PRE-LIM_MMW Flashcards
1
Q
The study of the relationships among numbers, quantities, and shapes.
A
Mathematics
2
Q
Study of Math Types
A
arithmetic
algebra,
trigonometry
geometry
statistics
calculus
3
Q
are visible regularities
found in the natural world.
A
Patterns in Nature
4
Q
Natural Patterns
A
spirals,
symmetries
mosaics
stripes
spots
5
Q
explains the pattern through music.
A
Plato
6
Q
explains the pattern through
geometry.
A
Phythagoras
7
Q
explains the nature through the
nature of God.
A
Empedocles
8
Q
Greek Philosophers Studied Patterns
A
Plato
Pythagoras
Empedocles
9
Q
Other scientist Studied Patterns
A
Joseph Plateau
Ernst Haeckel
D’Arcy Thompson
Alan Turing
Aristed Lindenmayer
Benoit Mandelbrot
10
Q
Belgian physicist in the 19th
century, who formulated the concept of minimal surface through soap films.
A
Joseph Plateau
11
Q
a German biologist and artist
who painted hundreds of marine organisms to
emphasize symmetry.
A
Ernst Haeckel
12
Q
a Scottish biologist who
pioneered the study of growth patterns in both
animals and plants that shows simple equations
could explain spiral growth.
A
D’ Arcy Thompson
13
Q
a British mathematician in the
20th century who predicted mechanisms of
morphogenesis that give rise to patterns of spots
and stripes.
A
Alan Turing
14
Q
a Hungarian theoretical
biologist and botanist at the University of Utrecht. Used L-systems to describe the behaviors of plant cells and to model the growth
processes of plant development
A
Aristed Lindenmayer
15
Q
a Polish-born French-American mathematician and polymath with broad interests in the practical sciences. He labeled “the act of roughness” of physical phenomena and “the uncontrolled element in
life”
A
Benoit Mandelbrot
16
Q
were the ones who showed how the
mathematics of fractals could create
growth patterns
A
Lindenmayer and Mandelbrot
17
Q
a never-ending pattern. It is an
infinitely complex pattern that is self-similar across different scales
A
Fractals
18
Q
adopts eight patterns in
landscape namely scattered, fractured, mosaic,
Naturalistic drift, serpentine, spiral, radial, and
dendritic. Occurs commonly in plants, animals,
rock formations, river flow, stars, and in human
creations.
A
W. Gary Smith
19
Q
W. Gary Smith 8 patterns
A
scattered
fractured
mosaic,
Naturalistic drift
serpentine
spiral
radial
dendritic
20
Q
“Fibonacci” means
A
Son of bonacci
21
Q
Father of Fibonacci sequence. Lived between 1170 and 1250 in Italy.
A
Leonardo Pisano Bogollo
22
Q
Fibonacci Day
A
November 23
23
Q
Fibonacci numbers are very close to
Golden Ratio, which is referred to
and represented as phi (ϕ) which is
approximately equal to
A
1.618034.
24
Q
a logarithmic spiral whose
growth factor is ϕ, the golden ratio.
A
Golden Spiral
25
a set of numbers or objects in
which all the members are related with each other by a specific rule.
Pattern
26
constitutes between two sets: a
collection of ordered pairs containing one object from each set.
Relation
27
Types of Function
1. One to One - a function.
2. One to Many - not a function.
3. Many to One - a function.
4. Many to Many - not a function.
28
a type of relation. A relation is
allowed to have the object x in the first set to be related to more than one subject in the second set.
Function
29
a partition of a plane into regions close to each of a given set of objects. It can be classified also as a tessellation. In the simplest case, these objects are just finitely many points in the plane (called seeds, sites,
or generators)
Voronoi diagrams
30
Voronoi diagrams were considered as early as 1644 by philosopher
René Descartes
31
defined and studied the general n-dimensional case in 1908. This type of
diagram is created by scattering points at random on a Euclidean plane
Georgy Voronoi
32
is an attribute of a shape or
relation; the exact reflection of form on opposite sides of a dividing line or plane.
Regularities
33
a period of time it
takes to swing back to its original position is
related to its length, but the relationship is
not linear
Motion of Pendulum
34
an image that is exactly the same size as the object and is far behind the mirror as the object is distant from the mirror.
