Midterm M1-3

Question 1

The ___________________. Mathematics covers designs that assist
us with understanding our general surroundings. As a study of dynamic
articles, Mathematics depends on rationale as opposed to on
perception as its standard of truth, logic, and even observation as
methods for finding truth

Answer 1

Nature of Mathematics

Question 2

• Study of numbers and Arithmetic Operations
• Science which involves logical reasoning, drawing conclusions
  from assumed premises and strategic reasoning based on
  accepted rules, Laws, or probabilities
• Is a language
• It is an art which studies patterns

Answer 2

What is Mathematics?

Question 3

—-is an arrangement which helps the observers
anticipate what they
Might see or what happen next.
—-it also shows what may have come before
—-it organizes information for it to be useful.
—–used to analyze and solve problems
—–
Pattern are studied because they are everywhere; people just
learn to notice them.

Answer 3

Pattern

Question 4

• indicates
  that you can draw an
  imaginary line across an
  object and resulting parts
  are mirror images of each
  other.
  The figure is symmetric about the axis if you divide the
  figure vertically the left and right portion are exactly the
  same.

This is known as line or bilateral symmetry , this is evident
in most animals , including human.

Answer 4

1.Symmetry

Question 5

This tree was described by Leonardo Da
Vinci and according to him, if all
branches of the tree are put together, its
thickness will equal to that of the trunk
Another version stated that when a
branch splits, when put together the thickness equals to the parent
branch.
Fractal-like patterns occur widely in nature, some examples are the
clouds, river networks, fault lines, mountains, coastlines, animal
coloration, snow flake and many more. Can you think of some?
The Growth patterns of certain trees resemble Lindenmayer system
fractals

Answer 5

2.Trees, fractal

Question 6

Spirals are common in plants and in some animals.Plants spirals can
be seen in the arrangement of leaves on a stem, and in the
arrangement of the plant parts as in composite flower heads , and the
seeds heads like the sunflower or fruit structure of pineapple .

Answer 6

3. Spirals

Question 7

3. Chaos, flow, meanders
   ___________________ is the study of how simple patterns can be generated from
   complicated underlying behavior. Chaos theory helps us to understand
   patterns in nature.

Answer 7

Chaos

Question 8

The flow pattern is the way in which fluids move through a reactor.
Density gradients, caused by temperature or composition variations,
tend to control the overall flow pattern of the fluid. . The flow pattern is
the way in which fluids move through a reactor.
(The motions of air water organize the skies ,the earth and the oceans)

Answer 8

Flows

Question 9

___________________ is one of a series of regular sinuous curves, bends, loops,
turns, or windings in the channel of a river, stream, or other
watercourse. It is produced by a stream or river swinging from side to
side as it flows across its floodplain or shifts its channel within a valley

Answer 9

Meanders

Question 10

: Waves, dunes Wind waves are sea surface waves that
create the characteristic chaotic pattern of any large body of water,
though their statistical behavior can be predicted with wind wave models.
As waves in water or wind pass over sand, they create patterns of ripples

Answer 10

4. Waves

Question 11

A soap bubble forms a sphere, a surface with minimal area. Two bubbles
together form a more complex shape: the outer surfaces of both bubbles
are spherical; these surfaces are joined by a third spherical surface as the
smaller bubble bulges slightly into the larger one.
A foam is a mass of bubbles; foams of different materials occur in
nature.

Answer 11

5. Bubbles, foams

Question 12

Tessellations are patterns formed by repeating tiles all over a flat
surface. There are 17 wallpaper groups of tillings. While common in art
and design, exactly repeating tillings are less easy to find in living
things.
ARRAYS: Honeycomb
Snake fruit
TILLINGS

Answer 12

6. Tessellations

Question 13

Cracks are linear openings that form in materials to relieve stress.
When an elastic material stretches or shrinks uniformly, it eventually
reaches its breaking strength and then fails suddenly in all directions,
creating cracks with 120 degree joints, so three cracks meet at a
node.
Drying inelastic mud with 90° cracks
Cracking Wood

Answer 13

7. Cracks

Question 14

A long narrow band distinguished, as by color or texture, from the
surrounding materi al or surface.
- A textile pattern of parallel bands or lines on a contrasting
background.
-A fabric having such a pattern..
-Leopards and ladybirds are spotted; angelfish and zebras are striped.
These patterns have
an evolutionary explanation: they have
functions which increase the chances that the offspring of the patterned
animal will survive to reproduce. One function of animal patterns is
camouflage;] for instance, a leopard that is harder to see catches more
prey.

Answer 14

8. Spots, stripes

Question 15

A pattern is a series or sequence that repeats. Math patterns are
sequences that repeat based on a rule, and a rule is a set way to
calculate or solve a problem. In mathematics, we can form patterns by
doing one or more mathematical operations repeatedly.

Answer 15

Number Pattern:

Question 16

A sequence is an enumerated collection of objects in which repetitions
are allowed and order does matter. Like a set, it contains members
(also called elements, or terms).

Answer 16

SEQUENCE:

Question 17

-Is a sequence in which the difference between each consecutive
term is constant can be defined by an explicit formula;
an = a1 + ( n – 1 ) d
where: an = nth term, a1 = 1st term ,n = term position ,d =
common difference

Answer 17

Arithmetic Sequence

Question 18

Is a progression formed by taking the reciprocal of an
arithmetic progression , formed by taking the reciprocals of an
arithmetic sequence.

Answer 18

Harmonic Sequence (Harmonic Progression)

Question 19

Mathematics is useful in the development of social, intellectual,
moral, spiritual and cultural

Answer 19

AT THE PERSONAL LEVEL:

Question 20

Changes in the social structure, like modern facilities, mode of
transportation, means of communication, science and technology is
possible because of mathematics.

