MMW MIDTERM Flashcards by Jasmine Tabangcora

set of ordered pairs.

relation

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may have more than 1 output for any given input.

relation

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The set whose elements are the first coordinates in the ordered pairs is the

domain

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The set whose elements are the second coordinates is the

range

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what are the 3 correspondence?

one is to many correspondence
one is to one correspondence
many is to one correspondence

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can have no more than 1 output for any given input.

function

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notion f(x)
The letter x

The letter y is replaced by f(x)

defines a function named f
represents the input value, or independent variable.
represents the output value, or dependent variable.

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It involves only one value or accepts one value or operand.

unary operation

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It can act on two operands “+” and “ – ”

binary operations

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It takes two values and include the operations of addition, subtraction, multiplication, division and exponentiation.

binary operations

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properties of two binary operations.

Closure of binary operations
commutativity of binary operations
Associativity of binary operations
Distributivity of binary operations
Identity elements of binary operations
Inverse of binary operations

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the product and the sum of any two real numbers is also a real number
5+3 =8. 5x3=15

Closure of binary operations

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Addition and multiplication of any two real numbers is commutative as seen in their mathematical symbols
x + y = y + x and x ● y = y ● x

Commutativity of Binary Operations

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three real numbers you may take any two and perform addition or multiplication as the case maybe and you will end with the same answer.
(x+y)+z= x+ (y+z)

(4+5)+7=4+(5+7)
9+7=4+12
16=16

Associativity of Binary Operations

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applies when multiplication is performed on a group of two numbers added or subtracted together.
z(x ± y) = zx ± zy

Distributivity of Binary Operations

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set of real numbers is an identity element for addition/multiplication. this means that the identity is the number that you add to any real numbers and the result will be the same real number.

5+0=0+5=5 50x1=1x50=50
e- zero for addition, one for multiplication

Identity Elements of binary operations

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x+(-x)=-x+x=0
4+(-4)=-4+4=0

inverse of binary operation
additive inverse/ reciprocal

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4 operation of functions

sum of function
difference of function
product of function
quotient of function

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father of problem

George polya(1887- 1985)

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who strongly believed that the skill problem can be taught

George polya(1887-1985)

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Polya’s Four-Step Problem Solving Strategy

Step 1 : Understand the problem.
Step 2 : Devise a plan.
Step 3: Carry out the plan.
Step 4: Review the solution

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it is the process of translating a problem scenario into a drawing

strategy 1: draw a diagram, picture or model

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data or information are organized by listing them or recording them systematically in tables.

The data are then analyzed to discover relationships and patterns and to draw out generalizations or solutions to the problem.

strategy 2: make a table or an organized list

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Making a logical guess at the answer. The student learns more about the problem.

strategy: guess and check

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Checking the guess.

strategy 3: guess and check

It is important that computation is accurate to avoid wastage of time and effort by making more guesses when in fact, the solution might have found some guesses before.st

strategy 3: guess and check

a strategy in which people physically act out what is taking place in a word problem.

strategy 4: act it out/ acting out a problem

One may use people or objects exactly as described in the problem, or you might use items that represent the people or objects.

strategy 4: act it out

people visualize and simulate the actions described in the problem.

strategy 4: act it out

method works well for problems where a series of operations is done on an unknown number and you’re only given the result.

strategy 5:word backwards

start with the result and apply the operations in reverse order until you find the starting number.

strategy 5:word backwards

Without mathematics, there's nothing you can do. Everything around you is mathematics. Everything around you is numbers.”

shakuntala devi

It is a type of reasoning that uses specific examples to reach a general conclusion.

inductive reasoning

The conclusion formed by using inductive reasoning is called a

CONJECTURE

is an idea that may or may not be correct.

CONJECTURE

to a conjecture is an example for which the conjecture is incorrect

counterexample

a special kind of example that disproves a statement or proposition.

COUNTEREXAMPLE

It is a type of reasoning that uses general procedures and principles to reach a conclusion.

deductive reasoning

It is the process of reaching a general conclusion by applying general assumptions, procedures, or principles.

deductive reasoning

8 properties of equality

addition property of equality subtraction property of equality multiplication property of equality division property of equality reflexive property of equality symmetric property of equality transitive property of equality substitution property of equality

a+c=b+c

addition property of equality

a-c=b-c

subtraction property of equality

ac=bc

multiplication property of equality

a/c=b/c

division property of equality

a=a

reflexive property of equality

if a=b, then b =a

symmetric property of equality]]]

if a=b and b=c, then a=c

transitive property of equality

if a=b, then b can be substituted for a in any expression

substitution property of equality

ax=b

closure property

can be solved by using deductive reasoning and a chart that enables us to display the given information in a visual manner.

Logic puzzles

Reaching conclusions based on a series of observations.

Inductive

Conjecture may or may not be valid or uncertain.

Inductive

Reaching conclusions based on previously known facts.

Deductive

Conjecture are correct and valid or certain.

Deductive

Forms of Deductive Reasoning

Hypothetical syllogism Categorical Syllogism

if a statement p implies another statement q and p is true, then q must also be true

modus ponens

opposite of modus ponens

modus tollens

It is a type of deductive reasoning consisting of a conditional major premise, an unconditional minor premise, and an unconditional conclusion.