Reflection in the Mirror Plane
35
any object that is
moving and being acted upon only be the force of gravity is said to be in state of free fall.
Free Falling Object
36
a pair of forces acting on
the two interacting objects.
Action-Reaction pair
37
Three examples of "Simplicity emerging from complexity"
Drops, Dynamics, and Daisies
38
The role of mathematics is to describe symmetry-breaking processes in order to explain in a unified way the fact that the patterns seen in San dunes and zebra’s stripes are caused by processes which, while physically different, are mathematically very similar.
Patterns in Nature
39
Mathematics solves puzzles in nature (such as why planets move in the way that they do), describes changing quantities via calculus, modelling change (such as the evolution of the eye), and predicts and controls physical systems.
Puzzles in Nature
40
Nurses routinely use addition, fractions,
ratios and algebraic equations each
workday to deliver the right amount of
medication to their patients or monitor
changes in their health.
Mathematics in Medicine
41
Political Scientists use mathematics
(statistics) to predict the behavior of group of people.
Mathematics in Political Science
42
Analysis and study in economics help
explain the interdependent relation
between different variables. Economists try to explain what causes rise in prices or unemployment or inflation.
Mathematics in Economics
43
Mathematics has enabled farming to be more
economically efficient and has increased productivity.
Mathematics in Farming and
Gardening
44
- Calculating prick per unit
- Figuring percentage discounts
- Comparing unit and bulk price of items
- Estimating total price
- Etc.
Mathematics in Planning a Market
and Grocery Shopping
45
- Plant pots in the inner garden and even
restroom fixtures
- Measuring ingredients
- Calculating cooking time
- Making ratios and proportions in baking
Mathematics Anywhere in the House
46
- Fuel required based on distance
- Total expenses for toll fees
- Tire pressure check
- Time allowance to the trip
- Short-cut routes alternatives
- Road map reading
- Speed limits and others
Mathematics in Travels
47
- Making accurate measurements of lengths,
widths, and angles
- Projecting detailed material estimate
- Getting the best value of valuable
resources
Mathematics in Construction
48
It combines mathematical theory, practical engineering and scientific computing to address the fast-changing technology.
Mathematics in Engineering
49
Individuals with poor math fundamentals typically make greater financial mistakes like underestimating how quickly interest
accumulates.
Mathematics in Investment
50
In a swift changing world, creating and following schedule prove beneficial, but it takes more mathematical skills than
simply using a clock and calendar to
manage time well and be on top of
others
Mathematics in Time
51
- is the system of words, signs and symbols which people use to express ideas, thoughts and feelings.
-consists of the words, their pronunciation and the methods of combining them to be understood by a community.
-is a systematic means of communicating ideas or feelings by the use of conventionalized signs, sounds, gestures or marks having understood meanings
Language
52
It is part of the English language used for making formal mathematical statements, specifically to communicate definitions, theorems, proofs and examples.
Mathematical English
53
is a special-purpose language. It has its own symbols and rules of grammar that are quite different from those of English.
Symbolic Language
54
A complete statement that stands alone as a sentence
Symbolic Assertions
54
A symbolic assertion without variables. It is either true or false.
Symbolic Statements
55
A symbolic expression that refers to some mathematical object.
Symbolic Terms
56
3 Types of symbolic Expressions
Symbolic Assertion
Symbolic Statements
Symbolic Terms
57
It is a collection of some rules which gives the procedures to perform first in order to evaluate a given mathematical expressions.
Order of operation
58
-is the system used to communicate mathematical ideas.
-has its own grammar, syntax, vocabulary, word order, synonyms, conventions, idioms, abbreviations, sentence structure and paragraph structure.
-also includes a large component of logic. The ordinary language which gradually expands to comprise symbolisms and logic leads to learning of mathematics and its useful application to problem situations.
Mathematical Language
59
Four main actions attributed to problem-solving and reasoning
Modelling and Formulating
Transforming and manipulating
Inferring
Communicating
60
Creating appropriate representations and relationships to mathematize the original problem.
Modelling and Formulating
61
Changing the mathematical form in which a problem is originally expressed to equivalent forms that represent solutions.
Transforming and manipulating
62
Applying derived results to the original problem situation, and interpreting and generalizing the results in that light.
