, and a tool for understanding the world.

A

Mathematics

34
Q

enable generalization in mathematics, allowing for the formulation of equations, functions, and models that can apply to many different situations.

A

Variables

35
Q

Learning mathematics stimulates _____development, enhancing memory, attention, and analytical abilities. It fosters an ability to think abstractly and systematically, which is beneficial in various intellectual pursuits.

A

Cognitive Development

36
Q

A value that does not change within a given context or equation.

A

Constant Variable

37
Q

Types of Variables:

A

Independent Variable: The variable that is manipulated or chosen in an equation or function. It represents the input or cause.
Dependent Variable: The variable whose value depends on the independent variable. It represents the output or effects.
Constant: A value that does not change within a given context or equation.
Parameter: A variable that remains constant within a specific context but can change when the context changes.
Random Variable: A variable that takes on different values based on the outcomes of a random process.
Discrete Variable: A variable that can take on a finite or countable number of values.
Continuous Variable: A variable that can take on any value within a given range, often involving decimals.

38
Q

The variable whose value depends on the independent variable. It represents the output or effects

A

Dependent Variable

39
Q

it provides a formal way to describe collections of objects and their relationships.

A

Language of sets

40
Q

The variable that is manipulated or chosen in an equation or function. It represents the input or cause.

A

Independent Variable

41
Q

underpins
statistical analysis which enables
medical, biological, psychological
and other research.

A

Mathematics

42
Q

provides a way to describe and analyze how different sets of elements are related to each other.

A

language of relations and functions

43
Q

Types of Relation:

A

Reflexive: Each element is related to itself.
Symmetric: If one element is related to another, the reverse is true.
Transitive: If one element is related to a second, and the second to a third, the first is related to the third.

44
Q

A variable that remains constant within a specific context but can change when the context changes.

A

Parameter Variable

45
Q

A variable that can take on any value within a given range, often involving decimals.

A

Continuous Variable

46
Q

A ____ is a way to describe a relationship between elements of two (or more) sets.

A

Relations

47
Q

A variable that can take on a finite or countable number of values.

A

Discrete Variable

48
Q

powers search
engines so that you can be sent
to the most popular hits within
seconds.

A

Mathematics

49
Q

Is the set of all x or input values. We may describe it as the collection of the first values in the ordered pairs.

A

Domain

50
Q

A set is a collection of distinct objects considered as a whole.

A

Language of sets

51
Q

If one element is related to another, the reverse is true.

A

Symmetric Relation

52
Q

A variables that takes on different values based on the outcomes of a random process.

A

Random Variable

53
Q

If one element is related to a second, and the second to a third, the first is related to the third.

A

Transitive Relation

54
Q

is simply a set or collection of ordered pairs, Nothing really special about it. An ordered pair, commonly known as a point, has two components which are the x and y coordinates.

A

Relation

54
Q

it drives
spreadsheets, which host millions
of models of businesses, projects
and such.

A

Mathematics

55
Q

is the set of all Y or output values. We may describe it as the collection of the second values in the ordered pairs.

A

Range

56
Q

Each element is related to itself.

A

Reflexive

57
Q

makes calculators,
which means you don’t need to
waste brain power on
calculations.

A

Mathematics

58
Q

it is a “special” kind of relation because it follows an extra rule. Just like a relation, a ____ is also a set of ordered pairs; however, every x-value must be associated to only one y-value.

A

function

59
Q

is when a shape looks identical to its original shape after being flipped or turned.

A

Symmetry

60
Q

is a fascinating topic that highlights the intrinsic connection between mathematics and the natural world. Mathematics is not just a tool for understanding the universe but is deeply embedded in the structures and patters we observe in nature.

A

Patterns and Numbers in Nature and the World

61
Q

Are linear openings that form in materials to relieve stress. The pattern of ____ indicates whether the material is elastic or not. Some examples are old pottery surface, drying inelastic mud, and palm trunk with branching vertical ___.

A

Cracks

62
Q

Two main types of symmetry:

A

Reflective, Rotational

63
Q

is when an object exhibits self-similar shape or form at any scale and repeat itself overtime. Trees are natural Fractals, patterns that repeat smaller and smaller copies of themselves to create the biodiversity of a forest.

A

Fractal Pattern

64
Q

allows us to weigh
up the trade-off between over forecasting tornadoes and failing
to warn.

A

Mathematics

65
Q

is an organized arrangement of objects in space or time., It must have something that is repeated either exactly or according to recognizable transformations.

A

Pattern

66
Q

The hexagonal pattern in honeycomb structures is an efficient way of using space and resources, minimizing the amount of wax needed to build the hive.

A

Bees and Hexagons

67
Q

means that one half of an image is the mirror image of the other half (think of a butterfly’s wings).

A

Reflective, or line symmetry

68
Q

Forms a class of patterns found in nature. The arrays of hexagonal cells in a honeycomb or the diamond-shaped scales that pattern snake-skin are natural examples of what?

A

Tesselation or Tiling Pattern

69
Q

is the greatest European mathematician of middle ages.

A

Fibonacci

70
Q

means that the object or image can be turned around a center point and match itself some number of times (as in a five-pointed star).

A

Rotational symmetry

71
Q

can be observed in many things around us.

A

Patterns

72
Q

Animals, such as birds and fish, often follow complex patterns during ___, which can be described mathematically using vectors and forces. (Patterns in Animal Behavior)

A

Migration and Navigation

73
Q

Known as Fibonacci

A

Leonardo of Pisa

74
Q

Date of Birth and Death of Leonardo of Pisa

A

Born in 1170 and died in 1240.

75
Q

a book that introduced to the western world

A

Liber Abaci (The Book of Calculation) published in 1202

76
Q

is an integer in the infinite sequence, 1,1,2,3,5,8,13 … of which the first two terms are 1 and 1 and each succeeding term is the sum of the two immediately preceding.

A

Fibonacci Sequence

77
Q

reduces waste
when used for inventory control,
for distribution networks, for
product creation.

A

Mathematics

78
Q

He introduced the Arabic number system in Europe

A

Leonardo of Pisa - Fibonacci

79
Q

Fibonacci presented a problem about rabbit population growth, which led to the sequence that become famous.

A

Fibonacci’s Problem

1ST SEM PRELIMS (9 decks)

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