Answer 20

Social

Question 21

Mathematics helps the brain active. Almost all courses in
tertiary level offers includes at least one mathematics subject in their
curriculum, Problem solving helps in the development of mental
abilities.

Answer 21

Intellectual

Question 22

Mathematics helps the students to be prepare for technical and
other vocation like engineering, architecture, accountancy, banking,
business, agriculture, tailoring, carpentry, surveying, baking and others.

Answer 22

Vocational

Question 23

Mathematics can contribute to the student’s character and
moral development. It helps in character and moral development.

Answer 23

Moral

Question 24

Student enjoy in solving math problem especially when she/he
gets the correct answer to his problem with that every student feels
satisfied , confident and self-reliant .

Answer 24

Spiritual

Question 25

Students understand the contribution of mathematics in the
development of civilization and culture.

Answer 25

Cultural

Question 26

Mathematics play a big role in the foundation of the development
of our society and the world as well, we have observed in living
creation and natural phenomena. We can see how mathematics play
the role in various sector of the society

Answer 26

SOCIETAL LEVEL:

Question 27

In education sector mathematics plays an important role in
shaping the future chances of young students. Education is essential in
the development of an individual, to make them self-reliant and become
wise and to make them a social contributor

Answer 27

Education

Question 28

Numerical financial aspects depends on factual perceptions to
demonstrate, discredit, and anticipate monetary conduct. Despite the
fact that the order of financial matters is intensely affected by the
predisposition of the analyst, arithmetic permits business analysts to
clarify detectable wonder and gives the spine to hypothetical translation.

Answer 28

Economics

Question 29

Structural designing coursework includes the use of numerical
standards and aptitudes to certifiable issues. Classes such as basic information look at structures like trusses, beams, and frames, and
concepts like virtual work, energy method and impact lines. Mechanics
of solids incorporates points like interior powers and disfigurement in
solids, stresses and diversions in shaft and segment hypothesis and
investigation. Courses in liquid mechanics include investigation of the
properties of liquids.
These classes apply the standards and abilities learned in the essential
arithmetic courses.

Answer 29

Infrastructure

Question 30

Mathematics assumed a crucial job in the definition of present day
science, using logical hypothesis that has a satisfactory scientific model.
Mathematics has been effectively utilized in the advancement of
science and innovation in the twentieth and 21 first century. The zones
like semi -conductor devise, bio innovation, advanced picture, nano -
technology, artificial satellite and rockets are for the most part base on
mathematical concept.

Answer 30

Science and Technology

Question 31

Mathematics is applied to farming, biology, the study of disease
transmission, tumor and heart demonstrating, DNA sequencing and
quality innovation. It is utilized to produce clinical gadgets and
diagnostics, opto-gadgets and sensor innovation. There are certain
faculties wherein arithmetic is unique. In the first place, by uprightness
of its major nature as a general conceptual language and its supporting
of technical disciplines, innovation and building, arithmetic has a case
to a naturally extraordinary status from generally other disciplines.
Furthermore, as we have set out above, Mathematics is in a general
sense significant in an all-inescapable way, both for the working
environment and for the individual resident.

Answer 31

Medical Science and Agricultural field:

Question 32

Mathematics is utilized in pretty much every calling, it helps in
improving the expectations for everyday comforts of an individual. The improvements in financial matters, science and innovation, medication
in a nutshell generally speaking of society builds up the way of life.
Along these lines, science plays a significant job in making the
expectations for everyday comforts high. In spite of the fact that the
pervasive utilization of data innovation in all segments has changed the
idea of the numerical aptitudes required, it has not diminished the
requirement for mathematics Last yet not the least any general public
can never be created without the empowering of women. Women is the
half piece of the general public. Hence, we will likewise observe the,
job of mathematics education in women empowerment.

Answer 32

Living Standard

Question 33

• equivalent to noun
• name given to mathematical object of interest

Answer 33

Expression

Question 34

• same as English sentence it expresses a
  complete thought.

Answer 34

Mathematical Sentence

Question 35

– could be constants such as numbers or expressions with
numbers: 12,
2(6- ¼), 3.

Answer 35

Nouns

Question 36

– could be the equal sign (=) or inequality (<, >)

Answer 36

Verb

Question 37

• could be variables like x or y
  5x -8 , 3xy , 6/a
  Sentence could be formed by putting together these parts
  3x + 6 = 27, 3x + 2y = 8

Answer 37

Pronouns

Question 38

A proposition is a complete declarative sentence that is either true or
false but not both .
(Note: Proposition built up by combining propositions using
propositional connectives
Are called “compound propositions”
The propositional connectives are Ʌ ,V ,
(the symbol above are called , conjunction,disjunction,exclusive or,implication and
biconditional respectively)

Answer 38

Proposition

Question 39

– Starts with specific examples or
observations and “deduces” the apparent rules or patterns that lie
behind them
-is a process of reaching a general
conclusion by examining the specific example.

Answer 39

Inductive Reasoning

Question 40

• mainly pertains to the aspect of using different thought to create a
  valid
  argument that can be used to make decision .As such ,it can be
  noted that

Answer 40

Reasoning

Question 41

• Starts with the rules ,and determines what
  the consequences will be . This is what we do in most math ,defining the
  rules for a mathematical entity (such as commutative property of
  addition
• is the process of reaching a conclusion by applying
  general assumption, procedures or principles.

Answer 41

Deductive Reasoning

Question 42

–is an educated guess based upon repeated observation of
a particular

Answer 42

Conjecture