Inferring
63
Reporting what has been learned about a problem to a specified audience.
Communicating
64
is a major contributor to overall comprehension in many content areas, including mathematics.
Vocabulary Understanding
65
consist of terms. The terms is separated from other terms with either plus or minus signs. A single term may contain an expression in parentheses or other grouping symbols.
Mathematical Expressions
66
Types of Mathematical Expressions
Monomial
Binomial
Trinomial
Polynomial
67
State whether the equation is true or false for the given value of the variable.
Open sentence
67
is a technique used by mathematicians, engineers, scientists in which each particular symbol has particular meaning.
Convention
68
refers to the particular topics being studied, and it is important to understand the ________ to understand mathematical symbols.
Context
69
Is a well defined collection of distinct objects
Set
70
The objects that make up a set is called
Elements
71
The elements in the given set are listed or enumerated, separated by a comma, inside a pair of braces
Roster/Tabular
72
The common characteristics of the elements are defined. This method uses set builder notation where x is used to represent any element of the given set.
Rule/Descriptive
73
has no element and is denoted by ∅ by a pair of braces with no element inside, i.e. {}
Empty/Null/Void Set
73
has countable number of elements, i.e. A = {1, 2, 3, 4, 5}
Finite Set
74
has uncountable number of elements, A = {…, -3, -2, -1, 0, …}
Infinite Set
75
is the totality of all the elements of the sets under consideration, denoted by U, i.e. U = {…-2, -1, 0, 1, 2,…}
Universal Set
75
is a set whose elements are found in A and B or in both. In symbol: 𝐴∪𝐵={𝑥/𝑥 ∈𝐴 𝑜𝑟 𝑥 ∈𝐵}.
Union of Sets A and B
75
have been the same elements
Equal Sets
76
have the same number of elements
Equivalent Sets
77
have at least one common element
Joint Sets
78
have no common element
Disjoint Sets
79
A friendly reminder na you're doing your best, Kyle. Just keep up, and continue to pursue your dreams! Aim High!
Trust God for all of your plans
80
is a set every element of which can be found on a bigger set. The symbol ⊂ means “a subset of” while ⊄ means “not a subset of”.
Subset
81
the set containing all the subsets of the given set with n number of elements.
Power Set
81
if the first set equals the second set.
Improper Subset (⊆)
82
other than the set itself and the null set, all are considered ___________.
Proper Subset (⊂)
83
is a set whose elements are common to both sets. In symbol: 𝐴∩𝐵={𝑥/𝑥" "∈𝐴 𝑎𝑛𝑑 𝑥 ∈𝐵}". "
Intersection of Sets A and B
84
is a set whose elements are found in set A but not in set B. In symbol: 𝐴−𝐵= {𝑥/𝑥∈𝐴 𝑎𝑛𝑑 𝑥∉𝐵}". "
Difference of Sets A and B
85
is a set whose elements are found in the universal set but not in set A. In symbol
Complement of Set A
86
The universal set is usually represented by a rectangle while circles with the rectangle usually represent it ___________.
Subset
86
(4 August 1834 – 4 April 1923) - an English Logician an Philosopher
John Venn
87
The pictorial representation of relationship and operations of set is the so-called
Venn-Euler Diagrams or simply Venn Diagrams
88
The ______________ is usually represented by a rectangle while circles with the rectangle usually represent it subsets.
Universal Set
89
(15 April 1707 – 18 September 1783) – was a Swiss mathematician, physicist, astronomer, logician, and engineer.
Leonhard Euler
90
-are mathematical entities that give unique outputs to particular inputs.
-consists of argument (input to a function), value (output), domain (set of all permitted inputs to given function) and codomain (set of permissible outputs).
Function
91
is a set of inputs and outputs, oftentimes expressed as ordered pairs (input, output)
relation
92
means consisting of two parts. In mathematics, _________ means that it belongs to a number system with base 2 and not base 10. A ________ is made up of 0’s and 1’s.
Binary
92
is a single binary digit.
bit
93
is a rule of combining two values to produce a new value.
Binary Operation
94
is the science of formal principles of reasoning or correct inference. It is the study of principles and methods used to distinguish valid arguments from those that are not valid.
Logic
95
is the study of reasoning in mathematics.
Mathematical Logic