Hypothetical syllogism

Premise 1-If p then q, Premise 2-and p,(true)-This is called Premise 3-Therefore, q.( True). This is called the

- ( Conditional statement) - antecedent - consequent.

valid argument form, meaning if the premises are true, then the conclusion must be true

modus ponens

It is a form of deductive reasoning wherein a categorical conclusion is based on two categorical premises.

Categorical Syllogism

There are four types of propositions that are used in the syllogism:

Positive Universal: “All A are B” Ex.All dogs are mammals. Negative Universal: “No A are B” Ex. No dogs are fish. Positive Existential: “Some A are B” Ex. Some dogs are brown. Negative Existential: “Some A are not B”. Ex.Some dogs are not brown.

three types of propositions will be used to create an argument

Major premise (universal quantifier) Minor premise (existential quantifier) Conclusion (universal or existential)

-a general statement about a category of things.

Major premise (universal quantifier)

a statement about a specific member or subset of that category.

Minor premise (existential quantifier)-

A statement that logically follows from the major and minor premises.

Conclusion (universal or existential)-

It is also denoted by All p are q. r is p. Therefore, r is q.

Categorical Syllogism

it is development, execution, and supervision of plans

data management

the word statistics originated from the word

"status" meaning "state"

it is the science that deals with the collection, classification, analysis, and interpretation of numerical

statistics

are used to organize and summarize the information so that the researcher can see what happened in the research study

statistics

help to researcher to answer the questioning that initiated the researcher by determining exactly what general conclusions are justified

statistics

5 methods of data gathering

direct or interview method indirect or questionnaire method registration method observation method experimental method

it is a person to person encounter between the source of information, the interviewee

direct or interview method

it is the technique in which questionnaire is used to elicit the information

indirect or questionnaire method

It obtains data from the records of government agency authorized by law to keep such data or information and made these available to researchers.

registration

It is the technique in which data particularly those pertaining to the behaviors of individuals or group of individuals during the given situation.

observation

To notice using a full range of appropriate senses. To see, hear, feel, taste, and smell.

observation

This is also used when the respondents cannot read nor write.

observation

used to gather data from the result of performed series

experimental

systematically manipulated by the investigator

Independent variable (IV)

Investigator measures to determine the effect of the independent variable

dependent variable(DV)

THE CAUSE THE EFFECT

Independent variable Dependent variable

experiment force a conclusion consonant with reality.

scientific method

It involves the collection and classification of data

descriptive statistics

It involves the analysis and interpretation of data.

inferential statistics

exampple: average and percentage

descriptive statistics

example: predict and estimate

inferential statistics

set of measurement corresponding to the entire collection of units

population

is a set of individuals selected from a population, usually intended to represent the population in a research study.

sample

sample formula

sample size= population size divide 1+ population size multiply by margin of error then squared

are measurements or observations.

Data

is a single measurement or observation and is commonly called a score or raw score.

datum

The measurements that are made on the subjects of an experiment are also called

data

The data as originally measured are often referred to as

raw or original scores.

2 types of data

Qualitative Data Quantitative Data

Data that deal with categories or attributes ex.Color of skin Courses in Computer Engineering

Qualitative Data

Data that deal with numerical values ex.Number of units in one semester Grade point average

Quantitative Data

Data that are obtained by counting ex. number of students in the classroom number of cars in the parking lot

Discrete Data

Data that are obtained by measuring ex. area of a mango farm in Pampanga volume of water in a pool in Pansol, Laguna

Continuous Data

It can assume any of an infinite number of values and can be associated with points on a continuous line interval. Example: Height, weight, volume

Continuous Data

It results from either a finite number of possible values or a countable number of possible values. Example: number of students, number of books, and number of patients

Discrete Data

is a value, usually a numerical value that describes a population.

Parameter

is usually derived from measurements of the individuals in the population

Parameter

is a value, usually a numerical value that describes a sample.

statistic

usually derived from measurements of the individuals in the sample.

statistic

occurring discrepancy, or error, that exists between a sample statistic

sampling error

characteristics of some events, object, or person that may have different values

variable

is a variable describing a characteristic.

qualitative variable

are also sometimes referred to as categorical variables because they can be separated into categories.

Qualitative variables

are often descriptive but can sometimes be given a numeric value.

Quantitative variables

has a value or numerical measurement for which operation can be applied. For example: age, height, and weight are quantitative.

quantitative variable

Interval and ratio are sometimes called

continuous or scale

the hierarchy of levels absolute zero distance is meaningful attributes can be ordered attributes are only named; weakest

ratio interval ordinal nominal

4 LEVELS OF MEASUREMENT

Nominal Ordinal Interval Ratio

- labels qualitative data into mutually exclusive categories

Nominal

ranks qualitative data according to its degree

Ordinal

numerical data that has order and its differences can be determined; do not have a “true” zero

Interval

numerical data that has order, differences can be determined and has a “true” zero

ratio

example: what is your civil status : single, married, separated, annulled

Nominal

example: how satisfied are you with our food? extremely satisfied, very satisfied , satisfied

Ordinal

example: temperature

Interval

example: Speed, Height, Weight

ratio

data is the precious thing that last together

Tim berners lee

A single value that describes the center of a distribution:

mean, median,mode

also known as the "average" or "arithmetic mean"

mean

the middlemost score

median

the most frequent score

mode

the sum of all values in a dataset divided by the total number of observations

mean

in excel when computing the mean type?

average (A1:A8) then enter

in excel when computing the meadian you''ll type?

median (A1:A8) then enter

in excel when computing the mode you''ll type?

mode(A1:A8) then entero